65 lines
1.6 KiB
Java
65 lines
1.6 KiB
Java
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import java.util.*;
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import java.util.stream.Stream;
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// https://en.wikipedia.org/wiki/Matching_(graph_theory)#In_unweighted_bipartite_graphs in O(V * E)
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public class MaxMatching {
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public static int maxMatching(List<Integer>[] graph, int n2) {
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int n1 = graph.length;
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int[] matching = new int[n2];
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Arrays.fill(matching, -1);
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int matches = 0;
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for (int u = 0; u < n1; u++) {
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if (findPath(graph, u, matching, new boolean[n1]))
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++matches;
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}
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return matches;
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}
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static boolean findPath(List<Integer>[] graph, int u1, int[] matching, boolean[] vis) {
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vis[u1] = true;
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for (int v : graph[u1]) {
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int u2 = matching[v];
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if (u2 == -1 || !vis[u2] && findPath(graph, u2, matching, vis)) {
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matching[v] = u1;
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return true;
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}
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}
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return false;
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}
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// random tests
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public static void main(String[] args) {
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Random rnd = new Random(1);
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for (int step = 0; step < 1000; step++) {
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int n1 = rnd.nextInt(20) + 1;
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int n2 = rnd.nextInt(20) + 1;
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List<Integer>[] g = Stream.generate(ArrayList::new).limit(n1).toArray(List[]::new);
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for (int i = 0; i < n1; i++)
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for (int j = 0; j < n2; j++)
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g[i].add(j);
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int res1 = maxMatching(g, n2);
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int res2 = slowMinVertexCover(g, n2);
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if (res1 != res2)
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throw new RuntimeException();
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}
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}
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static int slowMinVertexCover(List<Integer>[] g, int n2) {
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int n1 = g.length;
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int[] mask = new int[n1];
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for (int i = 0; i < n1; i++)
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for (int j : g[i])
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mask[i] |= 1 << j;
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int res = n2;
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for (int m = 0; m < 1 << n2; m++) {
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int cur = Integer.bitCount(m);
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for (int i = 0; i < n1; i++)
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if ((mask[i] & m) != mask[i])
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++cur;
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res = Math.min(res, cur);
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}
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return res;
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}
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}
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