Problem:
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Maximum Flow

A flow network is a directed graph which has a $source$ and a $sink$. In a flow network, each edge $(u, v)$ has a capacity $c(u, v)$. Each edge receives a flow, but the amount of flow on the edge can not exceed the corresponding capacity. Find the maximum flow from the $source$ to the $sink$.

Input

A flow network is given in the following format.

$|V|\;|E|$

$u_0\;v_0\;c_0$

$u_1\;v_1\;c_1$

:

$u_{|E|-1}\;v_{|E|-1}\;c_{|E|-1}$

$|V|$, $|E|$ is the number of vertices and edges of the flow network respectively. The vertices in $G$ are named with the numbers 0, 1,..., $|V|-1$. The source is 0 and the sink is $|V|-1$.

$u_i$, $v_i$, $c_i$ represent $i$-th edge of the flow network.
A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$ and $c_i$ is the capacity of $i$-th edge.

Output

Print the maximum flow.

Constraints

$2 \leq |V| \leq 100$

$1 \leq |E| \leq 1000$

$0 \leq c_i \leq 10000$

Sample Input 1

4 5
0 1 2
0 2 1
1 2 1
1 3 1
2 3 2

Sample Output 1

3

Solution in JAVA (judge verdict: Accepted)

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

public class Main {
	@SuppressWarnings("unchecked")
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int V = in.nextInt();
		int E = in.nextInt();

		used = new boolean[V];
		lEdge = new List[V];
		for (int i=0;i<V;i++) {
			lEdge[i] = new ArrayList<Edge>();
		}
		
		for (int i=0;i<E;i++) {
			addEdge(in.nextInt(), in.nextInt(), in.nextInt());
		}
		
		int res = 0;
		while(true) {
			Arrays.fill(used, false);
			int ret = dfs(0, V-1, Integer.MAX_VALUE);
			if (ret==0) break;
			res += ret;
		}
		System.out.println(res);
	}
	static List<Edge>[] lEdge;
	static void addEdge(int fr, int to, int cap) {
		lEdge[fr].add(new Edge(to, cap, lEdge[to].size()));
		lEdge[to].add(new Edge(fr, 0, lEdge[fr].size()-1));
	}
	
	static class Edge {
		int to, cap, rev;
		public Edge(int to, int cap, int rev) {
			this.to= to;
			this.cap = cap;
			this.rev = rev;
		}
	}

	static boolean[] used;
	
	static int dfs (int fr, int to, int f) {
		if (fr==to) return f;
		used[fr] = true;
		
		for (int i=0;i<lEdge[fr].size();i++) {
			Edge e = lEdge[fr].get(i);
			if (!used[e.to] && e.cap>0) {
				int dist = dfs(e.to, to, Math.min(f, e.cap));
				if (dist>0) {
					e.cap -=dist;
					lEdge[e.to].get(e.rev).cap += dist;
					return dist;
				}
			}
		}
		return 0;
	}
	
}