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;elsereturn 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;elsereturn 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;}