chematic_perception/

sssr.rs

//! Smallest Set of Smallest Rings (SSSR) via Horton's algorithm.
//!
//! Algorithm overview:
//! 1. Compute the cycle rank r = E - V + C (Euler characteristic),
//!    where C is the number of connected components.
//! 2. For every vertex v (as a candidate root) and every ring-eligible edge
//!    (x, y), form the candidate cycle SP(v, x) + edge(x, y) + SP(y, v),
//!    where SP is the shortest path in v's BFS tree. Keep it only if it's a
//!    genuine simple cycle (the two paths share no vertex other than v).
//!    This produces O(V*E) candidates and is guaranteed (Horton, 1987) to
//!    contain a minimum-weight cycle basis — unlike a single spanning tree's
//!    fundamental-cycle set (exactly r candidates, no redundancy), which can
//!    only ever report *a* valid basis, never guaranteed to be minimal.
//! 3. Represent each cycle as a set of bond indices (for GF(2) XOR independence
//!    testing) and sort candidates by (length, canonical tie-break) — the
//!    tie-break uses a local Weisfeiler-Leman-style atom ranking (see
//!    `canonical_atom_ranks`) so ring *selection* doesn't depend on input
//!    atom-numbering (i.e. SMILES parse/traversal order), only on molecular
//!    graph structure.
//! 4. Use Gaussian elimination over GF(2) to greedily build an independent
//!    basis of r cycles from that sorted candidate list.
//! 5. Convert the chosen bond-sets back to ordered atom sequences for the public API.

use rustc_hash::{FxHashMap, FxHashSet};
use std::collections::VecDeque;

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

/// Returns `true` if the bond order is eligible for ring perception.
///
/// Zero-order and Dative bonds are coordinate/non-valence connections that must
/// not form ring closures in the SSSR (RDKit PR #9118). Query bond types are
/// also excluded since they only appear in SMARTS patterns, never in real molecules.
fn is_ring_eligible(order: BondOrder) -> bool {
    matches!(
        order,
        BondOrder::Single
            | BondOrder::Double
            | BondOrder::Triple
            | BondOrder::Quadruple
            | BondOrder::Aromatic
            | BondOrder::Up
            | BondOrder::Down
    )
}

// ---------------------------------------------------------------------------
// 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();
    // Count only ring-eligible bonds for the cycle rank (E - V + C).
    // Zero-order and Dative bonds are excluded (RDKit PR #9118).
    let e = mol
        .bonds()
        .filter(|(_, b)| is_ring_eligible(b.order))
        .count();

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

    // Component count only (the parent tree itself isn't used any more —
    // candidate generation below builds its own BFS tree per root).
    let (components, _) = bfs_spanning_forest(mol);
    let r = (e as isize) - (v as isize) + (components as isize);

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

    let ring_bonds: Vec<(BondIdx, AtomIdx, AtomIdx)> = mol
        .bonds()
        .filter(|(_, b)| is_ring_eligible(b.order))
        .map(|(bidx, b)| (bidx, b.atom1, b.atom2))
        .collect();

    // Horton candidate generation: BFS from every vertex, then for every
    // ring-eligible edge form the candidate SP(root,x)+edge(x,y)+SP(y,root).
    // O(V*E) candidates total — enough redundancy to guarantee a
    // minimum-weight basis is representable in the pool (see module doc).
    let mut candidates: Vec<(Vec<BondIdx>, Vec<AtomIdx>)> = Vec::new();
    for root_idx in 0..v {
        let root = AtomIdx(root_idx as u32);
        let (dist, parent) = bfs_tree(mol, root);
        for &(bidx, x, y) in &ring_bonds {
            if x == root || y == root {
                continue; // degenerate: edge touches the root itself
            }
            if dist[x.0 as usize] == usize::MAX || dist[y.0 as usize] == usize::MAX {
                continue; // x or y unreachable from this root (different component)
            }
            if let Some(candidate) = horton_candidate(mol, root, x, y, bidx, &parent) {
                candidates.push(candidate);
            }
        }
    }

    // Deterministic ordering: shortest first, then a canonical (input-order-
    // independent) tie-break so ring *selection* doesn't depend on how the
    // molecule happened to be numbered by the parser.
    let ranks = canonical_atom_ranks(mol);
    candidates.sort_by_cached_key(|c| (c.0.len(), canonical_cycle_key(&c.1, &ranks)));
    // The same geometric cycle can be generated from multiple roots; collapse
    // duplicates (bond_set is already sorted, so identical cycles are equal).
    candidates.dedup_by(|a, b| a.0 == b.0);

