chematic-perception 0.1.0

//! Smallest Set of Smallest Rings (SSSR) via the Balducci-Pearlman algorithm.
//!
//! Algorithm overview:
//! 1. Compute the cycle rank r = E - V + C (Euler characteristic),
//!    where C is the number of connected components.
//! 2. Build a BFS spanning forest over all connected components.
//! 3. Each non-tree (back) edge gives one fundamental cycle:
//!    the unique path between its endpoints in the spanning tree, plus the edge itself.
//! 4. Represent each cycle as a set of bond indices (for GF(2) XOR independence testing).
//! 5. Use Gaussian elimination over GF(2) to greedily build an independent basis of r cycles,
//!    preferring shorter cycles.
//! 6. Convert the chosen bond-sets back to ordered atom sequences for the public API.

use std::collections::{HashMap, VecDeque};

use chematic_core::{AtomIdx, BondIdx, Molecule};

// ---------------------------------------------------------------------------
// Public types
// ---------------------------------------------------------------------------

/// The Smallest Set of Smallest Rings for a molecule.
///
/// Each ring is stored as a sequence of `AtomIdx` values listed in ring order.
/// The first atom is not repeated at the end.
#[derive(Debug, Clone)]
pub struct RingSet(Vec<Vec<AtomIdx>>);

impl RingSet {
    /// All rings as slices of atom indices.
    pub fn rings(&self) -> &[Vec<AtomIdx>] {
        &self.0
    }

    /// Number of rings in the SSSR.
    pub fn ring_count(&self) -> usize {
        self.0.len()
    }

    /// Whether atom `atom` is a member of at least one ring.
    pub fn contains_atom(&self, atom: AtomIdx) -> bool {
        self.0.iter().any(|ring| ring.contains(&atom))
    }

    /// Number of rings that atom `atom` belongs to.
    pub fn atoms_in_ring_count(&self, atom: AtomIdx) -> usize {
        self.0.iter().filter(|ring| ring.contains(&atom)).count()
    }
}

// ---------------------------------------------------------------------------
// Main entry point
// ---------------------------------------------------------------------------

/// Compute the Smallest Set of Smallest Rings for `mol`.
///
/// Returns a [`RingSet`] whose ring count equals the cycle rank r = E - V + C.
/// For acyclic molecules (r = 0) the returned set is empty.
pub fn find_sssr(mol: &Molecule) -> RingSet {
    let v = mol.atom_count();
    let e = mol.bond_count();

    if v == 0 || e == 0 {
        return RingSet(Vec::new());
    }

    // Count connected components and build the BFS spanning forest.
    let (components, parent, bfs_depth) = bfs_spanning_forest(mol);
    let c = components;
    let r = (e as isize) - (v as isize) + (c as isize);

    if r <= 0 {
        return RingSet(Vec::new());
    }
    let r = r as usize;

    // Collect all fundamental cycles from back edges as bond-index sets.
    let mut candidate_cycles: Vec<(Vec<BondIdx>, Vec<AtomIdx>)> = Vec::new();

    for (bidx, bond) in mol.bonds() {
        let u = bond.atom1;
        let v_atom = bond.atom2;

        // A bond is a back edge if neither endpoint is the parent of the other
        // in the spanning forest.
        let u_parent = parent[u.0 as usize];
        let v_parent = parent[v_atom.0 as usize];

        let is_tree_edge = (u_parent == Some(v_atom)) || (v_parent == Some(u));

        if !is_tree_edge {
            // This is a back edge — reconstruct the fundamental cycle.
            if let Some((bond_set, atom_seq)) = fundamental_cycle(mol, u, v_atom, bidx, &parent, &bfs_depth) {
                candidate_cycles.push((bond_set, atom_seq));
            }
        }
    }

    // Sort by cycle length (shorter first) for greedy shortest-cycle preference.
    candidate_cycles.sort_by_key(|(bonds, _)| bonds.len());

    // Gaussian elimination over GF(2) to select r linearly independent cycles.
    // The basis maps a pivot BondIdx to the full bond-set of that basis row.
    let mut basis: HashMap<BondIdx, Vec<BondIdx>> = HashMap::new();
    let mut selected_atoms: Vec<Vec<AtomIdx>> = Vec::new();

    for (bond_set, atom_seq) in candidate_cycles {
        // Reduce this cycle against the current basis.
        let reduced = gf2_reduce(&bond_set, &basis);

        if !reduced.is_empty() {
            // This cycle is independent — add it to the basis.
            let pivot = *reduced.iter().min().unwrap();
            basis.insert(pivot, reduced);
            selected_atoms.push(atom_seq);

            if selected_atoms.len() == r {
                break;
            }
        }
    }

    // Sort output rings by length for output consistency.
    selected_atoms.sort_by_key(|ring| ring.len());
    RingSet(selected_atoms)
}

