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.IO;
using SB = System.Text.StringBuilder;
//using System.Threading.Tasks;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using System.Numerics;
using static System.Math;
using pair = Pair<int, int>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }

    void solve()
    {
        int V = cin.nextint;
        int E = cin.nextint;
        var D = new Dinic(V);
        for (int i = 0; i < E; i++)
        {
            D.add_edge(cin.nextint, cin.nextint, cin.nextlong);
        }
        WriteLine(D.max_flow(0, V - 1));
    }

}


class Dinic
{
    // 辺を表すクラス（行き先、容量、逆辺）
    class Edge_
    {
        public int to;
        public long cap;
        public int rev;
        public Edge_(int to, long cap, int rev)
        {
            this.to = to;
            this.cap = cap;
            this.rev = rev;
        }
    }
    public const long INF = long.MaxValue / 3;
    List<Edge_>[] G; // グラフの隣接リスト表現
    int[] level;    // sからの距離
    int[] iter;     // どこまで調べ終わったか
    public Dinic(int V)
    {
        G = new List<Edge_>[V];
        for (int i = 0; i < V; i++) G[i] = new List<Edge_>();
        level = new int[V];
        iter = new int[V];
    }
    // fromからtoへ向かう容量capの辺をグラフに追加する
    public void add_edge(int from, int to, long cap)
    {
        G[from].Add(new Edge_(to, cap, G[to].Count));
        G[to].Add(new Edge_(from, 0, G[from].Count - 1));
    }
    // sからの最短距離をBFSで計算する
    void bfs(int s)
    {
        for (int i = 0; i < level.Length; i++) level[i] = -1;
        var que = new Queue<int>();
        level[s] = 0;
        que.Enqueue(s);
        while (que.Any())
        {
            int v = que.Dequeue();
            foreach (Edge_ e in G[v])
            {
                if (e.cap > 0 && level[e.to] < 0)
                {
                    level[e.to] = level[v] + 1;
                    que.Enqueue(e.to);
                }
            }
        }
    }
    //増加パスをDFSで探す
    long dfs(int v, int t, long f)
    {
        if (v == t) return f;
        for (; iter[v] < G[v].Count; iter[v]++)
        {
            Edge_ e = G[v][iter[v]];
            if (e.cap <= 0 || level[v] >= level[e.to]) continue;

            long df = dfs(e.to, t, Math.Min(f, e.cap));
            if (df <= 0) continue;
            e.cap -= df;
            G[e.to][e.rev].cap += df;
            return df;
        }
        return 0;
    }
    // sからtへの最大流を求める
    public long max_flow(int s, int t)
    {
        long flow = 0;
        while (true)
        {
            bfs(s);
            if (level[t] < 0) return flow;
            for (int i = 0; i < iter.Length; i++) iter[i] = 0;
            while (true)
            {
                long f = dfs(s, t, INF);
                if (f <= 0) break;
                flow += f;
            }
        }
    }
}

static class Ex
{
    public static void join<T>(this IEnumerable<T> values, string sep = " ") => WriteLine(string.Join(sep, values));
    public static string concat<T>(this IEnumerable<T> values) => string.Concat(values);
    public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); }

    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}

class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f; public U s;
    public Pair(T f, U s) { this.f = f; this.s = s; }
    public int CompareTo(Pair<T, U> a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    public override string ToString() => $"{f} {s}";
}

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