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.Linq;//リストの使用
using System.Collections.Generic;

class EdgeData//辺
{
  internal int cap, flow;
  public EdgeData(){}
  public EdgeData(int cap, int flow)
  {
    this.cap = cap;
    this.flow = flow;
  }
}

class EdmondsKerp
{
  enum Color {White, Gray, Black}
  int n;
  int INFTY = int.MaxValue;
  EdgeData[,] G;
  int[] parent;
  int[] minCap;
  Color[] color;
 
  public EdmondsKerp(int V)
  {
    n = V;
    G = new EdgeData[n, n];
    for (int i = 0; i < n; i++)
    {
      for (int j = 0; j < n; j++)
      {
        G[i, j] = new EdgeData();
      }
    }
    parent = new int[n];
  }
 
  public void AddEdge(int from, int to, int cap)//辺を加える。引数は、始点、終点、容量。
  {
    G[from, to] = new EdgeData(cap, 0);
    G[to, from] = new EdgeData(0, cap);
  }
 
  public int MaxFlow(int s, int t)//最大流を求める
  {
    int maxFlow = 0;
    while (BFS(s, t))
    {
      maxFlow += minCap[t];
      int v = t;
      while (v != s)
      {
        int u = parent[v];
        G[u, v].flow += minCap[t];
        G[v, u].flow -= minCap[t];
        G[u, v].cap -= minCap[t];
        G[v, u].cap += minCap[t];
        v = u;
      }
    }
    return maxFlow;
  }

  private bool BFS(int s, int t)
  {
    minCap = Enumerable.Repeat(INFTY, n).ToArray();
    color = new Color[n];
    Queue<int> que = new Queue<int>();
    que.Enqueue(s);
    color[s] = Color.Gray;
 
    while (que.Count > 0)
    {
      int v = que.Dequeue();
      for (int u = 0; u < n; u++)
      {
        if (color[u] == Color.White && G[v, u].cap > 0)
        {
          minCap[u] = Math.Min(minCap[v], G[v, u].cap);
          parent[u] = v;
          color[u] = Color.Gray;
          if (u == t) return true;
          que.Enqueue(u);
        }
      }
    }
    return false;
  }
}
 
class Program
{
  static void Main()
  {
    string[] input = Console.ReadLine().Split(' ');
    int V = int.Parse(input[0]);
    int E = int.Parse(input[1]);
    EdmondsKerp EK = new EdmondsKerp(V);//グラフの作成（引数は頂点数）
 
    for (int i = 0; i < E; i++)
    {
      input = Console.ReadLine().Split(' ');
      int u = int.Parse(input[0]);
      int v = int.Parse(input[1]);
      int c = int.Parse(input[2]);
      EK.AddEdge(u, v, c);//辺を加える（始点、終点、容量）
    }
    Console.WriteLine(EK.MaxFlow(0, V-1));//引数は始点と終点。最大流を求める。
  }
}