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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;
using Pair = System.Collections.Generic.KeyValuePair<int, int>;

//Ford-Fulkerson O(F*|E|)
class Program
{
    static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        new Program().solve();
        Console.Out.Flush();
    }
    Scanner cin = new Scanner();

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

    bool[] used;
    List<Edge>[] G;
    int V, E;
    void solve()
    {
        V = cin.nextint;
        E = cin.nextint;

        G = Enumerable.Range(0, V).Select(i => new List<Edge>()).ToArray();
        

        for (int i = 0; i < E; i++)
        {
            var u = cin.scanint;
            G[u[0]].Add(new Edge(u[1], u[2], G[u[1]].Count));
            G[u[1]].Add(new Edge(u[0], 0, G[u[0]].Count - 1));
        }

        int flow = 0;
        while (true)
        {
            used = new bool[V];
            int f = dfs(0, V - 1, int.MaxValue);
            if (f == 0) break;
            flow += f;
        }
        Console.WriteLine(flow);
    }

    int dfs(int v, int t, int f)
    {
        if (v == t) return f;
        used[v] = true;
        for (int i = 0; i < G[v].Count; i++)
        {
            var e = G[v][i];
            if (used[e.to] || e.cap == 0) continue;
            int d = dfs(e.to, t, Math.Min(f, e.cap));
            if (d > 0)
            {
                e.cap -= d;
                G[e.to][e.rev].cap += d;
                return d;
            }         
        }
        return 0;
    }
}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return Console.ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}