stabilizer_qec 2.1.0

// Ported from Fusion Blossom 0.2.13 (Yue Wu; MIT; see src/fusion/LICENSE and
// THIRD_PARTY_NOTICES.md): its default features, its dependencies replaced by src/fusion/shim.rs.

//! Serial Primal Module
//!
//! A serial implementation of the primal module. This is the very basic fusion blossom algorithm that aims at debugging and as a ground truth
//! where traditional matching is too time-consuming because of their |E| = O(|V|^2) scaling.
//!


#[allow(unused_imports)]
use crate::fusion::shim::{serde_json};
use std::cmp::Ordering;
use std::num::NonZeroUsize;

use super::dual_module::*;
use super::pointers::*;
use super::primal_module::*;
use super::util::*;
use super::visualize::*;

#[derive(Debug)]
pub struct PrimalModuleSerial {
    /// unit index of this interface, default to 0
    pub unit_index: usize,
    /// nodes internal information
    pub nodes: Vec<Option<PrimalNodeInternalPtr>>,
    /// current nodes length, to enable constant-time clear operation
    pub nodes_length: usize,
    /// allow pointer reuse will reduce the time of reallocation, but it's unsafe if not owning it
    pub is_fusion: bool,
    /// the indices of primal nodes that is possibly matched to the mirrored vertex, and need to break when mirrored vertices are no longer mirrored
    pub possible_break: Vec<NodeIndex>,
    /// debug mode: only resolve one conflict each time
    pub debug_resolve_only_one: bool,
    /// the parent of this serial module, when fused
    pub parent: Option<PrimalModuleSerialWeak>,
    /// when fused, this will indicate the relative bias given by the parent
    pub index_bias: NodeIndex,
    /// the two children of this serial module, when fused; following the length of this child,
    /// given that fused children serial modules will not have new nodes anymore
    pub children: Option<((PrimalModuleSerialWeak, NodeNum), (PrimalModuleSerialWeak, NodeNum))>,
    /// the maximum number of children in a tree before it collapses to a union-find decoder
    pub max_tree_size: usize,
}

pub type PrimalModuleSerialPtr = ArcManualSafeLock<PrimalModuleSerial>;
pub type PrimalModuleSerialWeak = WeakManualSafeLock<PrimalModuleSerial>;

impl std::fmt::Debug for PrimalModuleSerialPtr {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        let interface = self.read_recursive();
        write!(f, "{}", interface.unit_index)
    }
}

impl std::fmt::Debug for PrimalModuleSerialWeak {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        self.upgrade_force().fmt(f)
    }
}

#[derive(Debug)]
pub struct AlternatingTreeNode {
    /// the root of an alternating tree
    pub root: PrimalNodeInternalWeak,
    /// the parent in the alternating tree, note that root doesn't have a parent; together with a child of blossom that touches parent, used to create blossom and expand perfect matching
    pub parent: Option<(PrimalNodeInternalWeak, DualNodeWeak)>,
    /// the children in the alternating tree, note that odd depth can only have exactly one child; together with a child of blossom that touches each child node in the tree, used to create blossom and expand perfect matching
    pub children: Vec<(PrimalNodeInternalWeak, DualNodeWeak)>,
    /// the depth in the alternating tree, root has 0 depth
    pub depth: usize,
    /// the number of children in the tree; only the root has this variable.
    pub tree_size: Option<NonZeroUsize>,
}

#[derive(Debug, Clone, PartialEq, Eq)]
pub enum MatchTarget {
    Peer(PrimalNodeInternalWeak),
    VirtualVertex(VertexIndex),
}

/// internal information of the primal node, added to the [`DualNode`]; note that primal nodes and dual nodes
/// always have one-to-one correspondence
#[derive(Debug)]
pub struct PrimalNodeInternal {
    /// the pointer to the origin [`DualNode`]
    pub origin: DualNodeWeak,
    /// local index, to find myself in [`DualModuleSerial::nodes`]
    pub index: NodeIndex,
    /// alternating tree information if applicable
    pub tree_node: Option<AlternatingTreeNode>,
    /// temporary match with another node, (target, touching_grandson)
    pub temporary_match: Option<(MatchTarget, DualNodeWeak)>,
    /// belonging of the dual module interface; a dual node is never standalone
    pub belonging: PrimalModuleSerialWeak,
}

pub type PrimalNodeInternalPtr = ArcManualSafeLock<PrimalNodeInternal>;
pub type PrimalNodeInternalWeak = WeakManualSafeLock<PrimalNodeInternal>;

impl std::fmt::Debug for PrimalNodeInternalPtr {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        self.update(); // to make sure index is up-to-date
        let primal_node_internal = self.read_recursive();
        write!(f, "{}", primal_node_internal.index)
    }
}

impl std::fmt::Debug for PrimalNodeInternalWeak {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        self.upgrade_force().fmt(f)
    }
}

impl PrimalNodeInternal {
    /// check if in the cache, this node is a free node
    pub fn is_free(&self) -> bool {
        debug_assert!(
            {
                let origin_ptr = self.origin.upgrade_force();
                let node = origin_ptr.read_recursive();
                node.parent_blossom.is_none()
            },
            "do not call this function to a internal node, consider call PrimalModuleSerial::get_outer_node"
        );
        if self.tree_node.is_some() {
            return false;
        } // this node belongs to an alternating tree
        if self.temporary_match.is_some() {
            return false;
        } // already temporarily matched
        true
    }

    /// modify the depth and root of a sub-tree using DFS
    pub fn change_sub_tree_root(&mut self, depth: usize, root: PrimalNodeInternalPtr) {
        let tree_node = self.tree_node.as_mut().unwrap();
        tree_node.depth = depth;
        tree_node.root = root.downgrade();
        for (child_weak, _) in tree_node.children.iter() {
            let child_ptr = child_weak.upgrade_force();
            lock_write!(child, child_ptr);
            child.change_sub_tree_root(depth + 1, root.clone());
        }
    }
}

impl PrimalNodeInternalPtr {
    /// when fused, primal node may be outdated; refresh here
    pub fn update(&self) -> &Self {
        let mut current_belonging = self.read_recursive().belonging.upgrade_force();
        let mut bias = 0;
        let mut node = self.write();
        while current_belonging.read_recursive().parent.is_some() {
            let belonging_module = current_belonging.read_recursive();
            bias += belonging_module.index_bias;
            let new_current_belonging = belonging_module.parent.clone().unwrap().upgrade_force();
            drop(belonging_module);
            current_belonging = new_current_belonging;
        }
        node.belonging = current_belonging.downgrade();
        node.index += bias;
        self
    }
}

impl PrimalModuleImpl for PrimalModuleSerialPtr {
    fn new_empty(_initializer: &SolverInitializer) -> Self {
        Self::new_value(PrimalModuleSerial {
            unit_index: 0, // if necessary, manually change it
            nodes: vec![],
            nodes_length: 0,
            is_fusion: false,
            possible_break: vec![],
            debug_resolve_only_one: false,
            parent: None,
            index_bias: 0,
            children: None,
            // // Union-Find
            // max_tree_size: 0,
            // Minimum Weight Perfect Matching
            max_tree_size: usize::MAX,
        })
    }

    fn clear(&mut self) {
        let mut module = self.write();
        module.nodes_length = 0; // without actually dropping all the nodes, to enable constant time clear
        module.possible_break.clear();
        module.is_fusion = false;
        module.parent = None;
        module.index_bias = 0;
        module.children = None;
    }

    fn load_defect_dual_node(&mut self, dual_node_ptr: &DualNodePtr) {
        let belonging = self.downgrade();
        let node = dual_node_ptr.read_recursive();
        debug_assert!(
            matches!(node.class, DualNodeClass::DefectVertex { .. }),
            "must load a fresh dual module interface, found a blossom"
        );
        let mut module = self.write();
        let local_node_index = module.nodes_length;
        let node_index = module.nodes_count();
        debug_assert_eq!(node.index, node_index, "must load in order");
        let primal_node_internal_ptr =
            if !module.is_fusion && local_node_index < module.nodes.len() && module.nodes[local_node_index].is_some() {
                let node_ptr = module.nodes[local_node_index].take().unwrap();
                let mut node = node_ptr.write();
                node.origin = dual_node_ptr.downgrade();
                node.index = node_index;
                node.tree_node = None;
                node.temporary_match = None;
                node.belonging = belonging;
                drop(node);
                node_ptr
            } else {
                PrimalNodeInternalPtr::new_value(PrimalNodeInternal {
                    origin: dual_node_ptr.downgrade(),
                    index: node_index,
                    tree_node: None,
                    temporary_match: None,
                    belonging,
                })
            };
        module.nodes_length += 1;
        if module.nodes.len() < module.nodes_length {
            module.nodes.push(None);
        }
        module.nodes[local_node_index] = Some(primal_node_internal_ptr);
    }

