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 <string.h>
#include <vector>
using namespace std;

struct edge{ int to, cap, rev;};
int INF = 100000000;
bool used[100];

int dfs(vector< vector <edge> > &G, 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(G, 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(vector< vector <edge> > &G, int s, int t){
  int flow = 0;
  for(;;){
    memset(used, 0, sizeof(used));
    int f = dfs(G, s, t, INF);
    if(!f) return flow;
    flow += f;
  }
}


int main(){
  int V, E;
  cin >> V >> E;
  vector< vector <edge> > G(V);
  int u, v, c;
  for(int i = 0; i < E; ++i){
    cin >> u >> v >> c;
    G[u].push_back((edge){v,c,G[v].size()});
    G[v].push_back((edge){u,0,G[u].size()-1});
  }
  cout << max_flow(G, 0, V-1) << endl;;
  return 0;
}