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++14 (judge verdict: Accepted)

//AOJ-GRL-6-A
#include <bits/stdc++.h>
using namespace std;
#define REP(i,a) for(int i = 0; i < (a); i++)
#define ALL(a) (a).begin(),(a).end()
typedef long long ll;
typedef pair<int, int> P;
const int INF = 1e9;
const long long LINF = 1e18;
const long long MOD = 1e9 + 7;

template <typename T>
struct FordFulkerson{
    struct edge{
        int to;
        T cap;
        int rev;
        edge(int to, T cap, int rev) : to(to), cap(cap), rev(rev) {}
    };
    
    vector<vector<edge>> G;
    vector<bool> used;

    FordFulkerson(int n) : G(n), used(n) {}

    void add_edge(int from, int to, T cap){
        G[from].emplace_back(to, cap, G[to].size());
        G[to].emplace_back(from, 0, G[from].size() - 1);
    }

    T dfs(int v, int t, T f){
        if(v == t) return f;
        used[v] = true;
        for(int i = 0; i < G[v].size(); i++){
            edge & e = G[v][i];
            if(!used[e.to] && e.cap > 0){
                T 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;
    }

    T flow(int s, int t, T INF = 1e9){
        int fl = 0;
        while(true){
            fill(used.begin(), used.end(), false);
            T f = dfs(s, t, INF);
            if(f == 0) break;
            fl += f;
        }
        return fl;
    }
};

signed main(){
    int V,E;
    cin >> V >> E;
    FordFulkerson<ll> f(V);
    int u, v;
    ll c;
    REP(i,E){
        cin >> u >> v >> c;
        f.add_edge(u, v, c);
    }
    cout << f.flow(0, V - 1, LINF) << endl;
    return 0;
}