158 lines
5.4 KiB
Java
158 lines
5.4 KiB
Java
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/*This is a java program to implement Edmond’s Algorithm for maximum cardinality matching. In graph theory, a branch of mathematics, Edmonds’ algorithm or Chu–Liu/Edmonds’ algorithm is an algorithm for finding a maximum or minimum optimum branchings. This is similar to the minimum spanning tree problem which concerns undirected graphs. However, when nodes are connected by weighted edges that are directed, a minimum spanning tree algorithm cannot be used.*/
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import java.util.ArrayList;
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import java.util.Arrays;
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import java.util.List;
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import java.util.Scanner;
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public class EdmondsMaximumCardinalityMatching
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{
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static int lca(int[] match, int[] base, int[] p, int a, int b)
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{
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boolean[] used = new boolean[match.length];
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while (true)
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{
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a = base[a];
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used[a] = true;
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if (match[a] == -1)
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break;
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a = p[match[a]];
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}
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while (true)
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{
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b = base[b];
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if (used[b])
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return b;
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b = p[match[b]];
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}
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}
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static void markPath(int[] match, int[] base, boolean[] blossom, int[] p,
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int v, int b, int children)
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{
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for (; base[v] != b; v = p[match[v]])
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{
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blossom[base[v]] = blossom[base[match[v]]] = true;
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p[v] = children;
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children = match[v];
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}
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}
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static int findPath(List<Integer>[] graph, int[] match, int[] p, int root)
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{
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int n = graph.length;
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boolean[] used = new boolean[n];
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Arrays.fill(p, -1);
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int[] base = new int[n];
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for (int i = 0; i < n; ++i)
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base[i] = i;
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used[root] = true;
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int qh = 0;
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int qt = 0;
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int[] q = new int[n];
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q[qt++] = root;
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while (qh < qt)
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{
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int v = q[qh++];
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for (int to : graph[v])
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{
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if (base[v] == base[to] || match[v] == to)
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continue;
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if (to == root || match[to] != -1 && p[match[to]] != -1)
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{
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int curbase = lca(match, base, p, v, to);
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boolean[] blossom = new boolean[n];
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markPath(match, base, blossom, p, v, curbase, to);
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markPath(match, base, blossom, p, to, curbase, v);
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for (int i = 0; i < n; ++i)
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if (blossom[base[i]])
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{
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base[i] = curbase;
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if (!used[i])
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{
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used[i] = true;
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q[qt++] = i;
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}
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}
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}
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else if (p[to] == -1)
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{
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p[to] = v;
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if (match[to] == -1)
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return to;
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to = match[to];
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used[to] = true;
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q[qt++] = to;
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}
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}
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}
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return -1;
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}
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public static int maxMatching(List<Integer>[] graph)
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{
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int n = graph.length;
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int[] match = new int[n];
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Arrays.fill(match, -1);
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int[] p = new int[n];
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for (int i = 0; i < n; ++i)
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{
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if (match[i] == -1)
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{
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int v = findPath(graph, match, p, i);
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while (v != -1)
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{
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int pv = p[v];
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int ppv = match[pv];
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match[v] = pv;
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match[pv] = v;
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v = ppv;
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}
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}
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}
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int matches = 0;
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for (int i = 0; i < n; ++i)
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if (match[i] != -1)
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++matches;
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return matches / 2;
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}
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@SuppressWarnings("unchecked")
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public static void main(String[] args)
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{
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Scanner sc = new Scanner(System.in);
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System.out.println("Enter the number of vertices: ");
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int v = sc.nextInt();
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System.out.println("Enter the number of edges: ");
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int e = sc.nextInt();
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List<Integer>[] g = new List[v];
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for (int i = 0; i < v; i++)
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{
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g[i] = new ArrayList<Integer>();
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}
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System.out.println("Enter all the edges: <from> <to>");
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for (int i = 0; i < e; i++)
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{
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g[sc.nextInt()].add(sc.nextInt());
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}
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System.out.println("Maximum matching for the given graph is: "
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+ maxMatching(g));
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sc.close();
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}
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}
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/*
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Enter the number of vertices:
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6
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Enter the number of edges:
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7
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Enter all the edges: <from> <to>
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0 1
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1 2
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1 3
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3 4
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4 5
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5 3
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5 2
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Maximum matching for the given graph is: 3
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