    // 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: FxHashMap<BondIdx, Vec<BondIdx>> = FxHashMap::default();
    let mut selected_atoms: Vec<Vec<AtomIdx>> = Vec::new();

    for (bond_set, atom_seq) in candidates {
        // 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).
fn bfs_spanning_forest(mol: &Molecule) -> (usize, Vec<Option<AtomIdx>>) {
    let n = mol.atom_count();
    let mut visited = vec![false; n];
    let mut parent: Vec<Option<AtomIdx>> = vec![None; 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) {
                // Skip non-ring-eligible bonds (Zero, Dative, Query*) — they
                // must not form ring closures in the spanning forest (RDKit PR #9118).
                if !is_ring_eligible(mol.bond(bidx).order) {
                    continue;
                }
                let ni = neighbor.0 as usize;
                if !visited[ni] {
                    visited[ni] = true;
                    parent[ni] = Some(current);
                    queue.push_back(neighbor);
                }
            }
        }
    }

    (components, parent)
}

// ---------------------------------------------------------------------------
// Horton candidate generation
// ---------------------------------------------------------------------------

/// BFS shortest-path tree from `root`, restricted to ring-eligible bonds.
///
/// Returns `(dist, parent)`: `dist[i]` is the shortest-path distance from
/// `root` to atom `i` (`usize::MAX` if unreachable), `parent[i]` is the
/// preceding atom on that shortest path (`None` for `root` and unreachable
/// atoms).
fn bfs_tree(mol: &Molecule, root: AtomIdx) -> (Vec<usize>, Vec<Option<AtomIdx>>) {
    let n = mol.atom_count();
    let mut dist = vec![usize::MAX; n];
    let mut parent: Vec<Option<AtomIdx>> = vec![None; n];
    let mut queue: VecDeque<AtomIdx> = VecDeque::new();

    dist[root.0 as usize] = 0;
    queue.push_back(root);

    while let Some(current) = queue.pop_front() {
        for (neighbor, bidx) in mol.neighbors(current) {
            if !is_ring_eligible(mol.bond(bidx).order) {
                continue;
            }
            let ni = neighbor.0 as usize;
            if dist[ni] == usize::MAX {
                dist[ni] = dist[current.0 as usize] + 1;
                parent[ni] = Some(current);
                queue.push_back(neighbor);
            }
        }
    }

    (dist, parent)
}

/// Form the Horton candidate cycle `SP(root,x) + edge(x,y) + SP(y,root)`.
///
/// Returns `None` if the two root-rooted shortest paths share any vertex
/// other than `root` itself — in that case the paths actually meet at some
/// closer common ancestor, so this (root, edge) pair doesn't yield a *simple*
/// cycle (the true minimal cycle through that closer ancestor is correctly
/// picked up when *it* is tried as root instead).
fn horton_candidate(
    mol: &Molecule,
    root: AtomIdx,
    x: AtomIdx,
    y: AtomIdx,
    bidx: BondIdx,
    parent: &[Option<AtomIdx>],
) -> Option<(Vec<BondIdx>, Vec<AtomIdx>)> {
    let path_x = path_to_root(x, parent); // [x, ..., root]
    let path_y = path_to_root(y, parent); // [y, ..., root]
    debug_assert_eq!(*path_x.last().unwrap(), root);
    debug_assert_eq!(*path_y.last().unwrap(), root);

    // Simplicity check: the two paths must share only `root`.
    let interior_x: FxHashSet<AtomIdx> = path_x[..path_x.len() - 1].iter().copied().collect();
    if path_y[..path_y.len() - 1]
        .iter()
        .any(|a| interior_x.contains(a))
    {
        return None;
    }

    // Ordered ring atoms: x ... root ... y (then the edge x-y closes the cycle).
    let mut ring_atoms: Vec<AtomIdx> = path_x.clone();
    for &a in path_y.iter().rev().skip(1) {
        ring_atoms.push(a);
    }

    let mut bond_set: Vec<BondIdx> = Vec::new();
    for i in 0..path_x.len().saturating_sub(1) {
        let (b, _) = mol.bond_between(path_x[i], path_x[i + 1])?;
        bond_set.push(b);
    }
    for i in 0..path_y.len().saturating_sub(1) {
        let (b, _) = mol.bond_between(path_y[i], path_y[i + 1])?;
        bond_set.push(b);
    }
    bond_set.push(bidx);
    bond_set.sort();
    bond_set.dedup();

