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: Wrong Answer)


import java.io.*;
import java.util.*;
//import java.util.stream.Stream;

/**
 * @author baito
 */

public class Main
{
    //static List<Edge>[] edges;
    static boolean[] used;

    public static void main(String[] args)
    {
        Scanner sc = new Scanner(System.in);
        int V = sc.nextInt();
        int E = sc.nextInt();
        //edges = Stream.generate(ArrayList::new).limit(V).toArray(ArrayList[]::new);
        //edges = new ArrayList[V];
        for (int i = 0; i < V; i++)
        {
          //  edges[i] = new ArrayList<Edge>();
        }
//
//        used = new boolean[V];
//        for (int i = 0; i < E; i++)
//        {
//            addEdge(sc.nextInt(), sc.nextInt(), sc.nextInt());
//        }
//        int res = fordFulkerson(0, V - 1);
//        System.out.println(res);
    }

//    public static int dfs(int now, int goal, int f)
//    {
//        if (now == goal)
//        {
//            return f;
//        }
//        used[now] = true;
//        for (int i = 0; i < edges[now].size(); i++)
//        {
//            Edge e = edges[now].get(i);
//            if (!used[e.to] && e.cap > 0)
//            {
//                int flow = dfs(e.to, goal, Math.min(f, e.cap));
//                if (flow == 0) continue;
//                e.cap -= flow;
//                edges[e.to].get(e.rev).cap += flow;
//                return flow;
//            }
//        }
//        return 0;
//    }

//    public static int fordFulkerson(int s, int e)
//    {
//        int flow = 0;
//        while (true)
//        {
//            Arrays.fill(used, false);
//            int river = dfs(s, e, Integer.MAX_VALUE);
//            if (river == 0) return flow;
//            flow += river;
//        }
//    }
//
//    public static void addEdge(int f, int t, int c)
//    {
//        edges[f].add(new Edge(t, c, edges[t].size()));
//        edges[t].add(new Edge(f, 0, edges[f].size() - 1));
//    }

    static class Edge
    {
        int to, cap, rev;

        Edge(int to, int cap, int rev)
        {
            this.to = to;
            this.cap = cap;
            this.rev = rev;
        }
    }


}