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.ArrayDeque;
import java.util.Arrays;
import java.util.Scanner;

class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	class Edge {
		int src;
		int dst;
		int cap;

		public Edge(int src, int dst, int cap) {
			this.src = src;
			this.dst = dst;
			this.cap = cap;
		}
	}

	void solve(int V, int E, int[][] cap, int[][] flow, int s, int t) {
		int tot = 0;
		while (true) {
			int[] pre = new int[V];
			Arrays.fill(pre, -1);
			ArrayDeque<Integer> que = new ArrayDeque<>();
			que.add(s);
			out: while (!que.isEmpty()) {
				int cur = que.poll();
				for (int dst = 0; dst < V; ++dst) {
					if (cap[cur][dst] - flow[cur][dst] <= 0)
						continue;
					if (pre[dst] != -1 && dst != s)
						continue;
					pre[dst] = cur;
					if (dst == t)
						break out;
					que.add(dst);
				}
			}
			if (pre[t] == -1)
				break;
			int inc = Integer.MAX_VALUE / 16;
			for (int i = t; i != s; i = pre[i]) {
				inc = Math.min(inc, cap[pre[i]][i] - flow[pre[i]][i]);
			}
			for (int i = t; i != s; i = pre[i]) {
				flow[pre[i]][i] += inc;
				flow[i][pre[i]] -= inc;
			}
			tot += inc;
		}
		System.out.println(tot);

	}

	void run() {
		Scanner sc = new Scanner(System.in);
		int V = sc.nextInt();
		int E = sc.nextInt();
		int[][] cap = new int[V][V];
		int[][] flow = new int[V][V];
		for (int i = 0; i < E; ++i) {
			int u = sc.nextInt();
			int v = sc.nextInt();
			int c = sc.nextInt();
			cap[u][v] = c;
		}
		int s = 0;
		int t = V - 1;

		solve(V, E, cap, flow, s, t);
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}