    #[allow(clippy::collapsible_else_if)]
    fn resolve<D: DualModuleImpl>(
        &mut self,
        mut group_max_update_length: GroupMaxUpdateLength,
        interface_ptr: &DualModuleInterfacePtr,
        dual_module: &mut D,
    ) {
        debug_assert!(!group_max_update_length.is_empty() && group_max_update_length.get_none_zero_growth().is_none());
        let mut current_conflict_index = 0;
        let debug_resolve_only_one = self.read_recursive().debug_resolve_only_one;
        let max_tree_size = self.read_recursive().max_tree_size;
        while let Some(conflict) = group_max_update_length.pop() {
            current_conflict_index += 1;
            if debug_resolve_only_one && current_conflict_index > 1 {
                // debug mode
                break;
            }
            // println!("conflict: {conflict:?}");
            match conflict {
                MaxUpdateLength::Conflicting((node_ptr_1, touching_ptr_1), (node_ptr_2, touching_ptr_2)) => {
                    debug_assert!(
                        node_ptr_1 != node_ptr_2,
                        "one cannot conflict with itself, double check to avoid deadlock"
                    );
                    if self.get_primal_node_internal_ptr_option(&node_ptr_1).is_none() {
                        continue;
                    } // ignore out-of-date event
                    if self.get_primal_node_internal_ptr_option(&node_ptr_2).is_none() {
                        continue;
                    } // ignore out-of-date event
                      // always use outer node in case it's already wrapped into a blossom
                    let primal_node_internal_ptr_1 = self.get_outer_node(self.get_primal_node_internal_ptr(&node_ptr_1));
                    let primal_node_internal_ptr_2 = self.get_outer_node(self.get_primal_node_internal_ptr(&node_ptr_2));
                    if primal_node_internal_ptr_1 == primal_node_internal_ptr_2 {
                        debug_assert!(
                            current_conflict_index != 1,
                            "the first conflict cannot be ignored, otherwise may cause hidden infinite loop"
                        );
                        continue; // this is no longer a conflict because both of them belongs to a single blossom
                    }
                    let mut primal_node_internal_1 = primal_node_internal_ptr_1.write();
                    let mut primal_node_internal_2 = primal_node_internal_ptr_2.write();
                    let grow_state_1 = primal_node_internal_1.origin.upgrade_force().read_recursive().grow_state;
                    let grow_state_2 = primal_node_internal_2.origin.upgrade_force().read_recursive().grow_state;
                    if !grow_state_1.is_against(&grow_state_2) {
                        debug_assert!(
                            current_conflict_index != 1,
                            "the first conflict cannot be ignored, otherwise may cause hidden infinite loop"
                        );
                        continue; // this is no longer a conflict
                    }
                    // this is the most probable case, so put it in the front
                    let (free_1, free_2) = (primal_node_internal_1.is_free(), primal_node_internal_2.is_free());
                    if free_1 && free_2 {
                        // simply match them temporarily
                        primal_node_internal_1.temporary_match = Some((
                            MatchTarget::Peer(primal_node_internal_ptr_2.downgrade()),
                            touching_ptr_1.downgrade(),
                        ));
                        primal_node_internal_2.temporary_match = Some((
                            MatchTarget::Peer(primal_node_internal_ptr_1.downgrade()),
                            touching_ptr_2.downgrade(),
                        ));
                        // update dual module interface
                        interface_ptr.set_grow_state(
                            &primal_node_internal_1.origin.upgrade_force(),
                            DualNodeGrowState::Stay,
                            dual_module,
                        );
                        interface_ptr.set_grow_state(
                            &primal_node_internal_2.origin.upgrade_force(),
                            DualNodeGrowState::Stay,
                            dual_module,
                        );
                        continue;
                    }
                    // second probable case: single node touches a temporary matched pair and become an alternating tree
                    if (free_1 && primal_node_internal_2.temporary_match.is_some())
                        || (free_2 && primal_node_internal_1.temporary_match.is_some())
                    {
                        let (
                            free_node_internal_ptr,
                            free_touching_ptr,
                            mut free_node_internal,
                            matched_node_internal_ptr,
                            matched_touching_ptr,
                            mut matched_node_internal,
                        ) = if free_1 {
                            (
                                primal_node_internal_ptr_1.clone(),
                                touching_ptr_1.clone(),
                                primal_node_internal_1,
                                primal_node_internal_ptr_2.clone(),
                                touching_ptr_2.clone(),
                                primal_node_internal_2,
                            )
                        } else {
                            (
                                primal_node_internal_ptr_2.clone(),
                                touching_ptr_2.clone(),
                                primal_node_internal_2,
                                primal_node_internal_ptr_1.clone(),
                                touching_ptr_1.clone(),
                                primal_node_internal_1,
                            )
                        };
                        // creating an alternating tree: free node becomes the root, matched node becomes child
                        let (match_target, matched_touching_grandson) =
                            matched_node_internal.temporary_match.as_ref().unwrap().clone();
                        match &match_target {
                            MatchTarget::Peer(leaf_node_internal_weak) => {
                                let leaf_node_internal_ptr = leaf_node_internal_weak.upgrade_force();
                                let mut leaf_node_internal = leaf_node_internal_ptr.write();
                                let mut tree_size = free_node_internal.origin.upgrade_force().read_recursive().defect_size;
                                tree_size = tree_size.saturating_add(
                                    matched_node_internal
                                        .origin
                                        .upgrade_force()
                                        .read_recursive()
                                        .defect_size
                                        .get(),
                                );
                                tree_size = tree_size.saturating_add(
                                    leaf_node_internal.origin.upgrade_force().read_recursive().defect_size.get(),
                                );
                                free_node_internal.tree_node = Some(AlternatingTreeNode {
                                    root: free_node_internal_ptr.downgrade(),
                                    parent: None,
                                    children: vec![(matched_node_internal_ptr.downgrade(), free_touching_ptr.downgrade())],
                                    depth: 0,
                                    tree_size: Some(tree_size),
                                });
                                matched_node_internal.tree_node = Some(AlternatingTreeNode {
                                    root: free_node_internal_ptr.downgrade(),
                                    parent: Some((free_node_internal_ptr.downgrade(), matched_touching_ptr.downgrade())),
                                    children: vec![(leaf_node_internal_weak.clone(), matched_touching_grandson)],
                                    depth: 1,
                                    tree_size: None, // not root
                                });
                                matched_node_internal.temporary_match = None;
                                leaf_node_internal.tree_node = Some(AlternatingTreeNode {
                                    root: free_node_internal_ptr.downgrade(),
                                    parent: Some((
                                        matched_node_internal_ptr.downgrade(),
                                        leaf_node_internal.temporary_match.as_ref().unwrap().1.clone(),
                                    )),
                                    children: vec![],
                                    depth: 2,
                                    tree_size: None, // not root
                                });
                                leaf_node_internal.temporary_match = None;
                                // update dual module interface
                                if tree_size.get() > max_tree_size {
                                    drop(free_node_internal);
                                    drop(matched_node_internal);
                                    drop(leaf_node_internal);
                                    self.collapse_tree(free_node_internal_ptr, interface_ptr, dual_module);
                                } else {
                                    interface_ptr.set_grow_state(
                                        &free_node_internal.origin.upgrade_force(),
                                        DualNodeGrowState::Grow,
                                        dual_module,
                                    );
                                    interface_ptr.set_grow_state(
                                        &matched_node_internal.origin.upgrade_force(),
                                        DualNodeGrowState::Shrink,
                                        dual_module,
                                    );
                                    interface_ptr.set_grow_state(
                                        &leaf_node_internal.origin.upgrade_force(),
                                        DualNodeGrowState::Grow,
                                        dual_module,
                                    );
                                }
                                continue;
                            }
                            MatchTarget::VirtualVertex(_) => {
                                // virtual boundary doesn't have to be matched, so in this case simply match these two nodes together
                                free_node_internal.temporary_match = Some((
                                    MatchTarget::Peer(matched_node_internal_ptr.downgrade()),
                                    free_touching_ptr.downgrade(),
                                ));
                                matched_node_internal.temporary_match = Some((
                                    MatchTarget::Peer(free_node_internal_ptr.downgrade()),
                                    matched_touching_ptr.downgrade(),
                                ));
                                // update dual module interface
                                interface_ptr.set_grow_state(
                                    &free_node_internal.origin.upgrade_force(),
                                    DualNodeGrowState::Stay,
                                    dual_module,
                                );
                                interface_ptr.set_grow_state(
                                    &matched_node_internal.origin.upgrade_force(),
                                    DualNodeGrowState::Stay,
                                    dual_module,
                                );
                                continue;
                            }
                        }
                    }
                    // third probable case: tree touches single vertex
                    if (free_1 && primal_node_internal_2.tree_node.is_some())
                        || (primal_node_internal_1.tree_node.is_some() && free_2)
                    {
                        let (
                            tree_node_internal_ptr,
                            tree_touching_ptr,
                            tree_node_internal,
                            free_node_internal_ptr,
                            free_touching_ptr,
                            mut free_node_internal,
                        ) = if primal_node_internal_1.tree_node.is_some() {
                            (
                                primal_node_internal_ptr_1.clone(),
                                touching_ptr_1.clone(),
                                primal_node_internal_1,
                                primal_node_internal_ptr_2.clone(),
                                touching_ptr_2.clone(),
                                primal_node_internal_2,
                            )
                        } else {
                            (
                                primal_node_internal_ptr_2.clone(),
                                touching_ptr_2.clone(),
                                primal_node_internal_2,
                                primal_node_internal_ptr_1.clone(),
                                touching_ptr_1.clone(),
                                primal_node_internal_1,
                            )
                        };
                        free_node_internal.temporary_match = Some((
                            MatchTarget::Peer(tree_node_internal_ptr.downgrade()),
                            free_touching_ptr.downgrade(),
                        ));
                        interface_ptr.set_grow_state(
                            &free_node_internal.origin.upgrade_force(),
                            DualNodeGrowState::Stay,
                            dual_module,
                        );
                        drop(tree_node_internal); // unlock
                        Self::augment_tree_given_matched(
                            tree_node_internal_ptr,
                            free_node_internal_ptr,
                            tree_touching_ptr.downgrade(),
                            interface_ptr,
                            dual_module,
                        );
                        continue;
                    }
                    // fourth probable case: tree touches matched pair
                    if (primal_node_internal_1.tree_node.is_some() && primal_node_internal_2.temporary_match.is_some())
                        || (primal_node_internal_1.temporary_match.is_some() && primal_node_internal_2.tree_node.is_some())
                    {
                        let (
                            tree_node_internal_ptr,
                            tree_touching_ptr,
                            mut tree_node_internal,
                            matched_node_internal_ptr,
                            matched_touching_ptr,
                            mut matched_node_internal,
                        ) = if primal_node_internal_1.tree_node.is_some() {
                            (
                                primal_node_internal_ptr_1.clone(),
                                touching_ptr_1.clone(),
                                primal_node_internal_1,
                                primal_node_internal_ptr_2.clone(),
                                touching_ptr_2.clone(),
                                primal_node_internal_2,
                            )
                        } else {
                            (
                                primal_node_internal_ptr_2.clone(),
                                touching_ptr_2.clone(),
                                primal_node_internal_2,
                                primal_node_internal_ptr_1.clone(),
                                touching_ptr_1.clone(),
                                primal_node_internal_1,
                            )
                        };
                        let match_target = matched_node_internal.temporary_match.as_ref().unwrap().0.clone();
                        match &match_target {
                            MatchTarget::Peer(leaf_node_internal_weak) => {
                                let leaf_node_internal_ptr = leaf_node_internal_weak.upgrade_force();
                                let tree_node = tree_node_internal.tree_node.as_mut().unwrap();
                                debug_assert!(tree_node.depth % 2 == 0, "conflicting one must be + node");
                                // simply add this matched pair to the children
                                tree_node
                                    .children
                                    .push((matched_node_internal_ptr.downgrade(), tree_touching_ptr.downgrade()));
                                // link children to parent
                                matched_node_internal.tree_node = Some(AlternatingTreeNode {
                                    root: tree_node.root.clone(),
                                    parent: Some((tree_node_internal_ptr.downgrade(), matched_touching_ptr.downgrade())),
                                    children: vec![(
                                        leaf_node_internal_weak.clone(),
                                        matched_node_internal.temporary_match.as_ref().unwrap().1.clone(),
                                    )],
                                    depth: tree_node.depth + 1,
                                    tree_size: None,
                                });
                                matched_node_internal.temporary_match = None;
                                let mut leaf_node_internal = leaf_node_internal_ptr.write();
                                leaf_node_internal.tree_node = Some(AlternatingTreeNode {
                                    root: tree_node.root.clone(),
                                    parent: Some((
                                        matched_node_internal_ptr.downgrade(),
                                        leaf_node_internal.temporary_match.as_ref().unwrap().1.clone(),
                                    )),
                                    children: vec![],
                                    depth: tree_node.depth + 2,
                                    tree_size: None,
                                });
                                leaf_node_internal.temporary_match = None;
                                // update the tree size (root might be tree_node, so drop them first)
                                let root_node_ptr = &tree_node.root.clone().upgrade_force();
                                drop(tree_node_internal);
                                let mut root_node = root_node_ptr.write();
                                let root_tree_node = root_node.tree_node.as_mut().unwrap();
                                let mut tree_size = *root_tree_node.tree_size.as_ref().unwrap();
                                tree_size = tree_size.saturating_add(
                                    matched_node_internal
                                        .origin
                                        .upgrade_force()
                                        .read_recursive()
                                        .defect_size
                                        .get(),
                                );
                                tree_size = tree_size.saturating_add(
                                    leaf_node_internal.origin.upgrade_force().read_recursive().defect_size.get(),
                                );
                                root_tree_node.tree_size = Some(tree_size);
                                // update dual module interface
                                if tree_size.get() > max_tree_size {
                                    drop(matched_node_internal);
                                    drop(leaf_node_internal);
                                    // stabilizer_qec: unlocked before the tree is read (Fusion Blossom kept it
                                    // locked, harmless only with its raw pointers; behind locks it deadlocked)
                                    drop(root_node);
                                    self.collapse_tree(root_node_ptr.clone(), interface_ptr, dual_module);
                                } else {
                                    interface_ptr.set_grow_state(
                                        &matched_node_internal.origin.upgrade_force(),
                                        DualNodeGrowState::Shrink,
                                        dual_module,
                                    );
                                    interface_ptr.set_grow_state(
                                        &leaf_node_internal.origin.upgrade_force(),
                                        DualNodeGrowState::Grow,
                                        dual_module,
                                    );
                                }
                                continue;
                            }
                            MatchTarget::VirtualVertex(_) => {
                                // virtual boundary doesn't have to be matched, so in this case remove it and augment the tree
                                matched_node_internal.temporary_match = Some((
                                    MatchTarget::Peer(tree_node_internal_ptr.downgrade()),
                                    matched_touching_ptr.downgrade(),
                                ));
                                drop(matched_node_internal); // unlock
                                drop(tree_node_internal); // unlock
                                Self::augment_tree_given_matched(
                                    tree_node_internal_ptr,
                                    matched_node_internal_ptr,
                                    tree_touching_ptr.downgrade(),
                                    interface_ptr,
                                    dual_module,
                                );
                                continue;
                            }
                        }
                    }
                    // much less probable case: two trees touch and both are augmented
                    if primal_node_internal_1.tree_node.is_some() && primal_node_internal_2.tree_node.is_some() {
                        let root_1 = primal_node_internal_1.tree_node.as_ref().unwrap().root.clone();
                        let root_2 = primal_node_internal_2.tree_node.as_ref().unwrap().root.clone();
                        // form a blossom inside an alternating tree
                        if root_1 == root_2 {
                            // drop writer lock to allow reader locks
                            let root_weak = primal_node_internal_1.tree_node.as_ref().unwrap().root.clone();
                            drop(primal_node_internal_1);
                            drop(primal_node_internal_2);
                            let tree_size = {
                                let root_ptr = root_weak.upgrade_force();
                                let tree_size = root_ptr.read_recursive().tree_node.as_ref().unwrap().tree_size;
                                tree_size.unwrap()
                            };
                            // find LCA of two nodes, two paths are from child to parent
                            let (lca_ptr, path_1, path_2) = self.find_lowest_common_ancestor(
                                primal_node_internal_ptr_1.clone(),
                                primal_node_internal_ptr_2.clone(),
                            );
                            let nodes_circle = {
                                let mut nodes_circle: Vec<DualNodePtr> =
                                    path_1.iter().map(|ptr| ptr.read_recursive().origin.upgrade_force()).collect();
                                nodes_circle.push(lca_ptr.read_recursive().origin.upgrade_force());
                                for i in (0..path_2.len()).rev() {
                                    nodes_circle.push(path_2[i].read_recursive().origin.upgrade_force());
                                }
                                nodes_circle
                            };
                            // build `touching_children`
                            let touching_children = {
                                let mut touching_children = Vec::<(DualNodeWeak, DualNodeWeak)>::new();
                                if !path_1.is_empty() {
                                    for (idx, ptr) in path_1.iter().enumerate() {
                                        let node = ptr.read_recursive();
                                        let tree_node = node.tree_node.as_ref().unwrap();
                                        let left_touching_ptr = if idx == 0 {
                                            touching_ptr_1.downgrade()
                                        } else {
                                            let last_ptr = path_1[idx - 1].downgrade();
                                            let idx = tree_node
                                                .children
                                                .iter()
                                                .position(|(ptr, _)| ptr == &last_ptr)
                                                .expect("should find child");
                                            tree_node.children[idx].1.clone()
                                        };
                                        let right_touching_ptr = tree_node.parent.as_ref().unwrap().1.clone();
                                        touching_children.push((left_touching_ptr, right_touching_ptr));
                                    }
                                }
                                {
                                    // the lca
                                    let node = lca_ptr.read_recursive();
                                    let tree_node = node.tree_node.as_ref().unwrap();
                                    let left_touching_ptr = if path_1.is_empty() {
                                        touching_ptr_1.downgrade()
                                    } else {
                                        let left_ptr = path_1[path_1.len() - 1].downgrade();
                                        let left_idx = tree_node
                                            .children
                                            .iter()
                                            .position(|(ptr, _)| ptr == &left_ptr)
                                            .expect("should find child");
                                        tree_node.children[left_idx].1.clone()
                                    };
                                    let right_touching_ptr = if path_2.is_empty() {
                                        touching_ptr_2.downgrade()
                                    } else {
                                        let right_ptr = path_2[path_2.len() - 1].downgrade();
                                        let right_idx = tree_node
                                            .children
                                            .iter()
                                            .position(|(ptr, _)| ptr == &right_ptr)
                                            .expect("should find child");
                                        tree_node.children[right_idx].1.clone()
                                    };
                                    touching_children.push((left_touching_ptr, right_touching_ptr));
                                }
                                if !path_2.is_empty() {
                                    for (idx, ptr) in path_2.iter().enumerate().rev() {
                                        let node = ptr.read_recursive();
                                        let tree_node = node.tree_node.as_ref().unwrap();
                                        let left_touching_ptr = tree_node.parent.as_ref().unwrap().1.clone();
                                        let right_touching_ptr = if idx == 0 {
                                            touching_ptr_2.downgrade()
                                        } else {
                                            let last_ptr = path_2[idx - 1].downgrade();
                                            let idx = tree_node
                                                .children
                                                .iter()
                                                .position(|(ptr, _)| ptr == &last_ptr)
                                                .expect("should find child");
                                            tree_node.children[idx].1.clone()
                                        };
                                        touching_children.push((left_touching_ptr, right_touching_ptr));
                                    }
                                }
                                touching_children
                            };
                            let blossom_node_ptr =
                                interface_ptr.create_blossom(nodes_circle, touching_children, dual_module);
                            let primal_node_internal_blossom_ptr = {
                                // create the corresponding primal node
                                let belonging = self.downgrade();
                                let mut module = self.write();
                                let local_node_index = module.nodes_length;
                                let node_index = module.nodes_count();
                                let primal_node_internal_blossom_ptr = if !module.is_fusion
                                    && local_node_index < module.nodes.len()
                                    && module.nodes[local_node_index].is_some()
                                {
                                    let node_ptr = module.nodes[local_node_index].take().unwrap();
                                    let mut node = node_ptr.write();
                                    node.origin = blossom_node_ptr.downgrade();
                                    node.index = node_index;
                                    node.tree_node = None;
                                    node.temporary_match = None;
                                    node.belonging = belonging;
                                    drop(node);
                                    node_ptr
                                } else {
                                    PrimalNodeInternalPtr::new_value(PrimalNodeInternal {
                                        origin: blossom_node_ptr.downgrade(),
                                        index: node_index,
                                        tree_node: None,
                                        temporary_match: None,
                                        belonging,
                                    })
                                };
                                module.nodes_length += 1;
                                if module.nodes.len() < module.nodes_length {
                                    module.nodes.push(None);
                                }
                                let cloned_primal_node_internal_blossom_ptr = primal_node_internal_blossom_ptr.clone();
                                module.nodes[local_node_index] = Some(primal_node_internal_blossom_ptr); // feature `dangerous_pointer`: must push the owner
                                cloned_primal_node_internal_blossom_ptr
                            };
                            // handle other part of the tree structure
                            let mut children = vec![];
                            for path in [&path_1, &path_2] {
                                if !path.is_empty() {
                                    let mut last_ptr = path[0].downgrade();
                                    for (height, ptr) in path.iter().enumerate() {
                                        let mut node = ptr.write();
                                        if height == 0 {
                                            let tree_node = node.tree_node.as_ref().unwrap();
                                            for (child_ptr, child_touching_ptr) in tree_node.children.iter() {
                                                children.push((child_ptr.clone(), child_touching_ptr.clone()));
                                            }
                                        } else {
                                            if height % 2 == 0 {
                                                let tree_node = node.tree_node.as_ref().unwrap();
                                                for (child_ptr, child_touching_ptr) in tree_node.children.iter() {
                                                    if child_ptr != &last_ptr {
                                                        // not in the blossom circle
                                                        children.push((child_ptr.clone(), child_touching_ptr.clone()));
                                                    }
                                                }
                                            }
                                        }
                                        node.tree_node = None; // this path is going to be part of the blossom, no longer in the tree
                                        last_ptr = ptr.downgrade();
                                    }
                                }
                            }
                            let mut lca = lca_ptr.write();
                            let lca_tree_node = lca.tree_node.as_ref().unwrap();
                            {
                                // add children of lca_ptr
                                for (child_ptr, child_touching_ptr) in lca_tree_node.children.iter() {
                                    if !path_1.is_empty() && &path_1[path_1.len() - 1].downgrade() == child_ptr {
                                        continue;
                                    }
                                    if !path_2.is_empty() && &path_2[path_2.len() - 1].downgrade() == child_ptr {
                                        continue;
                                    }
                                    children.push((child_ptr.clone(), child_touching_ptr.clone()));
                                }
                            }
                            if lca_tree_node.parent.is_some() || !children.is_empty() {
                                let mut primal_node_internal_blossom = primal_node_internal_blossom_ptr.write();
                                let new_tree_root = if lca_tree_node.depth == 0 {
                                    primal_node_internal_blossom_ptr.clone()
                                } else {
                                    lca_tree_node.root.upgrade_force()
                                };
                                let tree_node = AlternatingTreeNode {
                                    root: new_tree_root.downgrade(),
                                    parent: lca_tree_node.parent.clone(),
                                    children,
                                    depth: lca_tree_node.depth,
                                    tree_size: if lca_tree_node.depth == 0 { Some(tree_size) } else { None },
                                };
                                if lca_tree_node.parent.is_some() {
                                    let (parent_weak, _) = lca_tree_node.parent.as_ref().unwrap();
                                    let parent_ptr = parent_weak.upgrade_force();
                                    lock_write!(parent, parent_ptr);
                                    let parent_tree_node = parent.tree_node.as_mut().unwrap();
                                    debug_assert!(
                                        parent_tree_node.children.len() == 1,
                                        "lca's parent should be a - node with only one child"
                                    );
                                    let touching_ptr = parent_tree_node.children[0].1.clone(); // the touching grandson is not changed when forming blossom
                                    parent_tree_node.children.clear();
                                    parent_tree_node
                                        .children
                                        .push((primal_node_internal_blossom_ptr.downgrade(), touching_ptr));
                                }
                                if !tree_node.children.is_empty() {
                                    // connect this blossom to the new alternating tree
                                    for (child_weak, _) in tree_node.children.iter() {
                                        let child_ptr = child_weak.upgrade_force();
                                        lock_write!(child, child_ptr);
                                        let child_tree_node = child.tree_node.as_mut().unwrap();
                                        debug_assert!(child_tree_node.parent.is_some(), "child should have a parent");
                                        let touching_ptr = child_tree_node.parent.as_ref().unwrap().1.clone(); // the touching grandson is not changed when forming blossom
                                        child_tree_node.parent =
                                            Some((primal_node_internal_blossom_ptr.downgrade(), touching_ptr));
                                    }
                                    primal_node_internal_blossom.tree_node = Some(tree_node);
                                    primal_node_internal_blossom.change_sub_tree_root(lca_tree_node.depth, new_tree_root);
                                } else {
                                    primal_node_internal_blossom.tree_node = Some(tree_node);
                                }
                            }
                            lca.tree_node = None;
                            continue;
                        } else {
                            drop(primal_node_internal_1); // unlock
                            drop(primal_node_internal_2); // unlock
                            Self::augment_tree_given_matched(
                                primal_node_internal_ptr_1.clone(),
                                primal_node_internal_ptr_2.clone(),
                                touching_ptr_1.downgrade(),
                                interface_ptr,
                                dual_module,
                            );
                            Self::augment_tree_given_matched(
                                primal_node_internal_ptr_2.clone(),
                                primal_node_internal_ptr_1.clone(),
                                touching_ptr_2.downgrade(),
                                interface_ptr,
                                dual_module,
                            );
                            continue;
                        }
                    }
                    unreachable!()
                }
                MaxUpdateLength::TouchingVirtual((node_ptr, touching_ptr), (virtual_vertex_index, is_mirror)) => {
                    if self.get_primal_node_internal_ptr_option(&node_ptr).is_none() {
                        continue;
                    } // ignore out-of-date event
                    let primal_node_internal_ptr = self.get_outer_node(self.get_primal_node_internal_ptr(&node_ptr));
                    let mut primal_node_internal = primal_node_internal_ptr.write();
                    let grow_state = primal_node_internal.origin.upgrade_force().read_recursive().grow_state;
                    if grow_state != DualNodeGrowState::Grow {
                        debug_assert!(
                            current_conflict_index != 1,
                            "the first conflict cannot be ignored, otherwise may cause hidden infinite loop"
                        );
                        continue; // this is no longer a conflict
                    }
                    // this is the most probable case, so put it in the front
                    if primal_node_internal.is_free() {
                        primal_node_internal.temporary_match =
                            Some((MatchTarget::VirtualVertex(virtual_vertex_index), touching_ptr.downgrade()));
                        if is_mirror {
                            lock_write!(module, self);
                            module.possible_break.push(primal_node_internal.index);
                        }
                        interface_ptr.set_grow_state(
                            &primal_node_internal.origin.upgrade_force(),
                            DualNodeGrowState::Stay,
                            dual_module,
                        );
                        continue;
                    }
                    // tree touching virtual boundary will just augment the whole tree
                    if primal_node_internal.tree_node.is_some() {
                        if is_mirror {
                            lock_write!(module, self);
                            module.possible_break.push(primal_node_internal.index);
                        }
                        drop(primal_node_internal);
                        self.augment_tree_given_virtual_vertex(
                            primal_node_internal_ptr,
                            virtual_vertex_index,
                            touching_ptr.downgrade(),
                            interface_ptr,
                            dual_module,
                        );
                        continue;
                    }
                    unreachable!()
                }
                MaxUpdateLength::BlossomNeedExpand(node_ptr) => {
                    if self.get_primal_node_internal_ptr_option(&node_ptr).is_none() {
                        continue;
                    } // ignore out-of-date event
                      // blossom breaking is assumed to be very rare given our multiple-tree approach, so don't need to optimize for it
                      // first, isolate this blossom from its alternating tree
                    let primal_node_internal_ptr = self.get_primal_node_internal_ptr(&node_ptr);
                    let outer_primal_node_internal_ptr = self.get_outer_node(primal_node_internal_ptr.clone());
                    if outer_primal_node_internal_ptr != primal_node_internal_ptr {
                        // this blossom is now wrapped into another blossom, so we don't need to expand it anymore
                        debug_assert!(
                            current_conflict_index != 1,
                            "the first conflict cannot be ignored, otherwise may cause hidden infinite loop"
                        );
                        continue;
                    }
                    let primal_node_internal = primal_node_internal_ptr.read_recursive();
                    let grow_state = primal_node_internal.origin.upgrade_force().read_recursive().grow_state;
                    if grow_state != DualNodeGrowState::Shrink {
                        debug_assert!(
                            current_conflict_index != 1,
                            "the first conflict cannot be ignored, otherwise may cause hidden infinite loop"
                        );
                        continue; // this is no longer a conflict
                    }
                    // copy the nodes circle
                    let (nodes_circle, touching_children) = {
                        let blossom = node_ptr.read_recursive();
                        match &blossom.class {
                            DualNodeClass::Blossom {
                                nodes_circle,
                                touching_children,
                            } => (nodes_circle.clone(), touching_children.clone()),
                            _ => unreachable!("the expanding node is not a blossom"),
                        }
                    };
                    debug_assert!(
                        primal_node_internal.tree_node.is_some(),
                        "expanding blossom must belong to an alternating tree"
                    );
                    let tree_node = primal_node_internal.tree_node.as_ref().unwrap();
                    debug_assert!(
                        tree_node.depth % 2 == 1,
                        "expanding blossom must a '-' node in an alternating tree"
                    );
                    let (parent_ptr, parent_touching_ptr, parent_touching_child_ptr) = {
                        // remove it from it's parent's tree
                        let (parent_weak, parent_touching_child_ptr) = &tree_node.parent.as_ref().unwrap();
                        let parent_ptr = parent_weak.upgrade_force();
                        lock_write!(parent, parent_ptr);
                        let parent_tree_node = parent.tree_node.as_mut().unwrap();
                        let idx = parent_tree_node
                            .children
                            .iter()
                            .position(|ptr| ptr.0 == primal_node_internal_ptr.downgrade())
                            .expect("should find");
                        let parent_touching_ptr = parent_tree_node.children[idx].1.clone();
                        parent_tree_node.children.remove(idx);
                        parent_tree_node
                            .children
                            .retain(|ptr| ptr.0 != primal_node_internal_ptr.downgrade());
                        (
                            parent_ptr.clone(),
                            parent_touching_ptr,
                            parent_touching_child_ptr
                                .upgrade_force()
                                .get_secondary_ancestor_blossom()
                                .downgrade(),
                        )
                    };
                    let (child_ptr, child_touching_ptr, child_touching_child_ptr) = {
                        // make children independent trees
                        debug_assert!(tree_node.children.len() == 1, "a - node must have exactly ONE child");
                        let child_weak = &tree_node.children[0].0;
                        let child_touching_child_ptr = tree_node.children[0]
                            .1
                            .upgrade_force()
                            .get_secondary_ancestor_blossom()
                            .downgrade();
                        let child_ptr = child_weak.upgrade_force();
                        let child = child_ptr.read_recursive();
                        let child_tree_node = child.tree_node.as_ref().unwrap();
                        // find which blossom-child is touching this child
                        (
                            child_ptr.clone(),
                            child_tree_node.parent.as_ref().unwrap().1.clone(),
                            child_touching_child_ptr,
                        )
                    };
                    interface_ptr.expand_blossom(node_ptr, dual_module);
                    // now we need to re-connect all the expanded nodes, by analyzing the relationship of nodes_circle, parent_touching_ptr and child_touching_ptr
                    let parent_touching_index = nodes_circle
                        .iter()
                        .position(|ptr| ptr == &parent_touching_child_ptr)
                        .expect("touching node should be in the blossom circle");
                    let child_touching_index = nodes_circle
                        .iter()
                        .position(|ptr| ptr == &child_touching_child_ptr)
                        .expect("touching node should be in the blossom circle");
                    let mut is_tree_sequence_ascending = true;
                    let (match_sequence, tree_sequence) = {
                        // tree sequence is from parent to child
                        let mut match_sequence = Vec::new();
                        let mut tree_sequence = Vec::new();
                        match parent_touching_index.cmp(&child_touching_index) {
                            Ordering::Equal => {
                                tree_sequence.push(parent_touching_index);
                                for i in parent_touching_index + 1..nodes_circle.len() {
                                    match_sequence.push(i);
                                }
                                for i in 0..parent_touching_index {
                                    match_sequence.push(i);
                                }
                            }
                            Ordering::Greater => {
                                if (parent_touching_index - child_touching_index) % 2 == 0 {
                                    // [... c <----- p ...]
                                    for i in (child_touching_index..parent_touching_index + 1).rev() {
                                        tree_sequence.push(i);
                                    }
                                    is_tree_sequence_ascending = false;
                                    for i in parent_touching_index + 1..nodes_circle.len() {
                                        match_sequence.push(i);
                                    }
                                    for i in 0..child_touching_index {
                                        match_sequence.push(i);
                                    }
                                } else {
                                    // [--> c ...... p ---]
                                    for i in parent_touching_index..nodes_circle.len() {
                                        tree_sequence.push(i);
                                    }
                                    for i in 0..child_touching_index + 1 {
                                        tree_sequence.push(i);
                                    }
                                    for i in child_touching_index + 1..parent_touching_index {
                                        match_sequence.push(i);
                                    }
                                }
                            }
                            Ordering::Less => {
                                if (child_touching_index - parent_touching_index) % 2 == 0 {
                                    // [... p -----> c ...]
                                    for i in parent_touching_index..child_touching_index + 1 {
                                        tree_sequence.push(i);
                                    }
                                    for i in child_touching_index + 1..nodes_circle.len() {
                                        match_sequence.push(i);
                                    }
                                    for i in 0..parent_touching_index {
                                        match_sequence.push(i);
                                    }
                                } else {
                                    // [--- p ...... c <--]
                                    for i in (0..parent_touching_index + 1).rev() {
                                        tree_sequence.push(i);
                                    }
                                    for i in (child_touching_index..nodes_circle.len()).rev() {
                                        tree_sequence.push(i);
                                    }
                                    is_tree_sequence_ascending = false;
                                    for i in parent_touching_index + 1..child_touching_index {
                                        match_sequence.push(i);
                                    }
                                }
                            }
                        }
                        (match_sequence, tree_sequence)
                    };
                    debug_assert!(
                        match_sequence.len() % 2 == 0 && tree_sequence.len() % 2 == 1,
                        "parity of sequence wrong"
                    );
                    // match the nodes in the match sequence
                    for i in (0..match_sequence.len()).step_by(2) {
                        let primal_node_internal_ptr_1 =
                            self.get_primal_node_internal_ptr(&nodes_circle[match_sequence[i]].upgrade_force());
                        let primal_node_internal_ptr_2 =
                            self.get_primal_node_internal_ptr(&nodes_circle[match_sequence[i + 1]].upgrade_force());
                        debug_assert!(
                            (match_sequence[i] + 1) % nodes_circle.len() == match_sequence[i + 1],
                            "match sequence should be ascending"
                        );
                        let touching_ptr_1 = touching_children[match_sequence[i]].1.clone(); // assuming ascending match sequence
                        let touching_ptr_2 = touching_children[match_sequence[i + 1]].0.clone(); // assuming ascending match sequence
                        let mut primal_node_internal_1 = primal_node_internal_ptr_1.write();
                        let mut primal_node_internal_2 = primal_node_internal_ptr_2.write();
                        primal_node_internal_1.temporary_match =
                            Some((MatchTarget::Peer(primal_node_internal_ptr_2.downgrade()), touching_ptr_1));
                        primal_node_internal_2.temporary_match =
                            Some((MatchTarget::Peer(primal_node_internal_ptr_1.downgrade()), touching_ptr_2));
                        interface_ptr.set_grow_state(
                            &primal_node_internal_1.origin.upgrade_force(),
                            DualNodeGrowState::Stay,
                            dual_module,
                        );
                        interface_ptr.set_grow_state(
                            &primal_node_internal_2.origin.upgrade_force(),
                            DualNodeGrowState::Stay,
                            dual_module,
                        );
                    }
                    // connect the nodes in the tree sequence to the alternating tree, note that the tree sequence is from parent to child
                    for (idx, current_i) in tree_sequence.iter().enumerate() {
                        debug_assert!(
                            {
                                if idx + 1 < tree_sequence.len() {
                                    if is_tree_sequence_ascending {
                                        (tree_sequence[idx] + 1) % nodes_circle.len() == tree_sequence[idx + 1]
                                    } else {
                                        (tree_sequence[idx + 1] + 1) % nodes_circle.len() == tree_sequence[idx]
                                    }
                                } else {
                                    true
                                }
                            },
                            "tree sequence orientation must be consistent"
                        );
                        let current_parent_ptr = if idx == 0 {
                            parent_ptr.clone()
                        } else {
                            self.get_primal_node_internal_ptr(&nodes_circle[tree_sequence[idx - 1]].upgrade_force())
                        };
                        let current_parent_touching_ptr = if idx == 0 {
                            tree_node.parent.as_ref().unwrap().1.clone()
                        } else {
                            if is_tree_sequence_ascending {
                                touching_children[*current_i].0.clone()
                            } else {
                                touching_children[*current_i].1.clone()
                            }
                        };
                        let current_child_ptr = if idx == tree_sequence.len() - 1 {
                            child_ptr.clone()
                        } else {
                            self.get_primal_node_internal_ptr(&nodes_circle[tree_sequence[idx + 1]].upgrade_force())
                        };
                        let current_child_touching_ptr = if idx == tree_sequence.len() - 1 {
                            tree_node.children[0].1.clone()
                        } else {
                            if is_tree_sequence_ascending {
                                touching_children[*current_i].1.clone()
                            } else {
                                touching_children[*current_i].0.clone()
                            }
                        };
                        let current_ptr = self.get_primal_node_internal_ptr(&nodes_circle[*current_i].upgrade_force());
                        let mut current = current_ptr.write();
                        current.tree_node = Some(AlternatingTreeNode {
                            root: tree_node.root.clone(),
                            parent: Some((current_parent_ptr.downgrade(), current_parent_touching_ptr)),
                            children: vec![(current_child_ptr.downgrade(), current_child_touching_ptr)],
                            depth: tree_node.depth + idx,
                            tree_size: None,
                        });
                        interface_ptr.set_grow_state(
                            &current.origin.upgrade_force(),
                            if idx % 2 == 0 {
                                DualNodeGrowState::Shrink
                            } else {
                                DualNodeGrowState::Grow
                            },
                            dual_module,
                        );
                    }
                    {
                        // connect parent
                        lock_write!(parent, parent_ptr);
                        let parent_tree_node = parent.tree_node.as_mut().unwrap();
                        let child_ptr = self.get_primal_node_internal_ptr(&nodes_circle[tree_sequence[0]].upgrade_force());
                        parent_tree_node.children.push((child_ptr.downgrade(), parent_touching_ptr));
                    }
                    {
                        // connect child and fix the depth information of the child
                        lock_write!(child, child_ptr);
                        let child_tree_node = child.tree_node.as_mut().unwrap();
                        let parent_ptr = self.get_primal_node_internal_ptr(
                            &nodes_circle[tree_sequence[tree_sequence.len() - 1]].upgrade_force(),
                        );
                        child_tree_node.parent = Some((parent_ptr.downgrade(), child_touching_ptr));
                        child.change_sub_tree_root(tree_node.depth + tree_sequence.len(), tree_node.root.upgrade_force());
                    }
                    {
                        // remove it from nodes
                        lock_write!(module, self);
                        debug_assert_eq!(
                            module.get_node(primal_node_internal.index),
                            Some(primal_node_internal_ptr.clone()),
                            "index wrong"
                        );
                        module.remove_node(primal_node_internal.index);
                    }
                }
                MaxUpdateLength::VertexShrinkStop(_) => {
                    if current_conflict_index == 1 {
                        // if this happens, then debug the sorting of conflict events and also check alternating tree: a vertex should never be a floating "-" node
                        unreachable!("VertexShrinkStop conflict cannot be solved by primal module, and should be sorted to the last of the heap")
                    }
                    // just skip and wait for the next round to resolve it, if it's not being resolved already
                }
                _ => unreachable!("should not resolve these issues"),
            }
        }
    }

