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;

namespace ConsoleApplication1
{
    class Edge
    {
        internal int to, cap, flow, rev;

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

    class Dinic
    {
        readonly int n;
        readonly int INFTY = int.MaxValue;

        Dictionary<int, List<Edge>> G;
        int[] level, prog;
        int s, t;

        public Dinic(int V)
        {
            n = V;

            G = new Dictionary<int, List<Edge>>();
            for (int i = 0; i < n; i++) G.Add(i, new List<Edge>());
        }

        public void AddEdge(int from, int to, int cap)
        {
            G[from].Add(new Edge(to, cap, 0, G[to].Count));
            G[to].Add(new Edge(from, cap, cap, G[from].Count - 1));
        }

        public int MaxFlow(int source, int sink)
        {
            s = source;
            t = sink;

            int maxFlow = 0;

            while (Levelize())
            {
                prog = new int[n];
                maxFlow += Augment(s, INFTY);
            }
            return maxFlow;
        }

        private bool Levelize()
        {
            Queue<int> que = new Queue<int>();
            que.Enqueue(s);

            level = Enumerable.Repeat(-1, n).ToArray();
            level[s] = 0;

            while (que.Count > 0)
            {
                int v = que.Dequeue();

                if (v == t) break;

                foreach (var e in G[v])
                {
                    int next = e.to;

                    if (level[next] == -1 && e.cap - e.flow != 0)
                    {
                        level[next] = level[v] + 1;
                        que.Enqueue(next);
                    }
                }
            }
            return level[t] != -1;
        }

        private int Augment(int v, int limit)
        {
            int ret = 0;

            if (v == t) return limit;

            for (int i = prog[v]; i < G[v].Count; i++)
            {
                if (limit == 0) break;

                Edge e = G[v][i];
                int next = e.to;

                if (level[v] < level[next] && e.cap - e.flow != 0)
                {
                    int aug = Augment(next, Math.Min(limit, e.cap - e.flow));
                    e.flow += aug;
                    G[next][e.rev].flow -= aug;
                    ret += aug;
                    limit -= aug;
                }
            }
            return ret;
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int V = int.Parse(input[0]);
            int E = int.Parse(input[1]);

            Dinic Dc = new Dinic(V);

            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]);

                Dc.AddEdge(u, v, c);
            }

            Console.WriteLine(Dc.MaxFlow(0, V - 1));
        }
    }
}