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66 lines
1.7 KiB
Java
66 lines
1.7 KiB
Java
import java.util.*;
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// https://en.wikipedia.org/wiki/Matching_(graph_theory)#In_unweighted_bipartite_graphs in O(V^3)
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public class MaxMatching2 {
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public static int maxMatching(boolean[][] graph) {
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int n1 = graph.length;
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int n2 = n1 == 0 ? 0 : graph[0].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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return matches;
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}
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static boolean findPath(boolean[][] graph, int u1, int[] matching, boolean[] vis) {
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vis[u1] = true;
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for (int v = 0; v < matching.length; ++v) {
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int u2 = matching[v];
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if (graph[u1][v] && (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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boolean[][] g = new boolean[n1][n2];
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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][j] = rnd.nextBoolean();
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int res1 = maxMatching(g);
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int res2 = slowMinVertexCover(g);
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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(boolean[][] g) {
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int n1 = g.length;
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int n2 = g[0].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 = 0; j < n2; j++)
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if (g[i][j])
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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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