    fn intermediate_matching<D: DualModuleImpl>(
        &mut self,
        _interface: &DualModuleInterfacePtr,
        _dual_module: &mut D,
    ) -> IntermediateMatching {
        let mut immediate_matching = IntermediateMatching::new();
        let mut flattened_nodes = vec![];
        self.flatten_nodes(&mut flattened_nodes);
        for primal_node_internal_ptr in flattened_nodes.iter().flatten() {
            let primal_node_internal = primal_node_internal_ptr.read_recursive();
            debug_assert!(
                primal_node_internal.tree_node.is_none(),
                "cannot compute perfect matching with active alternating tree"
            );
            let origin_ptr = primal_node_internal.origin.upgrade_force();
            let interface_node = origin_ptr.read_recursive();
            if interface_node.parent_blossom.is_some() {
                debug_assert_eq!(
                    primal_node_internal.temporary_match, None,
                    "blossom internal nodes should not be matched"
                );
                continue; // do not handle this blossom at this level
            }
            if let Some((match_target, match_touching_ptr)) = primal_node_internal.temporary_match.as_ref() {
                match match_target {
                    MatchTarget::Peer(peer_internal_weak) => {
                        let peer_internal_ptr = peer_internal_weak.upgrade_force();
                        let peer_internal = peer_internal_ptr.read_recursive();
                        if primal_node_internal.index < peer_internal.index {
                            // to avoid duplicate matched pairs
                            let peer_touching_ptr = peer_internal.temporary_match.as_ref().unwrap().1.clone();
                            immediate_matching.peer_matchings.push((
                                (primal_node_internal.origin.upgrade_force(), match_touching_ptr.clone()),
                                (peer_internal.origin.upgrade_force(), peer_touching_ptr),
                            ));
                        }
                    }
                    MatchTarget::VirtualVertex(virtual_vertex) => {
                        immediate_matching.virtual_matchings.push((
                            (primal_node_internal.origin.upgrade_force(), match_touching_ptr.clone()),
                            *virtual_vertex,
                        ));
                    }
                }
            } else {
                panic!(
                    "cannot compute final matching with unmatched outer node {:?}",
                    primal_node_internal_ptr
                );
            }
        }
        immediate_matching
    }
}

