hdu2426 Interesting Housing Problem (KM邻接表)

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=2426

题解：最大权值单边（nx的每一个点都在匹配中）完备匹配,不能把学生安排在rate小于0的房间,负权边舍弃。

#include <stdio.h>    
#include <string.h> 
#define INF 0x3f3f3f3f    
#define MAXN 502    

int w[MAXN][MAXN],match[MAXN];    
int lx[MAXN],ly[MAXN],slack[MAXN];    
int visitx[MAXN],visity[MAXN];  
int nx,ny;

int find(int x)
{  
	int i,temp;  
	visitx[x]=1;  
	for(i=0;i<ny;++i)  
	{  
		if(visity[i])  
			continue;  
		temp=lx[x]+ly[i]-w[x][i];  
		if(temp==0)  
		{  
			visity[i]=1;  
			if(match[i]==-1||find(match[i]))  
			{  
				match[i]=x;  
				return 1;  
			}  
		}  
		else if(slack[i]>temp)  
		{  
			slack[i]=temp;  
		}  
	}  
	return 0;  
}  

int KM()  
{  
	int i,j,d,sum,cnt;  
	memset(ly,0,sizeof(ly));  
	memset(match,-1,sizeof(match));  
	for(i=0;i<nx;++i)  
	{//lx初始化为与它关联边中最大的  
		lx[i]=w[i][0];  
		for(j=1;j<ny;++j)  
			if(w[i][j]>lx[i])  
				lx[i]=w[i][j];  
	}  
	for(i=0;i<nx;++i)  
	{  
		for(j=0;j<ny;++j)  
			slack[j]=INF;  
		while(1)  
		{  
			memset(visitx,0,sizeof(visitx));  
			memset(visity,0,sizeof(visity));  
			if(find(i))  
				break;  
			d=INF;  
			for(j=0;j<ny;++j)  
			{  
				if(!visity[j]&&d>slack[j])  
					d=slack[j];  
			}  
			for(j=0;j<nx;++j)  
			{  
				if(visitx[j])  
					lx[j]-=d;  
			}  
			for(j=0;j<ny;++j)  
			{  
				if(visity[j])  
					ly[j]+=d;  
				else  
					slack[j]-=d;  
			}  
		}  
	}  
	sum=0;
	cnt=0;  
	for(i=0;i<ny;++i)  
	{  
		if(match[i]==-1||w[match[i]][i]==(~INF+1))  
		    continue;
		sum+=w[match[i]][i];
		cnt++;
	}  
	if(cnt!=nx)//nx个学生是否都安排房间
        return -1;
	else
		return sum;
}  

int main()
{
	int E,s,r,val,ans,cases=1;
	while(scanf("%d %d %d",&nx,&ny,&E)!=EOF)
	{
		for(s=0;s<=nx;++s)
		{
			for(r=0;r<=ny;++r)
				w[s][r]=(~INF+1);
		}
		if(E==0)
		{
			printf("Case %d: -1\n",cases++);
			continue;
		}
		while(E--)
		{
			scanf("%d %d %d",&s,&r,&val);
			if(val>=0)
				w[s][r]=val;
		}
		ans=KM();
		printf("Case %d: %d\n",cases++,ans);
	}
	return 0;
}

#include <stdio.h>    
#include <string.h> 
#define INF 0x3f3f3f3f    
#define MAXN 501    
//邻接表
struct node
{
	int from,to,next,val;
}edge[MAXN*MAXN];

int match[MAXN],head[MAXN],tot;    
int lx[MAXN],ly[MAXN],slack[MAXN];    
int visitx[MAXN],visity[MAXN];  
int nx,ny;

void addEdge(int x,int y,int val)
{
	edge[tot].from=x;
	edge[tot].to=y;
	edge[tot].val=val;
	edge[tot].next=head[x];
	head[x]=tot++;
}

int find(int x)
{  
	int i,temp,y;  
	visitx[x]=1;  
	for(i=head[x];i!=-1;i=edge[i].next)  
	{  
		y=edge[i].to;
		if(visity[y])  
			continue;  
		temp=lx[x]+ly[y]-edge[i].val;  
		if(temp==0)  
		{  
			visity[y]=1;  
			if(match[y]==-1||find(match[y]))  
			{  
				match[y]=x;  
				return 1;  
			}  
		}  
		else if(slack[y]>temp)  
		{  
			slack[y]=temp;  
		}  
	}  
	return 0;  
}  

int KM()  
{  
	int i,j,d,sum,cnt;  
	memset(ly,0,sizeof(ly));  
	memset(match,-1,sizeof(match));
	for(i=0;i<nx;++i)  
	{  
		for(j=0;j<ny;++j)  
			slack[j]=INF;  
		while(1)  
		{  
			memset(visitx,0,sizeof(visitx));  
			memset(visity,0,sizeof(visity));  
			if(find(i))  
				break;  
			d=INF;  
			for(j=0;j<ny;++j)  
			{  
				if(!visity[j]&&d>slack[j])  
					d=slack[j];  
			}  
			for(j=0;j<nx;++j)  
			{  
				if(visitx[j])  
					lx[j]-=d;  
			}  
			for(j=0;j<ny;++j)  
			{  
				if(visity[j])  
					ly[j]+=d;  
				else  
					slack[j]-=d;  
			}  
		}  
	}  
	sum=0;
	cnt=0;  
	for(i=0;i<ny;++i)  
	{  
		if(match[i]!=-1)
		{
			cnt++;
			for(j=head[match[i]];j!=-1;j=edge[j].next)
			{
				if(edge[j].to==i)
				{
					sum+=edge[j].val;
					break;
				}
			}
		}
	}  
	if(cnt!=nx)//nx个学生是否都安排房间
        return -1;
	else
		return sum;
}  

int main()
{
	int i,E,s,r,val,ans,cases=1;
	while(scanf("%d %d %d",&nx,&ny,&E)!=EOF)
	{
		if(E==0)
		{
			printf("Case %d: -1\n",cases++);
			continue;
		}
		tot=0;
		memset(head,-1,sizeof(head));
		memset(lx,-1,sizeof(lx));
		while(E--)
		{
			scanf("%d %d %d",&s,&r,&val);
			if(val>=0)
			{
				addEdge(s,r,val);
				if(val>lx[s])
					lx[s]=val;
			}
		}
		for(i=0;i<nx;++i)
		{
			if(lx[i]<0)
				break;
		}
		if(i<nx)
		{
			printf("Case %d: -1\n",cases++);
			continue;
		}
		ans=KM();
		printf("Case %d: %d\n",cases++,ans);
	}
	return 0;
}