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 <iostream>
#include <cstdio>
#include <vector>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;
#define rep(i,n) for(int i=0;i<(n);i++)
const int INF = 1e9;
const int MAX_V = 110;

struct Flow{
    struct edge{
        int to, cap, rev;
    };
    vector<edge> G[MAX_V];//??£??\?????????
    bool used[MAX_V];

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

    //?¢???????????????¢???
    int dfs(int v, int t, int 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){
                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??????t???????????§???
    int max_flow(int s, int t){
        int flow = 0;
        while(1){
            memset(used, 0, sizeof(used));
            int f = dfs(s, t, INF);
            if(f == 0) return flow;
            flow += f;
        }
    }
};

int main(void){
	int V, E; cin >> V >> E;
	Flow mf;
	rep(i, E){
		int u, v, c; cin >> u >> v >> c;
		mf.add_edge(u, v, c);
	}
	printf("%d\n", mf.max_flow(0, V - 1));
	return 0;
}