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>
#include <cstring>

#define MAX_V 102
#define INF (int)1e9

using namespace std;


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,(int)G[to].size()});
	G[to].push_back((edge){from,0,(int)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(f,e.cap));
			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 flow = 0;
	for(;;){
		memset(used,0,sizeof(used));
		int f = dfs(s,t,INF);
		if(f == 0) return flow;
		flow += f;
	}
}
int main(){
	int V,E,c[3][E];
	cin >> V >> E;
	for (int i = 0; i < E; ++i)
	{
		int from,to,cap;
		cin >> from >> to >> cap;
		add_edge(from,to,cap);
	}
	int ans = max_flow(0,V-1);
	cout << ans << endl;
	return 0;
}