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>
#include<string.h>
#define MIN(a,b) ((a) < (b) ? (a) : (b))
#define MAX 100
#define INF 100000000

int adj[MAX][MAX];
int visited[MAX];
int v;

int dfs(int u,int t,int f){
	int i;

	if(u == t)return f;
	
	visited[u]=1;

	for(i=0;i<v;i++){
		if(visited[i]==0 && adj[u][i]>0){
			int d=dfs(i,t,MIN(f,adj[u][i]));
			if(d > 0){
				adj[u][i]-=d;
				adj[i][u]+=d;
				return d;
			}
		}
	}

	return 0;
}


int max_flow(int s,int t){
	int flow=0;
	
	while(1){
		memset(visited,0,sizeof(visited));
		int f=dfs(s,t,INF);
		if(f==0)return flow;
		flow+=f;
		
	}
	return 0;
	
}


int main(){
	int e;
	int x,y,z,i,j;
	
	scanf("%d %d",&v,&e);
	
	for(i=0;i<v;i++){
		for(j=0;j<v;j++){
			adj[i][j]=0;
		}
	}
	
	
	for(i=0;i<e;i++){
		scanf("%d %d %d",&x,&y,&z);
		adj[x][y]=z;
	}
	
	printf("%d\n",max_flow(0,v-1));
	

	
	return 0;
}