    Some((bond_set, ring_atoms))
}

/// Walk parent pointers from `start` to `root`, returning the chain
/// including `start` (first) and the root (last).
fn path_to_root(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
}

// ---------------------------------------------------------------------------
// Canonical tie-break (determinism, independent of atom-numbering)
// ---------------------------------------------------------------------------

/// A cheap, self-contained (no cross-crate dependency) approximation of
/// canonical atom ranking, used only to make candidate-cycle tie-breaking
/// deterministic: the same molecular graph always produces the same SSSR,
/// regardless of how its atoms happen to be numbered by the parser (SMILES
/// traversal order, SDF atom-block order, etc). This is a local
/// Weisfeiler-Leman-style refinement (seed on (element, degree, charge,
/// aromatic), then repeatedly fold in each atom's sorted neighbor keys) —
/// it does not aim for full canonical-labeling discriminating power (ties
/// among genuinely symmetric atoms are expected and fine; the point is
/// input-order-independence, not maximal refinement).
fn canonical_atom_ranks(mol: &Molecule) -> Vec<u64> {
    let n = mol.atom_count();
    let mut keys: Vec<u64> = (0..n)
        .map(|i| {
            let idx = AtomIdx(i as u32);
            let atom = mol.atom(idx);
            let z = atom.element.atomic_number() as u64;
            let degree = mol.degree(idx) as u64;
            let charge = (atom.charge as i64 + 8) as u64; // shift to non-negative
            let aromatic = u64::from(atom.aromatic);
            (z << 24) | (degree << 16) | (charge << 8) | aromatic
        })
        .collect();

    const ROUNDS: usize = 3;
    for _ in 0..ROUNDS {
        let mut next = Vec::with_capacity(n);
        for i in 0..n {
            let mut neighbor_keys: Vec<u64> = mol
                .neighbors(AtomIdx(i as u32))
                .map(|(nb, _)| keys[nb.0 as usize])
                .collect();
            neighbor_keys.sort_unstable();
            let mut h = keys[i];
            for nk in neighbor_keys {
                h = h.wrapping_mul(1_000_003).wrapping_add(nk);
            }
            next.push(h);
        }
        keys = next;
    }
    keys
}

/// Deterministic sort key for a candidate cycle: the sorted multiset of its
/// atoms' canonical ranks, combined order-independently — isomorphic cycles
/// (same molecule, different traversal) always collapse to the same key.
fn canonical_cycle_key(atom_seq: &[AtomIdx], ranks: &[u64]) -> u64 {
    let mut vals: Vec<u64> = atom_seq.iter().map(|a| ranks[a.0 as usize]).collect();
    vals.sort_unstable();
    let mut h: u64 = 0;
    for v in vals {
        h = h.wrapping_mul(1_000_003).wrapping_add(v);
    }
    h
}

// ---------------------------------------------------------------------------
// 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: &FxHashMap<BondIdx, Vec<BondIdx>>) -> Vec<BondIdx> {
    let mut current: Vec<BondIdx> = cycle.to_vec();
    while let Some(&pivot) = current.iter().min() {
        match basis.get(&pivot) {
            None => return current, // independent
            // XOR: symmetric difference of the two sorted sets.
            Some(basis_row) => current = sym_diff(&current, basis_row),
        }
    }
    current
}

/// 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_azulene_sssr_minimal() {
        // Azulene: cyclopentadiene fused to cycloheptatriene, sharing one
        // bond. RDKit's GetSymmSSSR ring-size multiset is [5, 7]; the old
        // single-spanning-tree find_sssr previously returned a non-minimal
        // basis for this topology (see aromaticity.rs's PROVISIONAL-tagged
        // azulene regression test for the downstream effect on Pass 1/2).
        let mol = chematic_smiles::parse("C1=CC2=CC=CC=CC2=C1").expect("azulene SMILES");
        let sssr = find_sssr(&mol);
        let mut sizes: Vec<usize> = sssr.rings().iter().map(|r| r.len()).collect();
        sizes.sort_unstable();
        assert_eq!(sizes, vec![5, 7], "azulene SSSR must be minimal [5, 7]");
    }

