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 <vector>

using namespace std;

struct edge{
	int to, cap, rev;
};

int V, E;
vector<edge> G[105];
bool used[105];

int dfs(int s, int t, int c)
{
	if(s == t) return c;
	used[s] = true;
	
	int ret;
	for(int i = 0; i < (int)G[s].size(); i++){
		if(used[G[s][i].to] || G[s][i].cap == 0) continue;
		ret = dfs(G[s][i].to, t, min(c, G[s][i].cap));
		if(ret > 0){
			G[s][i].cap -= ret;
			G[ G[s][i].to ][ G[s][i].rev ].cap += ret;
			return ret;
		}
	}
	return 0;
}

int main(void)
{
	cin >> V >> E;
	
	int a, b, c;
	for(int i = 0; i < E; i++){
		cin >> a >> b >> c;
		G[a].push_back((edge){b, c, G[b].size()});
		G[b].push_back((edge){a, 0, G[a].size()-1});
	}
	
	int ans = 0, ret;
	while(1){
		for(int i = 0; i < V; i++) used[i] = false;
		ret = dfs(0, V-1, 10000000);
		if(ret == 0) break;
		ans += ret;
	}
	
	cout << ans << endl;
	return 0;
}