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;

namespace No421{
    public class Program{
        public static void Main(string[] args){
            var sr = new StreamReader();
            //---------------------------------
            var V = sr.Next<int>();
            var E = sr.Next<int>();

            var dinic = new Dinic(V);
            for(var i = 0; i < E; i++){
                dinic.AddEdge(sr.Next<int>(), sr.Next<int>(), sr.Next<int>());
            }

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

    public class Dinic{//????P194
        public class Edge{
            public int To;
            public int Cap;
            public int Rev;
        }

        private readonly List<Edge>[] _adj;
        private readonly int[] _level;
        private readonly int[] _iter;

        public Dinic(int v){
            _adj = new List<Edge>[v];
            for(var i = 0; i < v; i++) _adj[i] = new List<Edge>();
            _level = new int[v];
            _iter = new int[v];
        }

        public void AddEdge(int from, int to, int cap){
            _adj[from].Add(new Edge{To = to, Cap = cap, Rev = _adj[to].Count});
            _adj[to].Add(new Edge{To = from, Cap = 0, Rev = _adj[from].Count - 1});
        }

        public int MaxFlow(int s, int t){
            var flow = 0;
            while(true){
                Bfs(s);
                if(_level[t] < 0) return flow;
                for(var i = 0; i < _iter.Length; i++) _iter[i] = 0;
                int f;
                while((f = Dfs(s, t, int.MaxValue)) > 0) flow += f;
            }
        }

        private void Bfs(int s){
            for(var i = 0; i < _level.Length; i++) _level[i] = -1;
            var que = new Queue<int>();
            _level[s] = 0;
            que.Enqueue(s);

            while(que.Count > 0){
                var v = que.Dequeue();
                for(var i = 0; i < _adj[v].Count; i++){
                    var e = _adj[v][i];
                    if(e.Cap > 0 && _level[e.To] < 0){
                        _level[e.To] = _level[v] + 1;
                        que.Enqueue(e.To);
                    }
                }
            }
        }

        private int Dfs(int v, int t, int f){
            if(v == t) return f;
            for(var i = _iter[v]; i < _adj[v].Count; i++){
                var e = _adj[v][i];
                if(e.Cap > 0 && _level[v] < _level[e.To]){
                    var d = Dfs(e.To, t, Math.Min(f, e.Cap));
                    if(d > 0){
                        e.Cap -= d;
                        _adj[e.To][e.Rev].Cap += d;
                        return d;
                    }
                }
            }
            return 0;
        }
    }

    public class StreamReader{
        private readonly char[] _c = {' '};
        private int _index = -1;
        private string[] _input = new string[0];
        private readonly System.IO.StreamReader _sr = new System.IO.StreamReader(Console.OpenStandardInput());

        public T Next<T>(){
            if(_index == _input.Length - 1){
                _index = -1;
                while(true){
                    string rl = _sr.ReadLine();
                    if(rl == null){
                        if(typeof(T).IsClass) return default(T);
                        return (T)typeof(T).GetField("MinValue").GetValue(null);
                    }
                    if(rl != ""){
                        _input = rl.Split(_c, StringSplitOptions.RemoveEmptyEntries);
                        break;
                    }
                }
            }
            return (T)Convert.ChangeType(_input[++_index], typeof(T), System.Globalization.CultureInfo.InvariantCulture);
        }

        public T[] Next<T>(int x){
            var ret = new T[x];
            for(var i = 0; i < x; ++i) ret[i] = Next<T>();
            return ret;
        }

        public T[][] Next<T>(int y, int x){
            var ret = new T[y][];
            for(var i = 0; i < y; ++i) ret[i] = Next<T>(x);
            return ret;
        }
    }
}