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 <cstdio>
#include <algorithm>
#include <vector>

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

using namespace std;

const int inf = (int)2e7;

struct E{
	E(int t, int c, int r) :
		t(t), c(c), r(r)
	{}

	int t, c, r;
};

int n, m;
vector<E> g[100];
bool used[100];

void mf_add_edge(int a, int b, int c){
	g[a].push_back(E(b, c, g[b].size()));
	g[b].push_back(E(a, 0, g[a].size() - 1));
}

int mf_dfs(int v, int t, int f){
	if(v == t){
		return f;
	}
	used[v] = true;
	rep(i, g[v].size()){
		E& e = g[v][i];
		if(!used[e.t] && e.c > 0){
			int d = mf_dfs(e.t, t, min(e.c, f));
			if(d > 0){
				e.c -= d;
				g[e.t][e.r].c += d;
				return d;
			}
		}
	}
	return 0;
}

int mf_max_flow(int s, int t){
	int ans = 0;
	while(1){
		fill(used, used + n, false);
		int f = mf_dfs(s, t, inf);
		if(f == 0){
			return ans;
		}
		ans += f;
	}
}

int main(){
	scanf("%d%d", &n, &m);
	rep(i, m){
		int a, b, c;
		scanf("%d%d%d", &a, &b, &c);
		mf_add_edge(a, b, c);
	}
	printf("%d\n", mf_max_flow(0, n - 1));
	return 0;
}