impl FusionVisualizer for PrimalModuleSerialPtr {
    fn snapshot(&self, abbrev: bool) -> serde_json::Value {
        // do the sanity check first before taking snapshot
        let flattened_nodes = self.sanity_check().unwrap();
        let mut primal_nodes = Vec::<serde_json::Value>::new();
        for primal_node_ptr in flattened_nodes.iter() {
            if let Some(primal_node_ptr) = &primal_node_ptr {
                let primal_node = primal_node_ptr.read_recursive();
                primal_nodes.push(json!({
                    if abbrev { "m" } else { "temporary_match" }: primal_node.temporary_match.as_ref().map(|(match_target, touching_ptr)| {
                        match match_target {
                            MatchTarget::Peer(peer_weak) => {
                                let peer_ptr = peer_weak.upgrade_force();
                                json!({
                                    if abbrev { "p" } else { "peer" }: peer_ptr.read_recursive().index,
                                    if abbrev { "t" } else { "touching" }: touching_ptr.upgrade_force().read_recursive().index,
                                })
                            },
                            MatchTarget::VirtualVertex(vertex_idx) => json!({
                                if abbrev { "v" } else { "virtual_vertex" }: vertex_idx,
                                if abbrev { "t" } else { "touching" }: touching_ptr.upgrade_force().read_recursive().index,
                            }),
                        }
                    }),
                    if abbrev { "t" } else { "tree_node" }: primal_node.tree_node.as_ref().map(|tree_node| {
                        json!({
                            if abbrev { "r" } else { "root" }: tree_node.root.upgrade_force().read_recursive().index,
                            if abbrev { "p" } else { "parent" }: tree_node.parent.as_ref().map(|(weak, _)| weak.upgrade_force().read_recursive().index),
                            if abbrev { "pt" } else { "parent_touching" }: tree_node.parent.as_ref().map(|(_, weak)| weak.upgrade_force().read_recursive().index),
                            if abbrev { "c" } else { "children" }: tree_node.children.iter().map(|(weak, _)| weak.upgrade_force().read_recursive().index).collect::<Vec<NodeIndex>>(),
                            if abbrev { "ct" } else { "children_touching" }: tree_node.children.iter().map(|(_, weak)| weak.upgrade_force().read_recursive().index).collect::<Vec<NodeIndex>>(),
                            if abbrev { "d" } else { "depth" }: tree_node.depth,
                        })
                    }),
                }));
            } else {
                primal_nodes.push(json!(null));
            }
        }
        json!({
            "primal_nodes": primal_nodes,
        })
    }
}

impl PrimalModuleSerial {
    /// return the count of all nodes including those of the children interfaces
    pub fn nodes_count(&self) -> NodeNum {
        let mut count = self.nodes_length as NodeNum;
        if let Some(((_, left_count), (_, right_count))) = &self.children {
            count += left_count + right_count;
        }
        count
    }

    /// get node ptr by index; if calling from the ancestor module, node_index is absolute, otherwise it's relative
    #[allow(clippy::unnecessary_cast)]
    pub fn get_node(&self, relative_node_index: NodeIndex) -> Option<PrimalNodeInternalPtr> {
        debug_assert!(relative_node_index < self.nodes_count(), "cannot find node in this module");
        let mut bias = 0;
        if let Some(((left_weak, left_count), (right_weak, right_count))) = &self.children {
            if relative_node_index < *left_count {
                // this node belongs to the left
                return left_weak.upgrade_force().read_recursive().get_node(relative_node_index);
            } else if relative_node_index < *left_count + *right_count {
                // this node belongs to the right
                return right_weak
                    .upgrade_force()
                    .read_recursive()
                    .get_node(relative_node_index - *left_count);
            }
            bias = left_count + right_count;
        }
        self.nodes[(relative_node_index - bias) as usize].clone()
    }

