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)

#include <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <cmath>
#include <stack>
#include <set>
#include <map>
typedef long long ll;
using namespace std;

//=========================================
#define MAX_V 10000
const int INF = 1 << 30;

//辺を表す構造体(行先，容量，逆辺)
struct edge{
  int to, cap, rev;
};

vector<edge> G[MAX_V];
bool used[MAX_V];

//辺の追加
void add_edge(int from, int to, int cap){
  G[from].push_back(edge{to, cap, (int)G[to].size()});
  G[to].push_back(edge{from, 0, (int)G[from].size() - 1});
}

//増加パスをDFSで探す
int dfs(int v, int t, int f){
  if(v == t) return f;
  used[v] = true;
  for(int i = 0; i < (int)G[v].size(); i++){
    edge &e = G[v][i];
    if(!used[e.to] && e.cap > 0){
      int d = dfs(e.to, t, min(f, e.cap));
      if(d > 0){
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}

//sからtへの最大流を求める
int max_flow(int s, int t){
  int flow = 0;
  for(;;){
    fill(used, used + MAX_V, false);
    int f = dfs(s, t, INF);
    if(f == 0) return flow;
    flow += f;
  }
}

//==============================================
int main(){
  int N, M;
  cin >> N >> M;

  for(int i = 0; i < M; i++){
    int u, v, c;
    cin >> u >> v >> c;
    add_edge(u, v, c);
  }

  cout << max_flow(0, N - 1) << endl;
  return 0;
}