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++11 (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <algorithm>

#define rep(i,n) for(int i=0; i<(n); i++)

using namespace std;
typedef pair<int,int> pii;

const int INF = 0x3fffffff;

int V, E;
int C[1005];
int F[1005];
vector<pii> e[105];
int solve(int n, int c, vector<bool> bf){
	if( bf[n] ) return 0;
	if( n == V-1 ) return c;
	bf[n] = true;
	for(auto to: e[n]){
		int i = to.second;
		int cc = ( i>0 ? C[i]-F[i] : F[-i] );
		int flow = solve(to.first, min(c, cc), bf); 
		if( flow > 0 ){
			F[ abs(i) ] += flow * (i/abs(i));
			return flow;
		}
	}
	return 0;
}

int main(){
	cin >> V >> E;
	rep(i,E+1){
		if(i==0) continue;
		int u, v, c;
		cin >> u >> v >> c;
		e[u].emplace_back(v,  i);
		e[v].emplace_back(u, -i);
		C[i] = c;
	}
	int ans = 0;
	vector<bool> bf(105, false);
	for(int add; add = solve(0,INF,bf);) ans += add;

	cout << ans << endl;

	return 0;
}