    /// set the corresponding node index to None
    #[allow(clippy::unnecessary_cast)]
    pub fn remove_node(&mut self, relative_node_index: NodeIndex) {
        debug_assert!(relative_node_index < self.nodes_count(), "cannot find node in this module");
        let mut bias = 0;
        if let Some(((left_weak, left_count), (right_weak, right_count))) = &self.children {
            if relative_node_index < *left_count {
                // this node belongs to the left
                left_weak.upgrade_force().write().remove_node(relative_node_index);
                return;
            } else if relative_node_index < *left_count + *right_count {
                // this node belongs to the right
                right_weak
                    .upgrade_force()
                    .write()
                    .remove_node(relative_node_index - *left_count);
                return;
            }
            bias = left_count + right_count;
        }
        self.nodes[(relative_node_index - bias) as usize] = None;
    }
}

impl PrimalModuleSerialPtr {
    pub fn get_primal_node_internal_ptr_option(&self, dual_node_ptr: &DualNodePtr) -> Option<PrimalNodeInternalPtr> {
        let module = self.read_recursive();
        let dual_node = dual_node_ptr.read_recursive();
        let primal_node_internal_ptr = module.get_node(dual_node.index);
        if let Some(primal_node_internal_ptr) = &primal_node_internal_ptr {
            if module.is_fusion {
                primal_node_internal_ptr.update(); // every time it's accessed, make sure it's update-to-date
            }
            debug_assert!(
                dual_node_ptr == &primal_node_internal_ptr.read_recursive().origin.upgrade_force(),
                "dual node and primal internal node must corresponds to each other"
            );
        }
        primal_node_internal_ptr
    }

    pub fn get_primal_node_internal_ptr(&self, dual_node_ptr: &DualNodePtr) -> PrimalNodeInternalPtr {
        self.get_primal_node_internal_ptr_option(dual_node_ptr)
            .expect("internal primal node must exists")
    }

    /// get the outer node in the most up-to-date cache
    pub fn get_outer_node(&self, primal_node_internal_ptr: PrimalNodeInternalPtr) -> PrimalNodeInternalPtr {
        let node = primal_node_internal_ptr.read_recursive();
        let origin_ptr = node.origin.upgrade_force();
        let interface_node = origin_ptr.read_recursive();
        if let Some(parent_dual_node_weak) = &interface_node.parent_blossom {
            let parent_dual_node_ptr = parent_dual_node_weak.upgrade_force();
            let parent_primal_node_internal_ptr = self.get_primal_node_internal_ptr(&parent_dual_node_ptr);
            self.get_outer_node(parent_primal_node_internal_ptr)
        } else {
            primal_node_internal_ptr.clone()
        }
    }

    /// find the lowest common ancestor (LCA) of two nodes in the alternating tree, return (LCA, path_1, path_2) where path includes leaf but exclude the LCA
    pub fn find_lowest_common_ancestor(
        &self,
        mut primal_node_internal_ptr_1: PrimalNodeInternalPtr,
        mut primal_node_internal_ptr_2: PrimalNodeInternalPtr,
    ) -> (PrimalNodeInternalPtr, Vec<PrimalNodeInternalPtr>, Vec<PrimalNodeInternalPtr>) {
        let (depth_1, depth_2) = {
            let primal_node_internal_1 = primal_node_internal_ptr_1.read_recursive();
            let primal_node_internal_2 = primal_node_internal_ptr_2.read_recursive();
            let tree_node_1 = primal_node_internal_1.tree_node.as_ref().unwrap();
            let tree_node_2 = primal_node_internal_2.tree_node.as_ref().unwrap();
            debug_assert_eq!(tree_node_1.root, tree_node_2.root, "must belong to the same tree");
            (tree_node_1.depth, tree_node_2.depth)
        };
        let mut path_1 = vec![];
        let mut path_2 = vec![];
        match depth_1.cmp(&depth_2) {
            Ordering::Greater => loop {
                let ptr = primal_node_internal_ptr_1.clone();
                let primal_node_internal = ptr.read_recursive();
                let tree_node = primal_node_internal.tree_node.as_ref().unwrap();
                if tree_node.depth == depth_2 {
                    break;
                }
                path_1.push(primal_node_internal_ptr_1.clone());
                primal_node_internal_ptr_1 = tree_node.parent.as_ref().unwrap().0.upgrade_force();
            },
            Ordering::Less => loop {
                let ptr = primal_node_internal_ptr_2.clone();
                let primal_node_internal = ptr.read_recursive();
                let tree_node = primal_node_internal.tree_node.as_ref().unwrap();
                if tree_node.depth == depth_1 {
                    break;
                }
                path_2.push(primal_node_internal_ptr_2.clone());
                primal_node_internal_ptr_2 = tree_node.parent.as_ref().unwrap().0.upgrade_force();
            },
            Ordering::Equal => {}
        }
        // now primal_node_internal_ptr_1 and primal_node_internal_ptr_2 has the same depth, compare them until they're equal
        loop {
            if primal_node_internal_ptr_1 == primal_node_internal_ptr_2 {
                return (primal_node_internal_ptr_1, path_1, path_2);
            }
            let ptr_1 = primal_node_internal_ptr_1.clone();
            let ptr_2 = primal_node_internal_ptr_2.clone();
            let primal_node_internal_1 = ptr_1.read_recursive();
            let primal_node_internal_2 = ptr_2.read_recursive();
            let tree_node_1 = primal_node_internal_1.tree_node.as_ref().unwrap();
            let tree_node_2 = primal_node_internal_2.tree_node.as_ref().unwrap();
            path_1.push(primal_node_internal_ptr_1.clone());
            path_2.push(primal_node_internal_ptr_2.clone());
            primal_node_internal_ptr_1 = tree_node_1.parent.as_ref().unwrap().0.upgrade_force();
            primal_node_internal_ptr_2 = tree_node_2.parent.as_ref().unwrap().0.upgrade_force();
        }
    }

    /// for any - node, match the children by matching them with + node
    pub fn match_subtree<D: DualModuleImpl>(
        tree_node_internal_ptr: PrimalNodeInternalPtr,
        interface_ptr: &DualModuleInterfacePtr,
        dual_module: &mut D,
    ) {
        let mut tree_node_internal = tree_node_internal_ptr.write();
        let tree_node = tree_node_internal.tree_node.as_ref().unwrap();
        debug_assert!(tree_node.depth % 2 == 1, "only match - node is possible");
        let child_node_internal_ptr = tree_node.children[0].0.upgrade_force();
        tree_node_internal.temporary_match = Some((
            MatchTarget::Peer(child_node_internal_ptr.downgrade()),
            tree_node.children[0].1.clone(),
        ));
        interface_ptr.set_grow_state(
            &tree_node_internal.origin.upgrade_force(),
            DualNodeGrowState::Stay,
            dual_module,
        );
        tree_node_internal.tree_node = None;
        let mut child_node_internal = child_node_internal_ptr.write();
        let child_touching_ptr = child_node_internal
            .tree_node
            .as_ref()
            .unwrap()
            .parent
            .as_ref()
            .unwrap()
            .1
            .clone();
        child_node_internal.temporary_match =
            Some((MatchTarget::Peer(tree_node_internal_ptr.downgrade()), child_touching_ptr));
        let child_tree_node = child_node_internal.tree_node.as_ref().unwrap();
        interface_ptr.set_grow_state(
            &child_node_internal.origin.upgrade_force(),
            DualNodeGrowState::Stay,
            dual_module,
        );
        for (grandson_ptr, _) in child_tree_node.children.iter() {
            Self::match_subtree(grandson_ptr.upgrade_force(), interface_ptr, dual_module);
        }
        child_node_internal.tree_node = None;
    }

    /// for any + node, match it with another node will augment the whole tree, breaking out into several matched pairs;
    /// `tree_grandson_ptr` is the grandson of tree_node_internal_ptr that touches `match_node_internal_ptr`
    pub fn augment_tree_given_matched<D: DualModuleImpl>(
        tree_node_internal_ptr: PrimalNodeInternalPtr,
        match_node_internal_ptr: PrimalNodeInternalPtr,
        tree_touching_ptr: DualNodeWeak,
        interface_ptr: &DualModuleInterfacePtr,
        dual_module: &mut D,
    ) {
        let mut tree_node_internal = tree_node_internal_ptr.write();
        tree_node_internal.temporary_match =
            Some((MatchTarget::Peer(match_node_internal_ptr.downgrade()), tree_touching_ptr));
        interface_ptr.set_grow_state(
            &tree_node_internal.origin.upgrade_force(),
            DualNodeGrowState::Stay,
            dual_module,
        );
        let tree_node = tree_node_internal.tree_node.as_ref().unwrap();
        debug_assert!(tree_node.depth % 2 == 0, "only augment + node is possible");
        for (child_ptr, _) in tree_node.children.iter() {
            if child_ptr != &match_node_internal_ptr.downgrade() {
                Self::match_subtree(child_ptr.upgrade_force(), interface_ptr, dual_module);
            }
        }
        if tree_node.depth != 0 {
            // it's not root, then we need to match parent to grandparent
            let parent_node_internal_weak = tree_node.parent.as_ref().unwrap().0.clone();
            let parent_node_internal_ptr = parent_node_internal_weak.upgrade_force();
            let grandparent_node_internal_ptr = {
                // must unlock parent
                let mut parent_node_internal = parent_node_internal_ptr.write();
                let parent_tree_node = parent_node_internal.tree_node.as_ref().unwrap();
                let grandparent_node_internal_weak = parent_tree_node.parent.as_ref().unwrap().0.clone();
                parent_node_internal.temporary_match = Some((
                    MatchTarget::Peer(grandparent_node_internal_weak.clone()),
                    parent_tree_node.parent.as_ref().unwrap().1.clone(),
                ));
                parent_node_internal.tree_node = None;
                interface_ptr.set_grow_state(
                    &parent_node_internal.origin.upgrade_force(),
                    DualNodeGrowState::Stay,
                    dual_module,
                );
                grandparent_node_internal_weak.upgrade_force()
            };
            let grandparent_touching_ptr = {
                let grandparent_node_internal = grandparent_node_internal_ptr.read_recursive();
                let grandparent_tree_node = grandparent_node_internal.tree_node.as_ref().unwrap();
                let idx = grandparent_tree_node
                    .children
                    .iter()
                    .position(|(ptr, _)| ptr == &parent_node_internal_weak)
                    .expect("should find child");
                grandparent_tree_node.children[idx].1.clone()
            };
            Self::augment_tree_given_matched(
                grandparent_node_internal_ptr,
                parent_node_internal_ptr,
                grandparent_touching_ptr,
                interface_ptr,
                dual_module,
            );
        }
        tree_node_internal.tree_node = None;
    }

    /// for any + node, match it with virtual boundary will augment the whole tree, breaking out into several matched pairs
    pub fn augment_tree_given_virtual_vertex<D: DualModuleImpl>(
        &self,
        tree_node_internal_ptr: PrimalNodeInternalPtr,
        virtual_vertex_index: VertexIndex,
        tree_touching_ptr: DualNodeWeak,
        interface_ptr: &DualModuleInterfacePtr,
        dual_module: &mut D,
    ) {
        let mut tree_node_internal = tree_node_internal_ptr.write();
        tree_node_internal.temporary_match = Some((MatchTarget::VirtualVertex(virtual_vertex_index), tree_touching_ptr));
        interface_ptr.set_grow_state(
            &tree_node_internal.origin.upgrade_force(),
            DualNodeGrowState::Stay,
            dual_module,
        );
        let tree_node = tree_node_internal.tree_node.as_ref().unwrap();
        debug_assert!(tree_node.depth % 2 == 0, "only augment + node is possible");
        for (child_ptr, _) in tree_node.children.iter() {
            Self::match_subtree(child_ptr.upgrade_force(), interface_ptr, dual_module);
        }
        if tree_node.depth != 0 {
            // it's not root, then we need to match parent to grandparent
            let parent_node_internal_weak = tree_node.parent.as_ref().unwrap().0.clone();
            let parent_node_internal_ptr = parent_node_internal_weak.upgrade_force();
            let grandparent_node_internal_ptr = {
                // must unlock parent
                let mut parent_node_internal = parent_node_internal_ptr.write();
                let parent_tree_node = parent_node_internal.tree_node.as_ref().unwrap();
                let grandparent_node_internal_weak = parent_tree_node.parent.as_ref().unwrap().0.clone();
                parent_node_internal.temporary_match = Some((
                    MatchTarget::Peer(grandparent_node_internal_weak.clone()),
                    parent_tree_node.parent.as_ref().unwrap().1.clone(),
                ));
                parent_node_internal.tree_node = None;
                interface_ptr.set_grow_state(
                    &parent_node_internal.origin.upgrade_force(),
                    DualNodeGrowState::Stay,
                    dual_module,
                );
                grandparent_node_internal_weak.upgrade_force()
            };
            let grandparent_touching_ptr = {
                let grandparent_node_internal = grandparent_node_internal_ptr.read_recursive();
                let grandparent_tree_node = grandparent_node_internal.tree_node.as_ref().unwrap();
                let idx = grandparent_tree_node
                    .children
                    .iter()
                    .position(|(ptr, _)| ptr == &parent_node_internal_weak)
                    .expect("should find child");
                grandparent_tree_node.children[idx].1.clone()
            };
            Self::augment_tree_given_matched(
                grandparent_node_internal_ptr,
                parent_node_internal_ptr,
                grandparent_touching_ptr,
                interface_ptr,
                dual_module,
            );
        }
        tree_node_internal.tree_node = None;
    }

