Problem:
Bipartite Matching

A bipartite graph G = (V, E) is a graph in which the vertex set V can be divided into two disjoint subsets X and Y such that every edge e ∈ E has one end point in X and the other end point in Y.

A matching M is a subset of edges such that each node in V appears in at most one edge in M.

Given a bipartite graph, find the size of the matching which has the largest size.

Input

|X| |Y| |E|
x0 y0
x1 y1
:
x|E|-1 y|E|-1

|X| and |Y| are the number of vertices in X and Y respectively, and |E| is the number of edges in the graph G. The vertices in X are named with the numbers 0, 1,..., |X|-1, and vertices in Y are named with the numbers 0, 1,..., |Y|-1, respectively.

xi and yi are the node numbers from X and Y respectevely which represent the end-points of the i-th edge.

Output

Print the largest size of the matching.

Constraints

1 ≤ |X|, |Y| ≤ 100

0 ≤ |E| ≤ 10,000

Sample Input 1

3 4 6
0 0
0 2
0 3
1 1
2 1
2 3

Sample Output 1

3

Solution in JAVA (judge verdict: Wrong Answer)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Main{
	static int V;
	static int []match;
	static boolean []used;
	static Map<Integer, List<Integer>> G = new HashMap<Integer, List<Integer>>();
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int X = sc.nextInt();
		int Y = sc.nextInt();
		int E = sc.nextInt();
		int []x = new int[E];
		int []y = new int[E];
		for(int i = 0; i < E; i++) {
			x[i] = sc.nextInt();
			y[i] = sc.nextInt();
		}
		sc.close();
		V = Math.min(X, Y);
		match = new int[V];
		used = new boolean[V];
		for(int i = 0; i < E; i++) {
			if(G.containsKey(x[i])) {
				G.get(x[i]).add(y[i]);
			}else {
				List<Integer> list = new ArrayList<Integer>();
				list.add(y[i]);
				G.put(x[i], list);
			}
			if(G.containsKey(y[i])) {
				G.get(y[i]).add(x[i]);
			}else {
				List<Integer> list = new ArrayList<Integer>();
				list.add(x[i]);
				G.put(y[i], list);
			}
		}
		int max = bipatricleMatching();
		System.out.println(max);
	}
	static boolean dfs(int v) {
		used[v] = true;
		for(int i = 0; i < G.get(v).size(); i++) {
			int u = G.get(v).get(i);
			int w = match[u];
			if(w < 0 || !used[w] && dfs(w)) {
				match[v] = u;
				match[u] = v;
				return true;
			}
		}
		return false;
	}
	static int bipatricleMatching() {
		int res = 0;
		Arrays.fill(match, -1);
		for(int v = 0; v < V; v++) {
			if(match[v] < 0) {
				Arrays.fill(used, false);
				if(dfs(v)) res++;
			}
		}
		return res;
	}
}