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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/Hopcroft–Karp_algorithm in (E * sqrt(V))
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public class MaxMatchingHopcroftKarp {
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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[] dist = new int[n1];
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int[] matching = new int[n2];
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Arrays.fill(matching, -1);
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boolean[] used = new boolean[n1];
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for (int res = 0; ; ) {
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bfs(graph, used, matching, dist);
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boolean[] vis = new boolean[n1];
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int f = 0;
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for (int u = 0; u < n1; ++u)
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if (!used[u] && dfs(graph, vis, used, matching, dist, u))
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++f;
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if (f == 0)
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return res;
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res += f;
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}
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}
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static void bfs(List<Integer>[] graph, boolean[] used, int[] matching, int[] dist) {
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Arrays.fill(dist, -1);
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int n1 = graph.length;
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int[] Q = new int[graph.length];
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int sizeQ = 0;
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for (int u = 0; u < n1; ++u) {
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if (!used[u]) {
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Q[sizeQ++] = u;
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dist[u] = 0;
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}
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}
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for (int i = 0; i < sizeQ; i++) {
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int u1 = Q[i];
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for (int v : graph[u1]) {
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int u2 = matching[v];
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if (u2 >= 0 && dist[u2] < 0) {
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dist[u2] = dist[u1] + 1;
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Q[sizeQ++] = u2;
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}
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}
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}
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}
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static boolean dfs(List<Integer>[] graph, boolean[] vis, boolean[] used, int[] matching, int[] dist, int u1) {
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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 < 0 || !vis[u2] && dist[u2] == dist[u1] + 1 && dfs(graph, vis, used, matching, dist, u2)) {
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matching[v] = u1;
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used[u1] = true;
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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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// Usage example
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public static void main(String[] args) {
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List<Integer>[] graph = Stream.generate(ArrayList::new).limit(3).toArray(List[]::new);
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graph[0].add(0);
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graph[0].add(1);
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graph[1].add(1);
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System.out.println(2 == maxMatching(graph, 2));
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}
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}
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