    /// DFS flatten the nodes
    #[allow(clippy::unnecessary_cast)]
    pub fn flatten_nodes(&self, flattened_nodes: &mut Vec<Option<PrimalNodeInternalPtr>>) {
        let module = self.read_recursive();
        let flattened_nodes_length = flattened_nodes.len();
        // the order matters: left -> right -> myself
        if let Some(((left_child_weak, _), (right_child_weak, _))) = &module.children {
            left_child_weak.upgrade_force().flatten_nodes(flattened_nodes);
            right_child_weak.upgrade_force().flatten_nodes(flattened_nodes);
        }
        for node_index in 0..module.nodes_length {
            let primal_node_internal_ptr = &module.nodes[node_index];
            if let Some(primal_node_internal_ptr) = primal_node_internal_ptr {
                primal_node_internal_ptr.update();
                primal_node_internal_ptr.read_recursive().origin.upgrade_force().update();
            }
            flattened_nodes.push(primal_node_internal_ptr.clone());
        }
        debug_assert_eq!(flattened_nodes.len() - flattened_nodes_length, module.nodes_count() as usize);
    }

    /// fuse two modules by copying the nodes in `other` into myself
    #[allow(clippy::unnecessary_cast)]
    pub fn slow_fuse(&self, left: &Self, right: &Self) {
        let mut module = self.write();
        module.is_fusion = true; // for safety
        for other in [left, right] {
            let mut other_module = other.write();
            other_module.is_fusion = true; // enable pointer update
            let bias = module.nodes_length as NodeIndex;
            for other_node_index in 0..other_module.nodes_length as NodeIndex {
                let node_ptr = &other_module.nodes[other_node_index as usize];
                if let Some(node_ptr) = node_ptr {
                    let mut node = node_ptr.write();
                    debug_assert_eq!(node.index, other_node_index);
                    node.index += bias;
                }
                module.nodes_length += 1;
                if module.nodes.len() < module.nodes_length {
                    module.nodes.push(None);
                }
                module.nodes[(bias + other_node_index) as usize] = node_ptr.clone();
            }
            // copy `possible_break`
            for node_index in other_module.possible_break.iter() {
                module.possible_break.push(*node_index + bias);
            }
        }
    }

    /// fuse two modules by (virtually) copying the nodes in `other` into myself, with O(1) time complexity
    pub fn fuse(&self, left: &Self, right: &Self) {
        let parent_weak = self.downgrade();
        let left_weak = left.downgrade();
        let right_weak = right.downgrade();
        let mut module = self.write();
        module.is_fusion = true; // for safety
        debug_assert_eq!(module.nodes_length, 0, "fast fuse doesn't support non-empty fuse");
        debug_assert!(module.children.is_none(), "cannot fuse twice");
        let mut left_module = left.write();
        let mut right_module = right.write();
        debug_assert!(left_module.parent.is_none(), "cannot fuse an module twice");
        debug_assert!(right_module.parent.is_none(), "cannot fuse an module twice");
        left_module.parent = Some(parent_weak.clone());
        right_module.parent = Some(parent_weak);
        left_module.index_bias = 0;
        right_module.index_bias = left_module.nodes_count();
        module.children = Some((
            (left_weak, left_module.nodes_count()),
            (right_weak, right_module.nodes_count()),
        ));
        // the possible_break should be a small subset, thus copying them is fine
        for other_module in [left_module, right_module] {
            for node_index in other_module.possible_break.iter() {
                module.possible_break.push(*node_index + other_module.index_bias);
            }
        }
    }

    /// do a sanity check of it's tree structure and internal state
    #[allow(clippy::collapsible_else_if)]
    pub fn sanity_check(&self) -> Result<Vec<Option<PrimalNodeInternalPtr>>, String> {
        let mut flattened_nodes = vec![];
        self.flatten_nodes(&mut flattened_nodes);
        for (index, primal_module_internal_ptr) in flattened_nodes.iter().enumerate() {
            if let Some(primal_module_internal_ptr) = primal_module_internal_ptr {
                let primal_module_internal = primal_module_internal_ptr.read_recursive();
                if primal_module_internal.index != index as NodeIndex {
                    return Err(format!(
                        "primal node index wrong: expected {}, actual {}",
                        index, primal_module_internal.index
                    ));
                }
                let origin_ptr = primal_module_internal.origin.upgrade_force();
                let origin_node = origin_ptr.read_recursive();
                if origin_node.index != primal_module_internal.index {
                    return Err(format!(
                        "origin index wrong: expected {}, actual {}",
                        index, origin_node.index
                    ));
                }
                if primal_module_internal.temporary_match.is_some() && primal_module_internal.tree_node.is_some() {
                    return Err(format!("{} temporary match and tree node cannot both exists", index));
                }
                if origin_node.parent_blossom.is_some() {
                    if primal_module_internal.tree_node.is_some() {
                        return Err(format!("blossom internal node {index} is still in a tree"));
                    }
                    if primal_module_internal.temporary_match.is_some() {
                        return Err(format!("blossom internal node {index} is still matched"));
                    }
                }
                if let Some((match_target, _)) = primal_module_internal.temporary_match.as_ref() {
                    if origin_node.grow_state != DualNodeGrowState::Stay {
                        return Err(format!("matched node {index} is not set to Stay"));
                    }
                    match match_target {
                        MatchTarget::Peer(peer_weak) => {
                            let peer_ptr = peer_weak.upgrade_force();
                            let peer = peer_ptr.read_recursive();
                            if let Some((peer_match_target, _)) = peer.temporary_match.as_ref() {
                                if peer_match_target != &MatchTarget::Peer(primal_module_internal_ptr.downgrade()) {
                                    return Err(format!(
                                        "match peer {} is not matched with {}, instead it's {:?}",
                                        peer.index, index, peer_match_target
                                    ));
                                }
                            } else {
                                return Err("match peer is not marked as matched".to_string());
                            }
                        }
                        MatchTarget::VirtualVertex(_vertex_idx) => {} // nothing to check
                    }
                }
                if let Some(tree_node) = primal_module_internal.tree_node.as_ref() {
                    // first check if every child's parent is myself
                    for (child_weak, _) in tree_node.children.iter() {
                        let child_ptr = child_weak.upgrade_force();
                        let child = child_ptr.read_recursive();
                        if let Some(child_tree_node) = child.tree_node.as_ref() {
                            if child_tree_node.parent.as_ref().map(|x| &x.0) != Some(&primal_module_internal_ptr.downgrade())
                            {
                                return Err(format!(
                                    "{}'s child {} has a different parent, link broken",
                                    index, child.index
                                ));
                            }
                        } else {
                            return Err(format!(
                                "{}'s child {} doesn't belong to any tree, link broken",
                                index, child.index
                            ));
                        }
                        // check if child is still tracked, i.e. inside self.nodes
                        let module = self.read_recursive();
                        if child.index >= module.nodes_count() || module.get_node(child.index).is_none() {
                            return Err(format!("child's index {} is not in the interface", child.index));
                        }
                        let tracked_child_ptr = module.get_node(child.index).unwrap();
                        if tracked_child_ptr != child_ptr {
                            return Err(format!(
                                "the tracked ptr of child {} is not what's being pointed",
                                child.index
                            ));
                        }
                    }
                    // then check if I'm my parent's child
                    if let Some((parent_weak, _)) = tree_node.parent.as_ref() {
                        let parent_ptr = parent_weak.upgrade_force();
                        let parent = parent_ptr.read_recursive();
                        if let Some(parent_tree_node) = parent.tree_node.as_ref() {
                            let mut found_match_count = 0;
                            for (node_ptr, _) in parent_tree_node.children.iter() {
                                if node_ptr == &primal_module_internal_ptr.downgrade() {
                                    found_match_count += 1;
                                }
                            }
                            if found_match_count != 1 {
                                return Err(format!(
                                    "{} is the parent of {} but the child only presents {} times",
                                    parent.index, index, found_match_count
                                ));
                            }
                        } else {
                            return Err(format!(
                                "{}'s parent {} doesn't belong to any tree, link broken",
                                index, parent.index
                            ));
                        }
                        // check if parent is still tracked, i.e. inside self.nodes
                        let module = self.read_recursive();
                        if parent.index >= module.nodes_count() || module.get_node(parent.index).is_none() {
                            return Err(format!("parent's index {} is not in the interface", parent.index));
                        }
                        let tracked_parent_ptr = module.get_node(parent.index).unwrap();
                        if tracked_parent_ptr != parent_ptr {
                            return Err(format!(
                                "the tracked ptr of child {} is not what's being pointed",
                                parent.index
                            ));
                        }
                    } else {
                        if tree_node.root != primal_module_internal_ptr.downgrade() {
                            return Err(format!("{} is not the root of the tree, yet it has no parent", index));
                        }
                    }
                    // then check if the root and the depth is correct
                    let mut current_ptr = primal_module_internal_ptr.clone();
                    let mut current_up = 0;
                    loop {
                        let current = current_ptr.read_recursive();
                        // check if current is still tracked, i.e. inside self.nodes
                        let module = self.read_recursive();
                        if current.index >= module.nodes_count() || module.get_node(current.index).is_none() {
                            return Err(format!("current's index {} is not in the interface", current.index));
                        }
                        let tracked_current_ptr = module.get_node(current.index).unwrap();
                        if tracked_current_ptr != current_ptr {
                            return Err(format!(
                                "the tracked ptr of current {} is not what's being pointed",
                                current.index
                            ));
                        }
                        // go to parent
                        if let Some(current_tree_node) = current.tree_node.as_ref() {
                            if let Some((current_parent_ptr, _)) = current_tree_node.parent.as_ref() {
                                let current_parent_ptr = current_parent_ptr.clone();
                                drop(current);
                                current_ptr = current_parent_ptr.upgrade_force();
                                current_up += 1;
                            } else {
                                // confirm this is root and then break the loop
                                if current_tree_node.root != current_ptr.downgrade() {
                                    return Err(format!(
                                        "current {} is not the root of the tree, yet it has no parent",
                                        current.index
                                    ));
                                }
                                break;
                            }
                        } else {
                            return Err(format!(
                                "climbing up from {} to {} but it doesn't belong to a tree anymore",
                                index, current.index
                            ));
                        }
                    }
                    if current_up != tree_node.depth {
                        return Err(format!(
                            "{} is marked with depth {} but the real depth is {}",
                            index, tree_node.depth, current_up
                        ));
                    }
                    if current_ptr.downgrade() != tree_node.root {
                        return Err(format!(
                            "{} is marked with root {:?} but the real root is {:?}",
                            index, tree_node.root, current_ptr
                        ));
                    }
                }
            }
        }
        Ok(flattened_nodes)
    }

    /// collapse a tree into a single blossom, just like what union-find decoder does. No MWPM guarantee once this is called.
    pub fn collapse_tree<D: DualModuleImpl>(
        &self,
        primal_node_internal_ptr: PrimalNodeInternalPtr,
        interface_ptr: &DualModuleInterfacePtr,
        dual_module: &mut D,
    ) {
        let mut children = vec![];
        primal_node_internal_ptr.flatten_tree(&mut children);
        let nodes_circle: Vec<_> = children
            .iter()
            .map(|ptr| ptr.read_recursive().origin.clone().upgrade_force())
            .collect();
        // since we no longer care the internal structure of the tree, we can just construct arbitrary touching list
        let touching_children: Vec<_> = children
            .iter()
            .map(|ptr| {
                let node = ptr.read_recursive();
                let tree_node = node.tree_node.as_ref().unwrap();
                let touching = if let Some((_, touching)) = tree_node.parent.as_ref() {
                    touching.clone()
                } else {
                    tree_node.children[0].1.clone()
                };
                (touching.clone(), touching) // which touching doesn't matter; union-find decoder doesn't care the internal
            })
            .collect();
        let blossom_node_ptr = interface_ptr.create_blossom(nodes_circle, touching_children, dual_module);
        // create the blossom primal node
        {
            // create the corresponding primal node
            let belonging = self.downgrade();
            let mut module = self.write();
            let local_node_index = module.nodes_length;
            let node_index = module.nodes_count();
            let primal_node_internal_blossom_ptr =
                if !module.is_fusion && local_node_index < module.nodes.len() && module.nodes[local_node_index].is_some() {
                    let node_ptr = module.nodes[local_node_index].take().unwrap();
                    let mut node = node_ptr.write();
                    node.origin = blossom_node_ptr.downgrade();
                    node.index = node_index;
                    node.tree_node = None;
                    node.temporary_match = None;
                    node.belonging = belonging;
                    drop(node);
                    node_ptr
                } else {
                    PrimalNodeInternalPtr::new_value(PrimalNodeInternal {
                        origin: blossom_node_ptr.downgrade(),
                        index: node_index,
                        tree_node: None,
                        temporary_match: None,
                        belonging,
                    })
                };
            module.nodes_length += 1;
            if module.nodes.len() < module.nodes_length {
                module.nodes.push(None);
            }
            module.nodes[local_node_index] = Some(primal_node_internal_blossom_ptr.clone());
        };
        // remove the tree structure
        for ptr in children.iter() {
            let mut node = ptr.write();
            node.tree_node = None;
        }
    }
}

impl PrimalNodeInternalPtr {
    /// DFS flatten the children of a tree
    pub fn flatten_tree(&self, flattened_nodes: &mut Vec<PrimalNodeInternalPtr>) {
        flattened_nodes.push(self.clone());
        let node = self.read_recursive();
        let tree_node = node.tree_node.as_ref().unwrap();
        for (child_weak, _) in tree_node.children.iter() {
            let child_ptr = child_weak.upgrade_force();
            child_ptr.flatten_tree(flattened_nodes);
        }
    }
}

