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Bipartite matching (#65)
* adding progress * finish yosupo test * nit * finish docs * fix code cov * another rename * move duplicate code to new file * I like this way more * add back other way as aizu test doesn't check actual matching * fix one nit * address another comment * add comment * remove duplicate code * convert * fix documentation * finish docs --------- Co-authored-by: Luke Videckis <lukevideckis@gmail.com>
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‎Cargo.toml‎

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@@ -127,6 +127,14 @@ path = "examples/graphs/hld_jump_on_tree_nodes.rs"
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name = "hld_jump_on_tree_edges"
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path = "examples/graphs/hld_jump_on_tree_edges.rs"
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[[example]]
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name = "hopcroft_karp_yosupo"
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path = "examples/graphs/hopcroft_karp_yosupo.rs"
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[[example]]
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name = "hopcroft_karp_aizu"
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path = "examples/graphs/hopcroft_karp_aizu.rs"
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[[example]]
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name = "lcp_query_yosupo_zfunc"
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path = "examples/strings/lcp_query_yosupo_zfunc.rs"

‎examples/graphs/hopcroft_karp_aizu.rs‎

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// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/GRL_7_A
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use proconio::input;
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use programming_team_code_rust::graphs::hopcroft_karp::HopcroftKarp;
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mod hopcroft_karp_asserts;
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use hopcroft_karp_asserts::hopcroft_karp_asserts;
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fn main() {
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input! {
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lsz: usize,
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rsz: usize,
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m: usize,
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edge_list: [(usize, usize); m],
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}
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let mut adj = vec![vec![]; lsz];
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for &(u, v) in edge_list.iter() {
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adj[u].push(v);
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}
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let HopcroftKarp {
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matching_siz,
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l_to_r,
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r_to_l,
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mvc_l,
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mvc_r,
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} = HopcroftKarp::new(&adj, rsz);
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hopcroft_karp_asserts(matching_siz, &l_to_r, &r_to_l, &mvc_l, &mvc_r, &edge_list);
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println!("{}", matching_siz);
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}

‎examples/graphs/hopcroft_karp_asserts.rs‎

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pub fn hopcroft_karp_asserts(
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matching_siz: usize,
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l_to_r: &[Option<usize>],
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r_to_l: &[Option<usize>],
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mvc_l: &[bool],
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mvc_r: &[bool],
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edge_list: &[(usize, usize)],
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) {
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for (left, right) in [(l_to_r, r_to_l), (r_to_l, l_to_r)] {
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assert_eq!(
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matching_siz,
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left.iter().filter(|elem| elem.is_some()).count()
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);
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for (i, elem) in left.iter().enumerate().filter(|(_, elem)| elem.is_some()) {
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assert_eq!(Some(i), right[elem.unwrap()]);
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}
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}
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fn count_true(a: &[bool]) -> usize {
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a.iter().filter(|&&elem| elem).count()
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}
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assert_eq!(matching_siz, count_true(mvc_l) + count_true(mvc_r));
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for &(u, v) in edge_list.iter() {
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// this might look weird, but it's done so that code coverage passes:
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//
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// this:
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// assert!(mvc_l[u] || mvc_r[v]);
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// will fail code coverage, saying that the false branch is never run
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let either = mvc_l[u] || mvc_r[v];
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assert!(either);
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}
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}

‎examples/graphs/hopcroft_karp_yosupo.rs‎

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// verification-helper: PROBLEM https://judge.yosupo.jp/problem/bipartitematching
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use proconio::input;
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use programming_team_code_rust::graphs::hopcroft_karp::HopcroftKarp;
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mod hopcroft_karp_asserts;
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use hopcroft_karp_asserts::hopcroft_karp_asserts;
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fn main() {
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input! {
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lsz: usize,
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rsz: usize,
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m: usize,
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edge_list: [(usize, usize); m],
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}
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let mut adj = vec![vec![]; lsz];
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for &(u, v) in edge_list.iter() {
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adj[u].push(v);
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}
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let HopcroftKarp {
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matching_siz,
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l_to_r,
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r_to_l,
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mvc_l,
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mvc_r,
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} = HopcroftKarp::new(&adj, rsz);
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hopcroft_karp_asserts(matching_siz, &l_to_r, &r_to_l, &mvc_l, &mvc_r, &edge_list);
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println!("{}", matching_siz);
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for (i, elem) in l_to_r.iter().enumerate().filter(|(_, elem)| elem.is_some()) {
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println!("{} {}", i, elem.unwrap());
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}
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}

