Add Bipartite Matching Kuhn's Algorithm (rust-lang#377)

Author: Arjun31415

src/graph/bipartite_matching.rs

@@ -0,0 +1,124 @@
+// Adjacency List
+type Graph = Vec<Vec<usize>>;
+
+pub struct BipartiteMatching {
+    pub adj: Graph,
+    pub num_vertices_grp1: usize,
+    pub num_vertices_grp2: usize,
+    // mt[i] = v is the matching of i in grp1 to v in grp2
+    pub mt: Vec<i32>,
+    pub used: Vec<bool>,
+}
+impl BipartiteMatching {
+    pub fn new(num_vertices_grp1: usize, num_vertices_grp2: usize) -> Self {
+        BipartiteMatching {
+            adj: vec![vec![]; num_vertices_grp1 + 1],
+            num_vertices_grp1,
+            num_vertices_grp2,
+            mt: vec![-1; num_vertices_grp2 + 1],
+            used: vec![false; num_vertices_grp1 + 1],
+        }
+    }
+    #[inline]
+    // Add an undirected edge u-v in the graph
+    pub fn add_edge(&mut self, u: usize, v: usize) {
+        self.adj[u].push(v);
+        // self.adj[v].push(u);
+    }
+
+    fn try_kuhn(&mut self, cur: usize) -> bool {
+        if self.used[cur] {
+            return false;
+        }
+        self.used[cur] = true;
+        for i in 0..self.adj[cur].len() {
+            let to = self.adj[cur][i];
+            if self.mt[to] == -1 || self.try_kuhn(self.mt[to] as usize) {
+                self.mt[to] = cur as i32;
+                return true;
+            }
+        }
+        false
+    }
+    pub fn kuhn(&mut self) {
+        self.mt = vec![-1; self.num_vertices_grp2 + 1];
+        for v in 1..self.num_vertices_grp1 + 1 {
+            self.used = vec![false; self.num_vertices_grp1 + 1];
+            self.try_kuhn(v);
+        }
+    }
+    pub fn print_matching(&self) {
+        for i in 1..self.num_vertices_grp2 + 1 {
+            if self.mt[i] == -1 {
+                continue;
+            }
+            println!("Vertex {} in grp1 matched with {} grp2", self.mt[i], i)
+        }
+    }
+}
+#[cfg(test)]
+mod tests {
+    use super::*;
+    #[test]
+    fn small_graph() {
+        let n1 = 6;
+        let n2 = 6;
+        let mut g = BipartiteMatching::new(n1, n2);
+        // vertex 1 in grp1 to vertex 1 in grp 2
+        // denote the ith grp2 vertex as n1+i
+        g.add_edge(1, 2);
+        g.add_edge(1, 3);
+        // 2 is not connected to any vertex
+        g.add_edge(3, 4);
+        g.add_edge(3, 1);
+        g.add_edge(4, 3);
+        g.add_edge(5, 3);
+        g.add_edge(5, 4);
+        g.add_edge(6, 6);
+        g.kuhn();
+        g.print_matching();
+        let answer: Vec<i32> = vec![-1, 2, -1, 1, 3, 4, 6];
+        for i in 1..g.mt.len() {
+            if g.mt[i] == -1 {
+                // 5 in group2 has no pair
+                assert_eq!(i, 5);
+                continue;
+            }
+            // 2 in group1 has no pair
+            assert!(g.mt[i] != 2);
+            assert_eq!(i as i32, answer[g.mt[i] as usize]);
+        }
+    }
+    #[test]
+    fn super_small_graph() {
+        let n1 = 1;
+        let n2 = 1;
+        let mut g = BipartiteMatching::new(n1, n2);
+        g.add_edge(1, 1);
+        g.kuhn();
+        g.print_matching();
+        assert_eq!(g.mt[1], 1);
+    }
+    #[test]
+    fn only_one_vertex_graph() {
+        let n1 = 10;
+        let n2 = 10;
+        let mut g = BipartiteMatching::new(n1, n2);
+        g.add_edge(1, 1);
+        g.add_edge(2, 1);
+        g.add_edge(3, 1);
+        g.add_edge(4, 1);
+        g.add_edge(5, 1);
+        g.add_edge(6, 1);
+        g.add_edge(7, 1);
+        g.add_edge(8, 1);
+        g.add_edge(9, 1);
+        g.add_edge(10, 1);
+        g.kuhn();
+        g.print_matching();
+        assert_eq!(g.mt[1], 1);
+        for i in 2..g.mt.len() {
+            assert!(g.mt[i] == -1);
+        }
+    }
+}

src/graph/mod.rs

@@ -1,4 +1,5 @@
 mod bellman_ford;
+mod bipartite_matching;
 mod breadth_first_search;
 mod centroid_decomposition;
 mod depth_first_search;
@@ -16,8 +17,8 @@ mod prufer_code;
 mod strongly_connected_components;
 mod topological_sort;
 mod two_satisfiability;
-
 pub use self::bellman_ford::bellman_ford;
+pub use self::bipartite_matching::BipartiteMatching;
 pub use self::breadth_first_search::breadth_first_search;
 pub use self::centroid_decomposition::CentroidDecomposition;
 pub use self::depth_first_search::depth_first_search;