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: Time Limit Exceeded)

#include<stdio.h>
int MIN(int a,int b){return a<b?a:b;}
int ta[100010],to[100010],co[100010],nt[100010],it[100010],l[100010];
void mklsb(int v,int e,int *a,int *b,int *c){
  int i;
  for(i=0;i<v;i++)ta[i]=-1;
  for(i=0;i<e;i++){
    nt[i  ]=ta[to[i+e]=a[i]];
    nt[i+e]=ta[to[i  ]=b[i]];
    co[ta[a[i]]=i  ]=c[i];      
    co[ta[b[i]]=i+e]=0;
  }
}
int MF(int e,int s,int t,int min){
  if(s==t)return min;
  int i,r;
  for(;it[s]+1;it[s]=nt[it[s]]){
    if(co[it[s]]==0||l[s]>=l[to[it[s]]])continue;
    r=MF(e,to[it[s]],t,MIN(min,co[it[s]]));
    co[it[s]]-=r;
    co[(it[s]+e)%(2*e)]+=r;
    if(r)return r;
  }
  return 0;
}
int maxf(int v,int e,int s,int g){
  int i,a=0,q[100010],t,r,c=3;
  while(1){
    for(i=t=0;i<v;i++)l[i]=0;
    l[q[0]=s]=1;
    for(r=1;r-t;t++){
      for(i=ta[q[t]];i+1;i=nt[i]){
	if(co[i]&&l[to[i]]==0)l[q[r++]=to[i]]=l[q[t]]+1;
      }
    }
    if(l[g]<0)return a;
    for(i=0;i<v;i++)it[i]=ta[i];
    while(r=MF(e,s,g,1e9))a+=r;
  }
}
int main(){
  int n,m,i,a[100010],b[100010],c[1000010],m1,m2;
  scanf("%d %d",&n,&m);
  for(i=0;i<m;i++)scanf("%d %d %d",&a[i],&b[i],&c[i]);
  mklsb(n,m,a,b,c);//prls(n);
  printf("%d\n",maxf (n,m,0,n-1));
  return 0;
}