    #[test]
    fn test_indolizine_sssr_minimal() {
        // Indolizine: pyrrole fused to pyridine sharing a bridgehead N.
        // RDKit's GetSymmSSSR ring-size multiset is [5, 6] — a fused
        // heterocycle oracle case distinct from azulene's all-carbon,
        // odd/odd-sized ring pair.
        let mol = chematic_smiles::parse("c1ccn2ccccc12").expect("indolizine SMILES");
        let sssr = find_sssr(&mol);
        let mut sizes: Vec<usize> = sssr.rings().iter().map(|r| r.len()).collect();
        sizes.sort_unstable();
        assert_eq!(sizes, vec![5, 6], "indolizine SSSR must be minimal [5, 6]");
    }

    #[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"
            );
        }
    }

    // Anthracene: 14 atoms, 16 bonds (3 fused 6-membered rings).
    // Linear fusion: central ring shares edges with two outer rings.
    fn anthracene() -> chematic_core::Molecule {
        let mut b = MoleculeBuilder::new();
        let atoms: Vec<_> = (0..14).map(|_| b.add_atom(Atom::new(Element::C))).collect();
        // Ring 1 (left): 0-1-2-3-8-9-0
        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();
        b.add_bond(atoms[3], atoms[8], BondOrder::Single).unwrap();
        b.add_bond(atoms[8], atoms[9], BondOrder::Single).unwrap();
        b.add_bond(atoms[9], atoms[0], BondOrder::Single).unwrap();
        // Ring 2 (center): 3-4-5-6-7-8-3
        b.add_bond(atoms[3], atoms[4], BondOrder::Single).unwrap();
        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();
        // Ring 3 (right): 7-10-11-12-13-6-7
        b.add_bond(atoms[7], atoms[10], BondOrder::Single).unwrap();
        b.add_bond(atoms[10], atoms[11], BondOrder::Single).unwrap();
        b.add_bond(atoms[11], atoms[12], BondOrder::Single).unwrap();
        b.add_bond(atoms[12], atoms[13], BondOrder::Single).unwrap();
        b.add_bond(atoms[13], atoms[6], BondOrder::Single).unwrap();
        b.build()
    }

    // Spiro[4.4]nonane: two 5-membered rings sharing a single bridgehead atom.
    // 9 atoms total, cycle rank 2.
    fn spiro_nonane() -> chematic_core::Molecule {
        let mut b = MoleculeBuilder::new();
        let atoms: Vec<_> = (0..9).map(|_| b.add_atom(Atom::new(Element::C))).collect();
        // Bridgehead: atom 0
        // Ring 1: 0-1-2-3-4-0
        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();
        b.add_bond(atoms[3], atoms[4], BondOrder::Single).unwrap();
        b.add_bond(atoms[4], atoms[0], BondOrder::Single).unwrap();
        // Ring 2: 0-5-6-7-8-0
        b.add_bond(atoms[0], 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[0], BondOrder::Single).unwrap();
        b.build()
    }

    // 12-membered macrocycle (1 ring, 12 atoms).
    fn dodecane_ring() -> chematic_core::Molecule {
        let mut b = MoleculeBuilder::new();
        let atoms: Vec<_> = (0..12).map(|_| b.add_atom(Atom::new(Element::C))).collect();
        for i in 0..12 {
            b.add_bond(atoms[i], atoms[(i + 1) % 12], BondOrder::Single)
                .unwrap();
        }
        b.build()
    }

    // Two disconnected rings (two components).
    fn disconnected_rings() -> chematic_core::Molecule {
        let mut b = MoleculeBuilder::new();
        // Benzene ring: atoms 0-5
        let benzene_atoms: Vec<_> = (0..6).map(|_| b.add_atom(Atom::new(Element::C))).collect();
        for i in 0..6 {
            b.add_bond(
                benzene_atoms[i],
                benzene_atoms[(i + 1) % 6],
                BondOrder::Single,
            )
            .unwrap();
        }
        // Separate cyclohexane ring: atoms 6-11
        let hexane_atoms: Vec<_> = (0..6).map(|_| b.add_atom(Atom::new(Element::C))).collect();
        for i in 0..6 {
            b.add_bond(
                hexane_atoms[i],
                hexane_atoms[(i + 1) % 6],
                BondOrder::Single,
            )
            .unwrap();
        }
        b.build()
    }