// ---------------------------------------------------------------------------
// BFS spanning forest
// ---------------------------------------------------------------------------

/// Build a BFS spanning forest over the entire molecule.
///
/// Returns:
/// - `components`: number of connected components.
/// - `parent`: for each atom, the atom from which it was first discovered
///   (None for BFS roots).
/// - `depth`: BFS depth of each atom from the root of its component.
fn bfs_spanning_forest(mol: &Molecule) -> (usize, Vec<Option<AtomIdx>>, Vec<u32>) {
    let n = mol.atom_count();
    let mut visited = vec![false; n];
    let mut parent: Vec<Option<AtomIdx>> = vec![None; n];
    let mut depth = vec![0u32; n];
    let mut components = 0;
    let mut queue: VecDeque<AtomIdx> = VecDeque::new();

    for start in 0..n {
        if visited[start] {
            continue;
        }
        components += 1;
        let start_idx = AtomIdx(start as u32);
        visited[start] = true;
        queue.push_back(start_idx);

        while let Some(current) = queue.pop_front() {
            for (neighbor, _bidx) in mol.neighbors(current) {
                let ni = neighbor.0 as usize;
                if !visited[ni] {
                    visited[ni] = true;
                    parent[ni] = Some(current);
                    depth[ni] = depth[current.0 as usize] + 1;
                    queue.push_back(neighbor);
                }
            }
        }
    }

    (components, parent, depth)
}

// ---------------------------------------------------------------------------
// Fundamental cycle reconstruction
// ---------------------------------------------------------------------------

/// Reconstruct the fundamental cycle introduced by the back edge (u, v, bond bidx).
///
/// Returns a pair of:
/// - Sorted `Vec<BondIdx>` representing the cycle as a set of bonds (for GF(2) operations).
/// - Ordered `Vec<AtomIdx>` representing the ring path (for the public API).
fn fundamental_cycle(
    mol: &Molecule,
    u: AtomIdx,
    v: AtomIdx,
    bidx: BondIdx,
    parent: &[Option<AtomIdx>],
    depth: &[u32],
) -> Option<(Vec<BondIdx>, Vec<AtomIdx>)> {
    // Walk both endpoints up to the LCA (lowest common ancestor) in the spanning tree.
    // path_u: atoms from u up to (and including) LCA
    // path_v: atoms from v up to (and including) LCA
    let (path_u, path_v) = paths_to_lca(u, v, parent, depth);

    if path_u.is_empty() || path_v.is_empty() {
        return None;
    }

    // Build the ordered atom ring: path_u (from u to LCA) ++ reverse(path_v[0..end-1])
    // i.e. u ... LCA ... v and then the back edge closes to u
    let mut ring_atoms: Vec<AtomIdx> = path_u.clone();
    // Add path_v in reverse order (excluding the LCA which is already in ring_atoms)
    for &a in path_v.iter().rev().skip(1) {
        ring_atoms.push(a);
    }

    // Collect the bond indices that form this ring.
    let mut bond_set: Vec<BondIdx> = Vec::new();

    // Bonds along path_u (tree edges)
    for i in 0..path_u.len().saturating_sub(1) {
        if let Some((b, _)) = mol.bond_between(path_u[i], path_u[i + 1]) {
            bond_set.push(b);
        } else {
            return None;
        }
    }
    // Bonds along path_v (tree edges, reversed — same bonds)
    for i in 0..path_v.len().saturating_sub(1) {
        if let Some((b, _)) = mol.bond_between(path_v[i], path_v[i + 1]) {
            bond_set.push(b);
        } else {
            return None;
        }
    }
    // The back edge itself
    bond_set.push(bidx);

    // Sort and deduplicate (each tree edge can appear in both path_u and path_v
    // only if they share the same edge — that cannot happen since paths diverge at LCA).
    bond_set.sort();
    bond_set.dedup();

    Some((bond_set, ring_atoms))
}

/// Compute the paths from `u` and `v` to their lowest common ancestor (LCA)
/// in the spanning tree defined by `parent`.
///
/// Returns `(path_u, path_v)` where each path includes the endpoint and the LCA.
fn paths_to_lca(
    u: AtomIdx,
    v: AtomIdx,
    parent: &[Option<AtomIdx>],
    depth: &[u32],
) -> (Vec<AtomIdx>, Vec<AtomIdx>) {
    // Collect ancestors of u and v by walking up the parent pointers.
    let ancestors_u = ancestors(u, parent);
    let ancestors_v = ancestors(v, parent);

    let set_u: HashMap<AtomIdx, usize> = ancestors_u
        .iter()
        .enumerate()
        .map(|(i, &a)| (a, i))
        .collect();