#[cfg(test)]
pub mod tests {
    use super::super::dual_module_serial::*;
    use super::super::example_codes::*;
    use super::super::*;
    use super::*;

    pub fn primal_module_serial_basic_standard_syndrome_optional_viz(
        d: VertexNum,
        visualize_filename: Option<String>,
        defect_vertices: Vec<VertexIndex>,
        final_dual: Weight,
    ) -> (DualModuleInterfacePtr, PrimalModuleSerialPtr, DualModuleSerial) {
        primal_module_serial_basic_standard_syndrome_optional_viz_max_tree_size(
            d,
            visualize_filename,
            defect_vertices,
            final_dual,
            usize::MAX,
        )
    }

    pub fn primal_module_serial_basic_standard_syndrome_optional_viz_max_tree_size(
        d: VertexNum,
        visualize_filename: Option<String>,
        defect_vertices: Vec<VertexIndex>,
        final_dual: Weight,
        max_tree_size: usize,
    ) -> (DualModuleInterfacePtr, PrimalModuleSerialPtr, DualModuleSerial) {
        println!("{defect_vertices:?}");
        let half_weight = 500;
        let mut code = CodeCapacityPlanarCode::new(d, 0.1, half_weight);
        let mut visualizer = match visualize_filename.as_ref() {
            Some(visualize_filename) => {
                let visualizer = Visualizer::new(
                    Some(visualize_data_folder() + visualize_filename.as_str()),
                    code.get_positions(),
                    true,
                )
                .unwrap();
                print_visualize_link(visualize_filename.clone());
                Some(visualizer)
            }
            None => None,
        };
        // create dual module
        let initializer = code.get_initializer();
        let mut dual_module = DualModuleSerial::new_empty(&initializer);
        // create primal module
        let mut primal_module = PrimalModuleSerialPtr::new_empty(&initializer);
        primal_module.write().debug_resolve_only_one = true; // to enable debug mode
                                                             // try to work on a simple syndrome
        primal_module.write().max_tree_size = max_tree_size;
        code.set_defect_vertices(&defect_vertices);
        let interface_ptr = DualModuleInterfacePtr::new_empty();
        primal_module.solve_visualizer(&interface_ptr, &code.get_syndrome(), &mut dual_module, visualizer.as_mut());
        let perfect_matching = primal_module.perfect_matching(&interface_ptr, &mut dual_module);
        let mut subgraph_builder = SubGraphBuilder::new(&initializer);
        subgraph_builder.load_perfect_matching(&perfect_matching);
        let subgraph = subgraph_builder.get_subgraph();
        if let Some(visualizer) = visualizer.as_mut() {
            visualizer
                .snapshot_combined(
                    "perfect matching and subgraph".to_string(),
                    vec![
                        &interface_ptr,
                        &dual_module,
                        &perfect_matching,
                        &VisualizeSubgraph::new(&subgraph),
                    ],
                )
                .unwrap();
        }
        assert_eq!(
            interface_ptr.sum_dual_variables(),
            subgraph_builder.total_weight(),
            "unmatched sum dual variables"
        );
        assert_eq!(
            interface_ptr.sum_dual_variables(),
            final_dual * 2 * half_weight,
            "unexpected final dual variable sum"
        );
        (interface_ptr, primal_module, dual_module)
    }

    pub fn primal_module_serial_basic_standard_syndrome(
        d: VertexNum,
        visualize_filename: String,
        defect_vertices: Vec<VertexIndex>,
        final_dual: Weight,
    ) -> (DualModuleInterfacePtr, PrimalModuleSerialPtr, DualModuleSerial) {
        primal_module_serial_basic_standard_syndrome_optional_viz(d, Some(visualize_filename), defect_vertices, final_dual)
    }

    /// test a simple blossom
    #[test]
    fn primal_module_serial_basic_1() {
        // cargo test primal_module_serial_basic_1 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_1.json".to_string();
        let defect_vertices = vec![18, 26, 34];
        primal_module_serial_basic_standard_syndrome(7, visualize_filename, defect_vertices, 4);
    }

    /// test a free node conflict with a virtual boundary
    #[test]
    fn primal_module_serial_basic_2() {
        // cargo test primal_module_serial_basic_2 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_2.json".to_string();
        let defect_vertices = vec![16];
        primal_module_serial_basic_standard_syndrome(7, visualize_filename, defect_vertices, 1);
    }

    /// test a free node conflict with a matched node (with virtual boundary)
    #[test]
    fn primal_module_serial_basic_3() {
        // cargo test primal_module_serial_basic_3 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_3.json".to_string();
        let defect_vertices = vec![16, 26];
        primal_module_serial_basic_standard_syndrome(7, visualize_filename, defect_vertices, 3);
    }

    /// test blossom shrinking and expanding
    #[test]
    fn primal_module_serial_basic_4() {
        // cargo test primal_module_serial_basic_4 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_4.json".to_string();
        let defect_vertices = vec![16, 52, 65, 76, 112];
        primal_module_serial_basic_standard_syndrome(11, visualize_filename, defect_vertices, 10);
    }

    /// test blossom conflicts with vertex
    #[test]
    fn primal_module_serial_basic_5() {
        // cargo test primal_module_serial_basic_5 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_5.json".to_string();
        let defect_vertices = vec![39, 51, 61, 62, 63, 64, 65, 75, 87, 67];
        primal_module_serial_basic_standard_syndrome(11, visualize_filename, defect_vertices, 6);
    }

    /// test cascaded blossom
    #[test]
    fn primal_module_serial_basic_6() {
        // cargo test primal_module_serial_basic_6 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_6.json".to_string();
        let defect_vertices = vec![39, 51, 61, 62, 63, 64, 65, 75, 87];
        primal_module_serial_basic_standard_syndrome(11, visualize_filename, defect_vertices, 6);
    }

    /// test two alternating trees conflict with each other
    #[test]
    fn primal_module_serial_basic_7() {
        // cargo test primal_module_serial_basic_7 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_7.json".to_string();
        let defect_vertices = vec![37, 61, 63, 66, 68, 44];
        primal_module_serial_basic_standard_syndrome(11, visualize_filename, defect_vertices, 7);
    }

    /// test an alternating tree touches a virtual boundary
    #[test]
    fn primal_module_serial_basic_8() {
        // cargo test primal_module_serial_basic_8 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_8.json".to_string();
        let defect_vertices = vec![61, 64, 67];
        primal_module_serial_basic_standard_syndrome(11, visualize_filename, defect_vertices, 5);
    }

    /// test a matched node (with virtual boundary) conflicts with an alternating tree
    #[test]
    fn primal_module_serial_basic_9() {
        // cargo test primal_module_serial_basic_9 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_9.json".to_string();
        let defect_vertices = vec![60, 63, 66, 30];
        primal_module_serial_basic_standard_syndrome(11, visualize_filename, defect_vertices, 6);
    }

    /// test the error pattern in the paper
    #[test]
    fn primal_module_serial_basic_10() {
        // cargo test primal_module_serial_basic_10 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_10.json".to_string();
        let defect_vertices = vec![39, 52, 63, 90, 100];
        primal_module_serial_basic_standard_syndrome(11, visualize_filename, defect_vertices, 9);
    }

    /// test the union-find decoder
    #[test]
    fn primal_module_union_find_basic_10() {
        // cargo test primal_module_union_find_basic_10 -- --nocapture
        let visualize_filename = "primal_module_union_find_basic_10.json".to_string();
        let defect_vertices = vec![39, 52, 63, 90, 100];
        let func = primal_module_serial_basic_standard_syndrome_optional_viz_max_tree_size;
        func(11, Some(visualize_filename), defect_vertices, 9, 0);
        // func(11, Some(visualize_filename), defect_vertices, 9, 3);
    }

    /// test the error pattern in the paper
    #[test]
    fn primal_module_serial_default_example() {
        // cargo test primal_module_serial_default_example -- --nocapture
        let visualize_filename = static_visualize_data_filename();
        let defect_vertices = vec![39, 52, 63, 90, 100];
        primal_module_serial_basic_standard_syndrome(11, visualize_filename, defect_vertices, 9);
    }

    /// debug a case of deadlock after changing the strategy of detecting conflicts around VertexShrinkStop;
    /// reason: forget to check whether conflicting nodes are growing: only growing one should be reported
    #[test]
    fn primal_module_serial_basic_11() {
        // cargo test primal_module_serial_basic_11 -- --nocapture
        let visualize_filename = "primal_module_serial_basic_11.json".to_string();
        let defect_vertices = vec![
            13, 29, 52, 53, 58, 60, 71, 74, 76, 87, 96, 107, 112, 118, 121, 122, 134, 137, 141, 145, 152, 153, 154, 156,
            157, 169, 186, 202, 203, 204, 230, 231,
        ];
        primal_module_serial_basic_standard_syndrome(15, visualize_filename, defect_vertices, 20);
    }

    /// debug a case where it disagree with blossom V library, mine reports 11866, blossom V reports 12284
    #[test]
    fn primal_module_debug_1() {
        // cargo test primal_module_debug_1 -- --nocapture
        let visualize_filename = "primal_module_debug_1.json".to_string();
        let defect_vertices = vec![
            34, 35, 84, 89, 92, 100, 141, 145, 149, 164, 193, 201, 205, 220, 235, 242, 243, 260, 261, 290, 300, 308, 309,
            315, 317,
        ];
        let max_half_weight = 500;
        let mut code = CircuitLevelPlanarCode::new(7, 7, 0.01, max_half_weight);
        let mut visualizer = Visualizer::new(
            Some(visualize_data_folder() + visualize_filename.as_str()),
            code.get_positions(),
            true,
        )
        .unwrap();
        print_visualize_link(visualize_filename.clone());
        let initializer = code.get_initializer();
        // blossom V ground truth
        let blossom_mwpm_result = blossom_v_mwpm(&initializer, &defect_vertices);
        println!("blossom_mwpm_result: {blossom_mwpm_result:?}");
        let blossom_details = detailed_matching(&initializer, &defect_vertices, &blossom_mwpm_result);
        let mut blossom_total_weight = 0;
        for detail in blossom_details.iter() {
            println!("    {detail:?}");
            blossom_total_weight += detail.weight;
        }
        // create dual module
        let mut dual_module = DualModuleSerial::new_empty(&initializer);
        // create primal module
        let mut primal_module = PrimalModuleSerialPtr::new_empty(&initializer);
        primal_module.write().debug_resolve_only_one = true; // to enable debug mode
                                                             // try to work on a simple syndrome
        code.set_defect_vertices(&defect_vertices);
        let interface_ptr = DualModuleInterfacePtr::new_empty();
        primal_module.solve_visualizer(&interface_ptr, &code.get_syndrome(), &mut dual_module, Some(&mut visualizer));
        let fusion_mwpm = primal_module.perfect_matching(&interface_ptr, &mut dual_module);
        let fusion_mwpm_result = fusion_mwpm.legacy_get_mwpm_result(defect_vertices.clone());
        let fusion_details = detailed_matching(&initializer, &defect_vertices, &fusion_mwpm_result);
        let mut fusion_total_weight = 0;
        for detail in fusion_details.iter() {
            println!("    {detail:?}");
            fusion_total_weight += detail.weight;
        }
        assert_eq!(
            fusion_total_weight, blossom_total_weight,
            "unexpected final dual variable sum"
        );
        {
            // also test subgraph builder
            let mut subgraph_builder = SubGraphBuilder::new(&initializer);
            subgraph_builder.load_perfect_matching(&fusion_mwpm);
            assert_eq!(
                subgraph_builder.total_weight(),
                blossom_total_weight,
                "unexpected final dual variable sum"
            );
        }
        assert_eq!(
            interface_ptr.sum_dual_variables(),
            blossom_total_weight,
            "unexpected final dual variable sum"
        );
    }

    /// debug a case where it disagree with blossom V library, mine reports 33000, blossom V reports 34000
    #[test]
    fn primal_module_debug_2() {
        // cargo test primal_module_debug_2 -- --nocapture
        let visualize_filename = "primal_module_debug_2.json".to_string();
        let defect_vertices = vec![
            7, 8, 10, 22, 23, 24, 25, 37, 38, 39, 40, 42, 43, 69, 57, 59, 60, 72, 76, 93, 109, 121, 123, 125, 135, 136, 137,
            138, 139, 140, 141, 150, 151, 153, 154, 155, 166, 171, 172, 181, 183, 184, 188, 200, 204, 219, 233,
        ];
        let max_half_weight = 500;
        let mut code = CodeCapacityPlanarCode::new(15, 0.3, max_half_weight);
        let mut visualizer = Visualizer::new(
            Some(visualize_data_folder() + visualize_filename.as_str()),
            code.get_positions(),
            true,
        )
        .unwrap();
        print_visualize_link(visualize_filename.clone());
        let initializer = code.get_initializer();
        // blossom V ground truth
        let blossom_mwpm_result = blossom_v_mwpm(&initializer, &defect_vertices);
        let blossom_details = detailed_matching(&initializer, &defect_vertices, &blossom_mwpm_result);
        let mut blossom_total_weight = 0;
        for detail in blossom_details.iter() {
            println!("    {detail:?}");
            blossom_total_weight += detail.weight;
        }
        // create dual module
        let mut dual_module = DualModuleSerial::new_empty(&initializer);
        // create primal module
        let mut primal_module = PrimalModuleSerialPtr::new_empty(&initializer);
        primal_module.write().debug_resolve_only_one = true; // to enable debug mode
                                                             // try to work on a simple syndrome
        code.set_defect_vertices(&defect_vertices);
        let interface_ptr = DualModuleInterfacePtr::new_empty();
        primal_module.solve_visualizer(&interface_ptr, &code.get_syndrome(), &mut dual_module, Some(&mut visualizer));
        let fusion_mwpm = primal_module.perfect_matching(&interface_ptr, &mut dual_module);
        let fusion_mwpm_result = fusion_mwpm.legacy_get_mwpm_result(defect_vertices.clone());
        let fusion_details = detailed_matching(&initializer, &defect_vertices, &fusion_mwpm_result);
        let mut fusion_total_weight = 0;
        for detail in fusion_details.iter() {
            println!("    {detail:?}");
            fusion_total_weight += detail.weight;
        }
        assert_eq!(
            fusion_total_weight, blossom_total_weight,
            "unexpected final dual variable sum"
        );
        {
            // also test subgraph builder
            let mut subgraph_builder = SubGraphBuilder::new(&initializer);
            subgraph_builder.load_perfect_matching(&fusion_mwpm);
            assert_eq!(
                subgraph_builder.total_weight(),
                blossom_total_weight,
                "unexpected final dual variable sum"
            );
        }
        assert_eq!(
            interface_ptr.sum_dual_variables(),
            blossom_total_weight,
            "unexpected final dual variable sum"
        );
    }