    // Adamantane-like tricyclic structure (simplified):
    // 10 atoms, 3 bridges between 2 bridgeheads
    fn adamantane() -> chematic_core::Molecule {
        let mut b = MoleculeBuilder::new();
        let atoms: Vec<_> = (0..10).map(|_| b.add_atom(Atom::new(Element::C))).collect();
        // Bridgehead atoms: 0, 5
        // Bridge 1: 0-1-2-5 (3 bonds in chain)
        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[5], BondOrder::Single).unwrap();
        // Bridge 2: 0-3-4-5 (3 bonds in chain)
        b.add_bond(atoms[0], atoms[3], BondOrder::Single).unwrap();
        b.add_bond(atoms[3], atoms[4], BondOrder::Single).unwrap();
        b.add_bond(atoms[4], atoms[5], BondOrder::Single).unwrap();
        // Bridge 3: 0-6-7-5 (3 bonds in chain)
        b.add_bond(atoms[0], atoms[6], BondOrder::Single).unwrap();
        b.add_bond(atoms[6], atoms[7], BondOrder::Single).unwrap();
        b.add_bond(atoms[7], atoms[5], BondOrder::Single).unwrap();
        // Cross-link bonds to connect bridges (forming tertiary center)
        // 1-3, 2-4, 6-? to complete cage
        b.add_bond(atoms[1], atoms[3], BondOrder::Single).unwrap();
        b.add_bond(atoms[2], atoms[4], BondOrder::Single).unwrap();
        b.build()
    }

    #[test]
    fn test_anthracene_sssr() {
        let mol = anthracene();
        let rings = find_sssr(&mol);
        // Cycle rank: 16 bonds - 14 atoms + 1 component = 3.
        // RDKit's GetSymmSSSR gives three 6-membered rings (linear acene) —
        // Horton's minimum-weight basis must match this exactly, not just
        // "3 rings covering most atoms" (the old spanning-tree algorithm
        // could substitute a larger non-minimal ring for one of these).
        assert_eq!(rings.ring_count(), 3, "anthracene SSSR has 3 rings");
        for ring in rings.rings() {
            assert_eq!(ring.len(), 6, "each anthracene SSSR ring has 6 atoms");
        }
        let all_ring_atoms: std::collections::HashSet<_> = rings
            .rings()
            .iter()
            .flat_map(|r| r.iter().copied())
            .collect();
        assert_eq!(
            all_ring_atoms.len(),
            14,
            "anthracene SSSR atoms cover every atom"
        );
    }

    #[test]
    fn test_spiro_nonane_sssr() {
        let mol = spiro_nonane();
        let rings = find_sssr(&mol);
        // Cycle rank: 8 bonds - 9 atoms + 1 component = 0... wait, let me recalculate
        // Actually: two 5-membered rings sharing 1 atom = 4 + 4 + 2 (bridge) = 10 bonds
        // 10 bonds - 9 atoms + 1 = 2 rings
        assert_eq!(rings.ring_count(), 2, "spiro[4.4]nonane SSSR has 2 rings");
        for ring in rings.rings() {
            assert_eq!(ring.len(), 5, "each spiro nonane SSSR ring is 5-membered");
        }
    }

    #[test]
    fn test_dodecane_ring_sssr() {
        let mol = dodecane_ring();
        let rings = find_sssr(&mol);
        assert_eq!(rings.ring_count(), 1, "12-membered ring has 1 SSSR entry");
        assert_eq!(
            rings.rings()[0].len(),
            12,
            "12-membered ring SSSR has 12 atoms"
        );
    }

    #[test]
    fn test_disconnected_rings_sssr() {
        let mol = disconnected_rings();
        let rings = find_sssr(&mol);
        // Cycle rank: 12 bonds - 12 atoms + 2 components = 2 rings
        assert_eq!(
            rings.ring_count(),
            2,
            "two disconnected rings yield 2 SSSR entries"
        );
        let sizes: Vec<_> = rings.rings().iter().map(|r| r.len()).collect();
        assert!(sizes.contains(&6), "one ring should be 6-membered");
    }

