上下界最大流(邻接表形式).txt

ACM资料大集合

//求上下界网络最大流,邻接表形式
//返回最大流量,-1表示无可行流,flow返回每条边的流量
//传入网络节点数n,容量mat,流量下界bf,源点source,汇点sink
//MAXN应比最大结点数多2,无可行流返回-1时mat未复原!

#define MAXN 100
#define inf 1000000000

int _max_flow(int n,int mat[][MAXN],int source,int sink,int flow[][MAXN]){
	int pre[MAXN],que[MAXN],d[MAXN],p,q,t,i,j,r;
	vector<int> e[MAXN];	
	for (i=0;i<n;i++)
		for (e[i].clear(),j=0;j<n;j++)
			if (mat[i][j]) e[i].push_back(j),e[j].push_back(i);
	for (;;){
		for (i=0;i<n;pre[i++]=0);
		pre[t=source]=source+1,d[t]=inf;
		for (p=q=0;p<=q&&!pre[sink];t=que[p++])
			for (r=0;r<e[t].size();++r){
				i=e[t][r];			
				if (!pre[i]&&(j=mat[t][i]-flow[t][i]))
					pre[que[q++]=i]=t+1,d[i]=d[t]<j?d[t]:j;
				else if (!pre[i]&&(j=flow[i][t]))
					pre[que[q++]=i]=-t-1,d[i]=d[t]<j?d[t]:j;
			}
		if (!pre[sink]) break;
		for (i=sink;i!=source;)
			if (pre[i]>0)
				flow[pre[i]-1][i]+=d[sink],i=pre[i]-1;
			else
				flow[i][-pre[i]-1]-=d[sink],i=-pre[i]-1;
	}
	for (j=i=0;i<n;j+=flow[source][i++]);
	return j;
}
int limit_max_flow(int n,int mat[][MAXN],int bf[][MAXN],int source,int sink,int flow[][MAXN]){
	int i,j,sk,ks;
	if (source==sink) return inf;
	for (mat[n][n+1]=mat[n+1][n]=mat[n][n]=mat[n+1][n+1]=i=0;i<n;i++)
		for (mat[n][i]=mat[i][n]=mat[n+1][i]=mat[i][n+1]=j=0;j<n;j++)
			mat[i][j]-=bf[i][j],mat[n][i]+=bf[j][i],mat[i][n+1]+=bf[i][j];
	sk=mat[source][sink],ks=mat[sink][source],mat[source][sink]=mat[sink][source]=inf;
	for (i=0;i<n+2;i++)
		for (j=0;j<n+2;flow[i][j++]=0);
	_max_flow(n+2,mat,n,n+1,flow);
	for (i=0;i<n;i++)
		if (flow[n][i]<mat[n][i]) return -1;
	flow[source][sink]=flow[sink][source]=0,mat[source][sink]=sk,mat[sink][source]=ks;
	_max_flow(n,mat,source,sink,flow);
	for (i=0;i<n;i++)
		for (j=0;j<n;j++)
			mat[i][j]+=bf[i][j],flow[i][j]+=bf[i][j];
	for (j=i=0;i<n;j+=flow[source][i++]);
	return j;
}