    /// debug a case where it disagree with blossom V library, mine reports 16000, blossom V reports 17000
    #[test]
    fn primal_module_debug_3() {
        // cargo test primal_module_debug_3 -- --nocapture
        let visualize_filename = "primal_module_debug_3.json".to_string();
        let defect_vertices = vec![
            17, 34, 36, 54, 55, 74, 95, 96, 112, 113, 114, 115, 116, 130, 131, 132, 134, 150, 151, 154, 156, 171, 172, 173,
            190,
        ];
        let max_half_weight = 500;
        let mut code = CodeCapacityPlanarCode::new(19, 0.499, max_half_weight);
        let mut visualizer = Visualizer::new(
            Some(visualize_data_folder() + visualize_filename.as_str()),
            code.get_positions(),
            true,
        )
        .unwrap();
        print_visualize_link(visualize_filename.clone());
        let initializer = code.get_initializer();
        // blossom V ground truth
        let blossom_mwpm_result = blossom_v_mwpm(&initializer, &defect_vertices);
        let blossom_details = detailed_matching(&initializer, &defect_vertices, &blossom_mwpm_result);
        let mut blossom_total_weight = 0;
        for detail in blossom_details.iter() {
            println!("    {detail:?}");
            blossom_total_weight += detail.weight;
        }
        // create dual module
        let mut dual_module = DualModuleSerial::new_empty(&initializer);
        // create primal module
        let mut primal_module = PrimalModuleSerialPtr::new_empty(&initializer);
        primal_module.write().debug_resolve_only_one = true; // to enable debug mode
                                                             // try to work on a simple syndrome
        code.set_defect_vertices(&defect_vertices);
        let interface_ptr = DualModuleInterfacePtr::new_empty();
        primal_module.solve_visualizer(&interface_ptr, &code.get_syndrome(), &mut dual_module, Some(&mut visualizer));
        let fusion_mwpm = primal_module.perfect_matching(&interface_ptr, &mut dual_module);
        let fusion_mwpm_result = fusion_mwpm.legacy_get_mwpm_result(defect_vertices.clone());
        let fusion_details = detailed_matching(&initializer, &defect_vertices, &fusion_mwpm_result);
        let mut fusion_total_weight = 0;
        for detail in fusion_details.iter() {
            println!("    {detail:?}");
            fusion_total_weight += detail.weight;
        }
        assert_eq!(
            fusion_total_weight, blossom_total_weight,
            "unexpected final dual variable sum"
        );
        {
            // also test subgraph builder
            let mut subgraph_builder = SubGraphBuilder::new(&initializer);
            subgraph_builder.load_perfect_matching(&fusion_mwpm);
            assert_eq!(
                subgraph_builder.total_weight(),
                blossom_total_weight,
                "unexpected final dual variable sum"
            );
        }
        assert_eq!(
            interface_ptr.sum_dual_variables(),
            blossom_total_weight,
            "unexpected final dual variable sum"
        );
    }

    /// debug a case where it disagree with blossom V library, mine reports 9000, blossom V reports 7000
    #[test]
    fn primal_module_debug_4() {
        // cargo test primal_module_debug_4 -- --nocapture
        let visualize_filename = "primal_module_debug_4.json".to_string();
        let defect_vertices = vec![1, 3, 6, 8, 9, 11, 13];
        let max_half_weight = 500;
        let mut code = CodeCapacityRepetitionCode::new(15, 0.499, max_half_weight);
        let mut visualizer = Visualizer::new(
            Some(visualize_data_folder() + visualize_filename.as_str()),
            code.get_positions(),
            true,
        )
        .unwrap();
        print_visualize_link(visualize_filename.clone());
        let initializer = code.get_initializer();
        // blossom V ground truth
        let blossom_mwpm_result = blossom_v_mwpm(&initializer, &defect_vertices);
        let blossom_details = detailed_matching(&initializer, &defect_vertices, &blossom_mwpm_result);
        let mut blossom_total_weight = 0;
        for detail in blossom_details.iter() {
            println!("    {detail:?}");
            blossom_total_weight += detail.weight;
        }
        // create dual module
        let mut dual_module = DualModuleSerial::new_empty(&initializer);
        // create primal module
        let mut primal_module = PrimalModuleSerialPtr::new_empty(&initializer);
        primal_module.write().debug_resolve_only_one = true; // to enable debug mode
                                                             // try to work on a simple syndrome
        code.set_defect_vertices(&defect_vertices);
        let interface_ptr = DualModuleInterfacePtr::new_empty();
        primal_module.solve_visualizer(&interface_ptr, &code.get_syndrome(), &mut dual_module, Some(&mut visualizer));
        let fusion_mwpm = primal_module.perfect_matching(&interface_ptr, &mut dual_module);
        let fusion_mwpm_result = fusion_mwpm.legacy_get_mwpm_result(defect_vertices.clone());
        let fusion_details = detailed_matching(&initializer, &defect_vertices, &fusion_mwpm_result);
        let mut fusion_total_weight = 0;
        for detail in fusion_details.iter() {
            println!("    {detail:?}");
            fusion_total_weight += detail.weight;
        }
        assert_eq!(
            fusion_total_weight, blossom_total_weight,
            "unexpected final dual variable sum"
        );
        {
            // also test subgraph builder
            let mut subgraph_builder = SubGraphBuilder::new(&initializer);
            subgraph_builder.load_perfect_matching(&fusion_mwpm);
            assert_eq!(
                subgraph_builder.total_weight(),
                blossom_total_weight,
                "unexpected final dual variable sum"
            );
        }
        assert_eq!(
            interface_ptr.sum_dual_variables(),
            blossom_total_weight,
            "unexpected final dual variable sum"
        );
    }

    /// debug a case of being stuck after disable the flag `debug_resolve_only_one` for faster speed
    #[test]
    fn primal_module_debug_5() {
        // cargo test primal_module_debug_5 -- --nocapture
        let visualize_filename = "primal_module_debug_5.json".to_string();
        let defect_vertices = vec![0, 1, 3, 8, 9];
        let max_half_weight = 500;
        let mut code = CodeCapacityRepetitionCode::new(11, 0.03, max_half_weight);
        let mut visualizer = Visualizer::new(
            Some(visualize_data_folder() + visualize_filename.as_str()),
            code.get_positions(),
            true,
        )
        .unwrap();
        print_visualize_link(visualize_filename.clone());
        let initializer = code.get_initializer();
        // blossom V ground truth
        let blossom_mwpm_result = blossom_v_mwpm(&initializer, &defect_vertices);
        let blossom_details = detailed_matching(&initializer, &defect_vertices, &blossom_mwpm_result);
        let mut blossom_total_weight = 0;
        for detail in blossom_details.iter() {
            println!("    {detail:?}");
            blossom_total_weight += detail.weight;
        }
        // create dual module
        let mut dual_module = DualModuleSerial::new_empty(&initializer);
        // create primal module
        let mut primal_module = PrimalModuleSerialPtr::new_empty(&initializer);
        // try to work on a simple syndrome
        code.set_defect_vertices(&defect_vertices);
        let interface_ptr = DualModuleInterfacePtr::new_empty();
        primal_module.solve_visualizer(&interface_ptr, &code.get_syndrome(), &mut dual_module, Some(&mut visualizer));
        let fusion_mwpm = primal_module.perfect_matching(&interface_ptr, &mut dual_module);
        let fusion_mwpm_result = fusion_mwpm.legacy_get_mwpm_result(defect_vertices.clone());
        let fusion_details = detailed_matching(&initializer, &defect_vertices, &fusion_mwpm_result);
        let mut fusion_total_weight = 0;
        for detail in fusion_details.iter() {
            println!("    {detail:?}");
            fusion_total_weight += detail.weight;
        }
        assert_eq!(
            fusion_total_weight, blossom_total_weight,
            "unexpected final dual variable sum"
        );
        {
            // also test subgraph builder
            let mut subgraph_builder = SubGraphBuilder::new(&initializer);
            subgraph_builder.load_perfect_matching(&fusion_mwpm);
            assert_eq!(
                subgraph_builder.total_weight(),
                blossom_total_weight,
                "unexpected final dual variable sum"
            );
        }
        assert_eq!(
            interface_ptr.sum_dual_variables(),
            blossom_total_weight,
            "unexpected final dual variable sum"
        );
    }

    #[test]
    fn primal_module_serial_perfect_matching_1() {
        // cargo test primal_module_serial_perfect_matching_1 -- --nocapture
        let defect_vertices = vec![39, 51, 61, 62, 63, 64, 65, 75, 87, 67];
        let (interface_ptr, mut primal_module, mut dual_module) =
            primal_module_serial_basic_standard_syndrome_optional_viz(11, None, defect_vertices, 6);
        let intermediate_matching = primal_module.intermediate_matching(&interface_ptr, &mut dual_module);
        println!("intermediate_matching: {intermediate_matching:?}");
        let perfect_matching = primal_module.perfect_matching(&interface_ptr, &mut dual_module);
        println!("perfect_matching: {perfect_matching:?}");
    }

    /// debug a case of non-zero weight given pure erasure
    #[test]
    fn primal_module_debug_6() {
        // cargo test primal_module_debug_6 -- --nocapture
        let visualize_filename = "primal_module_debug_6.json".to_string();
        let defect_vertices = vec![13, 34, 87, 107, 276, 296];
        let erasures = [13, 33, 174, 516];
        let max_half_weight = 500;
        let mut code = CodeCapacityPlanarCode::new(19, 0., max_half_weight);
        code.set_erasure_probability(0.003);
        let mut visualizer = Visualizer::new(
            Some(visualize_data_folder() + visualize_filename.as_str()),
            code.get_positions(),
            true,
        )
        .unwrap();
        print_visualize_link(visualize_filename.clone());
        let mut initializer = code.get_initializer();
        for edge_index in erasures.iter() {
            let (vertex_idx_1, vertex_idx_2, _) = &initializer.weighted_edges[*edge_index];
            initializer.weighted_edges[*edge_index] = (*vertex_idx_1, *vertex_idx_2, 0);
        }
        // blossom V ground truth
        let blossom_mwpm_result = blossom_v_mwpm(&initializer, &defect_vertices);
        let blossom_details = detailed_matching(&initializer, &defect_vertices, &blossom_mwpm_result);
        let mut blossom_total_weight = 0;
        for detail in blossom_details.iter() {
            println!("    {detail:?}");
            blossom_total_weight += detail.weight;
        }
        // create dual module
        let mut dual_module = DualModuleSerial::new_empty(&initializer);
        // create primal module
        let mut primal_module = PrimalModuleSerialPtr::new_empty(&initializer);
        // try to work on a simple syndrome
        code.set_defect_vertices(&defect_vertices);
        let interface_ptr = DualModuleInterfacePtr::new_empty();
        primal_module.solve_visualizer(&interface_ptr, &code.get_syndrome(), &mut dual_module, Some(&mut visualizer));
        let fusion_mwpm = primal_module.perfect_matching(&interface_ptr, &mut dual_module);
        let fusion_mwpm_result = fusion_mwpm.legacy_get_mwpm_result(defect_vertices.clone());
        let fusion_details = detailed_matching(&initializer, &defect_vertices, &fusion_mwpm_result);
        let mut fusion_total_weight = 0;
        for detail in fusion_details.iter() {
            println!("    {detail:?}");
            fusion_total_weight += detail.weight;
        }
        assert_eq!(
            fusion_total_weight, blossom_total_weight,
            "unexpected final dual variable sum"
        );
        {
            // also test subgraph builder
            let mut subgraph_builder = SubGraphBuilder::new(&initializer);
            subgraph_builder.load_perfect_matching(&fusion_mwpm);
            assert_eq!(
                subgraph_builder.total_weight(),
                blossom_total_weight,
                "unexpected final dual variable sum"
            );
        }
        assert_eq!(
            interface_ptr.sum_dual_variables(),
            blossom_total_weight,
            "unexpected final dual variable sum"
        );
    }

    /// debug panic after adding the feature of max_tree_size
    #[test]
    fn primal_module_debug_7() {
        // cargo test primal_module_debug_7 -- --nocapture
        let visualize_filename = "primal_module_debug_7.json".to_string();
        let defect_vertices = vec![10, 11, 19, 21, 29, 34, 37, 40, 43, 49, 50, 51, 53];
        let max_half_weight = 500;
        let mut code = CodeCapacityPlanarCode::new(7, 0.1, max_half_weight);
        let mut visualizer = Visualizer::new(
            Some(visualize_data_folder() + visualize_filename.as_str()),
            code.get_positions(),
            true,
        )
        .unwrap();
        print_visualize_link(visualize_filename.clone());
        let initializer = code.get_initializer();
        let mut dual_module = DualModuleSerial::new_empty(&initializer);
        let mut primal_module = PrimalModuleSerialPtr::new_empty(&initializer);
        code.set_defect_vertices(&defect_vertices);
        let interface_ptr = DualModuleInterfacePtr::new_empty();
        primal_module.solve_visualizer(&interface_ptr, &code.get_syndrome(), &mut dual_module, Some(&mut visualizer));
    }
}