    #[test]
    fn test_adamantane_sssr() {
        let mol = adamantane();
        let rings = find_sssr(&mol);
        // Simplified adamantane: 10 atoms, 12 bonds, 1 component
        // Cycle rank: 12 - 10 + 1 = 3
        // (May be 3-4 depending on cross-link structure and Gaussian elimination)
        assert!(
            rings.ring_count() >= 3,
            "adamantane SSSR has at least 3 rings"
        );
        // Each ring should be reasonable size
        for ring in rings.rings() {
            assert!(!ring.is_empty(), "each ring should have atoms");
            assert!(ring.len() <= 10, "ring should not exceed molecule size");
        }
    }

    #[test]
    fn test_macrocycle_atom_in_ring_count() {
        let mol = dodecane_ring();
        let rings = find_sssr(&mol);
        for i in 0..12u32 {
            assert_eq!(
                rings.atoms_in_ring_count(AtomIdx(i)),
                1,
                "each dodecane atom is in exactly 1 ring"
            );
        }
    }

    #[test]
    fn test_cubane_sssr() {
        // Cubane C8H8 — a cage molecule with 12 C-C bonds and 8 vertices.
        // Cycle rank = E - V + 1 = 12 - 8 + 1 = 5.
        // Cubane has 6 square (4-membered) faces but only 5 are linearly
        // independent in GF(2) — the 6th is the XOR of the other 5 (not just
        // any pair of them, since Sum-of-all-6-faces = 0 in GF(2): each edge
        // is shared by exactly 2 faces).
        //
        // Horton's candidate generation (O(V*E) candidates, guaranteed to
        // contain a minimum-weight basis) finds a truly minimal SSSR here:
        // all 5 basis rings are 4-membered (weight 20), strictly better than
        // the old single-spanning-tree algorithm's typical "4 four-membered +
        // 1 six-membered diagonal" (weight 22) — see module doc / project
        // history for why the old algorithm couldn't guarantee this.
        //
        // Recovering the 6th (symmetry-equivalent) face requires XOR-ing all
        // 5 basis rings together, not a pairwise XOR — augmented_ring_set
        // only does pairwise XOR, so it cannot find it from an already-fully-
        // 4-membered basis (two same-size adjacent cube faces XOR to a
        // 6-membered "belt", not another 4-ring). This is expected: full
        // symmetrization (all 6 symmetry-equivalent minimal rings, matching
        // RDKit's GetSymmSSSR on cubane) is out of scope for Horton alone and
        // deferred to a later Vismara "relevant cycles" pass (see project
        // plan) — not a regression, since Horton's SSSR is still a strict
        // minimality improvement over the previous algorithm.
        let mol = chematic_smiles::parse("C12C3C4C1C5C4C3C25").expect("cubane SMILES");
        let sssr = find_sssr(&mol);

        assert_eq!(
            sssr.rings().len(),
            5,
            "cubane must have exactly 5 SSSR rings (cycle rank 12−8+1=5)"
        );
        for ring in sssr.rings() {
            assert!(
                ring.len() <= 6,
                "cubane SSSR rings must be ≤ 6-membered, got {}",
                ring.len()
            );
        }
        let four_membered = sssr.rings().iter().filter(|r| r.len() == 4).count();
        assert_eq!(
            four_membered, 5,
            "Horton SSSR should find all 5 basis rings as 4-membered faces, got {four_membered}"
        );
    }

    /// Rebuild `mol` with atoms relabeled by `perm` (perm[new_idx] = old_idx),
    /// preserving the same graph but a different atom insertion order.
    fn permute_molecule(mol: &chematic_core::Molecule, perm: &[usize]) -> chematic_core::Molecule {
        let mut old_to_new = vec![0u32; perm.len()];
        for (new_idx, &old_idx) in perm.iter().enumerate() {
            old_to_new[old_idx] = new_idx as u32;
        }
        let mut builder = MoleculeBuilder::new();
        for &old_idx in perm {
            builder.add_atom(mol.atom(AtomIdx(old_idx as u32)).clone());
        }
        for (_, bond) in mol.bonds() {
            let a = AtomIdx(old_to_new[bond.atom1.0 as usize]);
            let b = AtomIdx(old_to_new[bond.atom2.0 as usize]);
            let _ = builder.add_bond(a, b, bond.order);
        }
        builder.build()
    }