    // Find LCA: first ancestor of v (in order from v to root) that is also in set_u.
    let mut lca = None;
    let mut idx_in_v = 0;
    for (i, &a) in ancestors_v.iter().enumerate() {
        if set_u.contains_key(&a) {
            lca = Some(a);
            idx_in_v = i;
            break;
        }
    }

    let lca = match lca {
        Some(a) => a,
        None => {
            // u and v are in different components — not a valid back edge
            // (should not happen if called correctly).
            return (Vec::new(), Vec::new());
        }
    };

    let idx_in_u = *set_u.get(&lca).unwrap();

    let path_u = ancestors_u[..=idx_in_u].to_vec();
    let path_v = ancestors_v[..=idx_in_v].to_vec();

    // Suppress the depth parameter warning — we keep it for potential future use.
    let _ = depth;

    (path_u, path_v)
}

/// Walk parent pointers from `start` to the root, returning the full ancestor chain
/// including `start` itself.
fn ancestors(start: AtomIdx, parent: &[Option<AtomIdx>]) -> Vec<AtomIdx> {
    let mut chain = Vec::new();
    let mut current = start;
    loop {
        chain.push(current);
        match parent[current.0 as usize] {
            Some(p) => current = p,
            None => break,
        }
    }
    chain
}

// ---------------------------------------------------------------------------
// GF(2) Gaussian elimination
// ---------------------------------------------------------------------------

/// Reduce `cycle` over GF(2) against the current `basis`.
///
/// Each basis entry maps a pivot bond (the minimum BondIdx in that row)
/// to the full row (sorted Vec<BondIdx>).
///
/// Returns the reduced cycle (empty if dependent on existing basis).
fn gf2_reduce(cycle: &[BondIdx], basis: &HashMap<BondIdx, Vec<BondIdx>>) -> Vec<BondIdx> {
    let mut current: Vec<BondIdx> = cycle.to_vec();

    loop {
        if current.is_empty() {
            return current;
        }
        let pivot = *current.iter().min().unwrap();
        match basis.get(&pivot) {
            None => return current, // independent
            Some(basis_row) => {
                // XOR: symmetric difference of the two sorted sets.
                current = sym_diff(&current, basis_row);
            }
        }
    }
}

/// Symmetric difference of two sorted slices (GF(2) addition / XOR for sets).
fn sym_diff(a: &[BondIdx], b: &[BondIdx]) -> Vec<BondIdx> {
    let mut result = Vec::new();
    let mut i = 0;
    let mut j = 0;
    while i < a.len() && j < b.len() {
        match a[i].cmp(&b[j]) {
            std::cmp::Ordering::Less => {
                result.push(a[i]);
                i += 1;
            }
            std::cmp::Ordering::Greater => {
                result.push(b[j]);
                j += 1;
            }
            std::cmp::Ordering::Equal => {
                // Both contain this element — XOR removes it.
                i += 1;
                j += 1;
            }
        }
    }
    result.extend_from_slice(&a[i..]);
    result.extend_from_slice(&b[j..]);
    result
}

// ---------------------------------------------------------------------------
// Tests
// ---------------------------------------------------------------------------

#[cfg(test)]
mod tests {
    use super::*;
    use chematic_core::{Atom, BondOrder, Element, MoleculeBuilder};

    // Build a cyclohexane molecule (6 carbons, 6 single bonds).
    fn cyclohexane() -> chematic_core::Molecule {
        let mut b = MoleculeBuilder::new();
        let atoms: Vec<_> = (0..6).map(|_| b.add_atom(Atom::new(Element::C))).collect();
        for i in 0..6 {
            b.add_bond(atoms[i], atoms[(i + 1) % 6], BondOrder::Single).unwrap();
        }
        b.build()
    }

    // Build a benzene molecule (6 aromatic carbons, 6 single bonds for topology).
    fn benzene() -> chematic_core::Molecule {
        let mut b = MoleculeBuilder::new();
        let atoms: Vec<_> = (0..6).map(|_| b.add_atom(Atom::new(Element::C))).collect();
        for i in 0..6 {
            b.add_bond(atoms[i], atoms[(i + 1) % 6], BondOrder::Single).unwrap();
        }
        b.build()
    }

    // Build naphthalene: 10 atoms, 11 bonds (two fused 6-membered rings).
    // Atom numbering:
    //   0-1-2-3-4-5-0  (ring 1 perimeter, 6 atoms)
    //   4-6-7-8-9-5    (ring 2, sharing bond 4-5)
    fn naphthalene() -> chematic_core::Molecule {
        let mut b = MoleculeBuilder::new();
        let atoms: Vec<_> = (0..10).map(|_| b.add_atom(Atom::new(Element::C))).collect();
        // Ring 1: 0-1-2-3-4-9-0
        let ring1 = [0usize, 1, 2, 3, 4, 9];
        for i in 0..6 {
            b.add_bond(atoms[ring1[i]], atoms[ring1[(i + 1) % 6]], BondOrder::Single).unwrap();
        }
        // Ring 2: 4-5-6-7-8-9 (shares bond 4-9)
        // Bonds to add: 4-5, 5-6, 6-7, 7-8, 8-9
        b.add_bond(atoms[4], atoms[5], BondOrder::Single).unwrap();
        b.add_bond(atoms[5], atoms[6], BondOrder::Single).unwrap();
        b.add_bond(atoms[6], atoms[7], BondOrder::Single).unwrap();
        b.add_bond(atoms[7], atoms[8], BondOrder::Single).unwrap();
        b.add_bond(atoms[8], atoms[9], BondOrder::Single).unwrap();
        b.build()
    }