‎src/graphs/hopcroft_karp.rs‎

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//! # Hopcroft Karp algorithm for Bipartite Matching
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use std::collections::VecDeque;
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/// # Example
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/// ```
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/// use programming_team_code_rust::graphs::hopcroft_karp::HopcroftKarp;
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///
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/// let mut adj = vec![vec![]; 2];
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/// for (u, v) in [(0, 0), (0, 2), (1, 2)] {
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/// adj[u].push(v);
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/// }
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///
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/// let HopcroftKarp {
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/// matching_siz,
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/// l_to_r,
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/// r_to_l,
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/// mvc_l,
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/// mvc_r,
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/// } = HopcroftKarp::new(&adj, 3);
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///
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/// assert_eq!(matching_siz, 2);
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/// assert_eq!(l_to_r, [Some(0), Some(2)]);
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/// assert_eq!(r_to_l, [Some(0), None, Some(1)]);
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/// assert_eq!(mvc_l, [true, true]);
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/// assert_eq!(mvc_r, [false, false, false]);
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/// ```
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///
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/// # Complexity
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/// - V: number of vertices; V = lsz + rsz
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/// - E: number of edges
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/// - Time: O(V + E * sqrt(v))
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/// - Space: O(V)
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pub struct HopcroftKarp {
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/// number of edges in matching
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pub matching_siz: usize,
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/// l_to_r\[u_left_side\] = Some(v_right_side) iff edge u_left_side <=> v_right_side is in matching
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pub l_to_r: Vec<Option<usize>>,
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/// r_to_l\[v_right_side\] = Some(u_left_side) iff edge u_left_side <=> v_right_side is in matching
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pub r_to_l: Vec<Option<usize>>,
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/// mvc_l\[u_left_side\] = true iff u_left_side is in min vertex cover
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pub mvc_l: Vec<bool>,
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/// mvc_r\[v_right_side\] = true iff v_right_side is in min vertex cover
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pub mvc_r: Vec<bool>,
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}
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impl HopcroftKarp {
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/// Calculates a max matching and min vertex cover
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pub fn new(adj: &[Vec<usize>], rsz: usize) -> Self {
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let lsz = adj.len();
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let mut e = HopcroftKarp {
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matching_siz: 0,
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l_to_r: vec![None; lsz],
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r_to_l: vec![None; rsz],
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mvc_l: vec![false; lsz],
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mvc_r: vec![false; rsz],
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};
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loop {
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let mut dist = vec![usize::MAX; lsz];
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let mut q = VecDeque::new();
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for (i, _) in e
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.l_to_r
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.iter()
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.enumerate()
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.filter(|&(_, elem)| elem.is_none())
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{
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dist[i] = 0;
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q.push_back(i);
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}
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let mut found = false;
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for v in &mut e.mvc_l {
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*v = true;
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}
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for v in &mut e.mvc_r {
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*v = false;
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}
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while let Some(u) = q.pop_front() {
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e.mvc_l[u] = false;
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for &v in &adj[u] {
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e.mvc_r[v] = true;
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if let Some(w) = e.r_to_l[v] {
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if dist[w] > 1 + dist[u] {
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dist[w] = 1 + dist[u];
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q.push_back(w);
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}
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} else {
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found = true;
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}
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}
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}
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if !found {
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return e;
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}
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fn dfs(u: usize, adj: &[Vec<usize>], dist: &mut [usize], e: &mut HopcroftKarp) -> bool {
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for &v in &adj[u] {
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let w = e.r_to_l[v];
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if w.is_none()
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|| dist[u] + 1 == dist[w.unwrap()] && dfs(w.unwrap(), adj, dist, e)
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{
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(e.l_to_r[u], e.r_to_l[v]) = (Some(v), Some(u));
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return true;
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}
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}
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dist[u] = usize::MAX;
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false
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}
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e.matching_siz += (0..lsz)
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.filter(|&i| e.l_to_r[i].is_none() && dfs(i, adj, &mut dist, &mut e))
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.count();
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}
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}
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}

‎src/graphs/mod.rs‎

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mod dfs_order;
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pub mod dijk;
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pub mod hld;
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pub mod hopcroft_karp;
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pub mod lca;
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pub mod scc;
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pub mod two_sat;

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