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<vector>
#include<algorithm>
using namespace std;

struct edge{int to,cap,rev;};
const int INF = 1000000000;

vector <edge> G[100];
bool used[100];

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

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(e.cap,f));
			if(d>0){
				e.cap -= d;
				G[e.to][e.rev].cap += d;
				return d;
			}
		}
	}
	return 0;
}

int max_flow(int s,int t,int V){
	int flow = 0;
	while(true){
		fill(used,used+V,false);
		int f = dfs(0,t,INF);
		if(f==0) return flow;
		else flow += f;
	}
}

int main(){
	int V,E;
	scanf("%d %d",&V,&E);
	for(int i=0;i<E;i++){
		int u,v,c;
		scanf("%d %d %d",&u,&v,&c);
		add_edge(u,v,c);
	}
	printf("%d\n",max_flow(0,V-1,V));
	return 0;
}