    // Build norbornane (bicyclo[2.2.1]heptane): 7 carbons, 8 bonds, 2 rings.
    // Numbering:
    //   bridgehead atoms: 0, 3
    //   bridge 1: 0-1-2-3
    //   bridge 2: 0-4-5-3
    //   bridge 3: 0-6-3  (one-carbon bridge)
    fn norbornane() -> chematic_core::Molecule {
        let mut b = MoleculeBuilder::new();
        let atoms: Vec<_> = (0..7).map(|_| b.add_atom(Atom::new(Element::C))).collect();
        // Bridge 1: 0-1-2-3
        b.add_bond(atoms[0], atoms[1], BondOrder::Single).unwrap();
        b.add_bond(atoms[1], atoms[2], BondOrder::Single).unwrap();
        b.add_bond(atoms[2], atoms[3], BondOrder::Single).unwrap();
        // Bridge 2: 0-4-5-3
        b.add_bond(atoms[0], atoms[4], BondOrder::Single).unwrap();
        b.add_bond(atoms[4], atoms[5], BondOrder::Single).unwrap();
        b.add_bond(atoms[5], atoms[3], BondOrder::Single).unwrap();
        // Bridge 3: 0-6-3
        b.add_bond(atoms[0], atoms[6], BondOrder::Single).unwrap();
        b.add_bond(atoms[6], atoms[3], BondOrder::Single).unwrap();
        b.build()
    }

    #[test]
    fn test_cyclohexane_sssr() {
        let mol = cyclohexane();
        let rings = find_sssr(&mol);
        assert_eq!(rings.ring_count(), 1, "cyclohexane has exactly 1 ring");
        assert_eq!(rings.rings()[0].len(), 6, "cyclohexane ring has 6 atoms");
    }

    #[test]
    fn test_benzene_sssr() {
        let mol = benzene();
        let rings = find_sssr(&mol);
        assert_eq!(rings.ring_count(), 1, "benzene has exactly 1 ring");
        assert_eq!(rings.rings()[0].len(), 6, "benzene ring has 6 atoms");
    }

    #[test]
    fn test_naphthalene_sssr() {
        let mol = naphthalene();
        let rings = find_sssr(&mol);
        // Cycle rank: 11 bonds - 10 atoms + 1 component = 2
        // SSSR should have 2 rings, both 6-membered.
        assert_eq!(rings.ring_count(), 2, "naphthalene SSSR has 2 rings");
        for ring in rings.rings() {
            assert_eq!(ring.len(), 6, "each naphthalene SSSR ring has 6 atoms");
        }
    }

    #[test]
    fn test_norbornane_sssr() {
        let mol = norbornane();
        let rings = find_sssr(&mol);
        // Cycle rank: 8 bonds - 7 atoms + 1 component = 2
        assert_eq!(rings.ring_count(), 2, "norbornane SSSR has 2 rings");
        // The two smallest rings are both 5-membered.
        for ring in rings.rings() {
            assert_eq!(ring.len(), 5, "each norbornane SSSR ring has 5 atoms");
        }
    }

    #[test]
    fn test_acyclic_molecule() {
        // Ethane: no rings.
        let mut b = MoleculeBuilder::new();
        let c1 = b.add_atom(Atom::new(Element::C));
        let c2 = b.add_atom(Atom::new(Element::C));
        b.add_bond(c1, c2, BondOrder::Single).unwrap();
        let mol = b.build();
        let rings = find_sssr(&mol);
        assert_eq!(rings.ring_count(), 0);
    }

    #[test]
    fn test_contains_atom() {
        let mol = cyclohexane();
        let rings = find_sssr(&mol);
        for i in 0..6u32 {
            assert!(rings.contains_atom(AtomIdx(i)), "atom {} should be in a ring", i);
        }
    }

    #[test]
    fn test_atoms_in_ring_count_benzene() {
        let mol = benzene();
        let rings = find_sssr(&mol);
        for i in 0..6u32 {
            assert_eq!(
                rings.atoms_in_ring_count(AtomIdx(i)),
                1,
                "each benzene atom is in exactly 1 ring"
            );
        }
    }
}