BOJ 313 Candy

源向每个小孩连边，容量是该小孩的初始糖数；
每个小孩向汇连边，容量是糖的平均数；
每个小孩想相邻的格子各连一条边，容量是1.

把图建好就很简单了

 

#include<stdio.h>
#include<cstring>
#include<math.h>
#define inf 100000000
#define min(a,b) ((a)>(b))?(b):(a)
using namespace std;
int a,b,map[55][55];
int n,k,dist[3000],gap[3000],edgeHead[3000];//双向边
struct{
    int v,cap,next,re;
}edge[40000];

void addEdge(int u,int v,int ca){
    edge[k].v=v;
    edge[k].cap=ca;
    edge[k].next=edgeHead[u];
    edge[k].re=k + 1;               //这个用来记录此边的反边
    edgeHead[u]=k ++;
    edge[k].v=u;
    edge[k].cap=0;                 //这里是双向边
    edge[k].next=edgeHead[v];
    edge[k].re=k - 1;
    edgeHead[v]=k ++;
}
int dfs (int p , int limit)
{
    if(p==n)return limit;

    for(int i=edgeHead[p];i!=0;i=edge[i].next){
        int v = edge[i].v;
        if(dist[p]==(dist[v]+1) && edge[i].cap>0){
            int t=dfs(v,min(limit , edge[i].cap));
            if(t<0)return t;//没有增广路了
            if(t>0)//更新流
            {
                edge[i].cap-=t;
                edge[edge[i].re].cap+=t;
                return t;
            }
        }
    }

    int tmp=n+1;
    for(int i=edgeHead[p];i!=0;i=edge[i].next){
        int v = edge[i].v;
        if(edge[i].cap>0)
            tmp=min(tmp,dist[v]+1);
    }

    if(--gap[dist[p]]==0 || dist[0]>n)return -1;//出现断层或回流已满
    ++gap[dist[p]=tmp];
    return 0;
}

int SAP()
{
    gap[0]=n+1;
    int f = 0 , t=0;
    while (~(t=dfs(0,inf))) f+=t;
    return f;
}
int main(){
	int i,j,v,e,sum;
	while(scanf("%d %d",&v,&e)!=EOF){
		sum=0;
		memset(edgeHead,0,sizeof(edgeHead));
		memset(dist,0,sizeof(dist));
		memset (gap , 0 , sizeof(gap));
		k=1;
		for(i=1;i<=v;i++)
			for(j=1;j<=e;j++){
				scanf("%d",&map[i][j]);
				sum+=map[i][j];
			}
		if(sum%(v*e)!=0){
			printf("NO\n");
			continue;
		}
		for(i=1;i<=v;i++)
			for(j=1;j<=e;j++){
				addEdge(0,(i-1)*e+j,map[i][j]);
				addEdge((i-1)*e+j,v*e+1,sum/(v*e));
				if(i-1>0)
					addEdge((i-1)*e+j,(i-1)*e-e+j,1);
				if(j-1>0)
					addEdge((i-1)*e+j,(i-1)*e+j-1,1);
				if(i+1<=v)
					addEdge((i-1)*e+j,(i-1)*e+e+j,1);
				if(j+1<=e)
					addEdge((i-1)*e+j,(i-1)*e+j+1,1);
			}
		n=v*e+1;
		int k=SAP();
		if(k==sum)
			printf("YES\n");
		else
			printf("NO\n");
	}
}