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<stdio.h>
int MIN(int a,int b){return a<b?a:b;}
int V,D[1000][1000]={0};
int F[1000]={0};
int MF(int s,int t,int min){
  if(s==t)return min;
  int i,r;
  F[s]=1;//printf("\ns:%d ",s);
  for(i=0;i<V;i++){
    if(F[i]||D[s][i]==0)continue;//printf("i:%d ",i);
    r=MF(i,t,MIN(min,D[s][i]));
    D[s][i]-=r;
    D[i][s]+=r;
    if(r)return r;
  }
  return 0;
}
int maxf(int s,int t){
  int i,a,b=0;
  for(;a=MF(s,t,10000000);b+=a){
    for(i=0;i<V;i++)F[i]=0;
    /*for(i=0;i<V*V;i++){
      if(i%V==0)printf("\n");
      printf("%d ",D[i/V][i%V]);
    }
    printf("\n");//*/
  }
  return b;
}
int main(){
  int m,a,b,c,i;
  scanf("%d %d",&V,&m);
  for(;m--;D[a][b]=c)scanf("%d %d %d",&a,&b,&c);
  /*for(i=0;i<V*V;i++){
      if(i%V==0)printf("\n");
      printf("%d ",D[i/V][i%V]);
    }
    printf("\n");//*/
  printf("%d\n",maxf(0,V-1));
  return 0;
}