    /// find_sssr's ring-size multiset must not depend on atom insertion order.
    /// Probes the fused/bridged/cage systems this project has already
    /// identified as the hard cases for canonical_atom_ranks' 3-round
    /// (not-fixpoint) Weisfeiler-Leman tie-break -- unlike
    /// `canonical_atom_order` (chematic-smiles), this function's doc comment
    /// does not claim full canonical-labeling power, and find_sssr's
    /// self-stability was already measured at 0% on a 5000-molecule corpus
    /// during the Horton rewrite (698ba3f); this is a permanent regression
    /// guard for that claim, not a first-time probe.
    #[test]
    fn find_sssr_ring_size_multiset_is_permutation_invariant() {
        let cases: Vec<(&str, chematic_core::Molecule)> = vec![
            ("naphthalene", naphthalene()),
            ("norbornane", norbornane()),
            ("spiro_nonane", spiro_nonane()),
            ("adamantane", adamantane()),
            (
                "cubane",
                chematic_smiles::parse("C12C3C4C1C5C4C3C25").expect("cubane SMILES"),
            ),
        ];

        for (name, mol) in cases {
            let n = mol.atom_count();
            let mut orig_sizes: Vec<usize> = find_sssr(&mol).rings().iter().map(Vec::len).collect();
            orig_sizes.sort_unstable();

            let perms: Vec<Vec<usize>> = vec![(0..n).rev().collect(), {
                let mut p: Vec<usize> = (0..n).collect();
                if n > 2 {
                    p.rotate_left(n / 3 + 1);
                }
                p
            }];
            for perm in perms {
                let permuted = permute_molecule(&mol, &perm);
                let mut perm_sizes: Vec<usize> =
                    find_sssr(&permuted).rings().iter().map(Vec::len).collect();
                perm_sizes.sort_unstable();
                assert_eq!(
                    orig_sizes, perm_sizes,
                    "{name}: SSSR ring-size multiset changed under atom permutation {perm:?}"
                );
            }
        }
    }

    // ── RDKit PR #9118: SSSR excludes Zero-order and Dative bonds ────────────

    #[test]
    fn sssr_ignores_zero_order_bonds() {
        // A--B via a single bond PLUS a Zero-order bond between the same atoms
        // must NOT create a ring. Zero-order bonds are non-valence connections.
        let mut b = MoleculeBuilder::new();
        let mut a_atom = Atom::new(chematic_core::Element::C);
        a_atom.hydrogen_count = Some(3);
        let mut b_atom = Atom::new(chematic_core::Element::C);
        b_atom.hydrogen_count = Some(3);
        let a = b.add_atom(a_atom);
        let bb = b.add_atom(b_atom);
        b.add_bond(a, bb, BondOrder::Single).unwrap();
        b.add_bond(a, bb, BondOrder::Zero)
            .expect_err("duplicate bond — MoleculeBuilder should reject or ignore it");
        // Build a proper molecule: just two atoms with a single bond.
        // The zero-order bond attempt is rejected, so the molecule is acyclic.
        let mol = b.build();
        let sssr = find_sssr(&mol);
        assert_eq!(
            sssr.rings().len(),
            0,
            "single bond between two atoms → no ring"
        );
    }

    #[test]
    fn sssr_ignores_zero_order_bond_as_third_bond() {
        // Benzene ring (6 aromatic bonds) PLUS one Zero-order bond closing an
        // extra connection should NOT add a phantom 2-membered ring.
        // We build cyclohexane (all single bonds) and verify no extra ring from
        // a Zero-order bond added between two non-adjacent atoms.
        let mut b = MoleculeBuilder::new();
        let atoms: Vec<_> = (0..4)
            .map(|_| {
                let mut a = Atom::new(chematic_core::Element::C);
                a.hydrogen_count = Some(2);
                b.add_atom(a)
            })
            .collect();
        // Square ring: 0-1-2-3-0
        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();
        b.add_bond(atoms[3], atoms[0], BondOrder::Single).unwrap();
        // Zero-order bond between non-adjacent atoms: should NOT create a new ring.
        // Note: builder may reject parallel bonds; if so the test still passes.
        let _ = b.add_bond(atoms[0], atoms[2], BondOrder::Zero);
        let mol = b.build();
        let sssr = find_sssr(&mol);
        // Should find exactly 1 ring (the 4-membered ring), NOT 2 or 3.
        assert_eq!(
            sssr.rings().len(),
            1,
            "zero-order diagonal bond must not create extra rings: found {:?}",
            sssr.rings().iter().map(|r| r.len()).collect::<Vec<_>>()
        );
    }
}