POJ3189 Steady Cow Assignment(最大流)

时间:2023-03-09 03:29:37
POJ3189 Steady Cow Assignment(最大流)

题目大概说,有n头牛和b块草地,每头牛心中分别对每块草地都有排名,草地在牛中排名越高牛安排在那的幸福度就越小(。。。),每块草地都能容纳一定数量的牛。现在要给这n头牛分配草地,牛中的幸福度最大与幸福度最小的差值越小越好,问最小能多小。

显然又是枚举结果跑最大流看是否合法。不过,枚举幸福度的差值是做不了的,应该要枚举的是幸福度的最大值和幸福度的最小值。然后建图没啥好说的。。最后的结果要加1,因为题目说“including the endpoints”,虽然不知道什么意思。。

 #include<cstdio>
#include<cstring>
#include<queue>
#include<algorithm>
using namespace std;
#define INF (1<<30)
#define MAXN 1111
#define MAXM 44444 struct Edge{
int v,cap,flow,next;
}edge[MAXM];
int vs,vt,NE,NV;
int head[MAXN]; void addEdge(int u,int v,int cap){
edge[NE].v=v; edge[NE].cap=cap; edge[NE].flow=;
edge[NE].next=head[u]; head[u]=NE++;
edge[NE].v=u; edge[NE].cap=; edge[NE].flow=;
edge[NE].next=head[v]; head[v]=NE++;
} int level[MAXN];
int gap[MAXN];
void bfs(){
memset(level,-,sizeof(level));
memset(gap,,sizeof(gap));
level[vt]=;
gap[level[vt]]++;
queue<int> que;
que.push(vt);
while(!que.empty()){
int u=que.front(); que.pop();
for(int i=head[u]; i!=-; i=edge[i].next){
int v=edge[i].v;
if(level[v]!=-) continue;
level[v]=level[u]+;
gap[level[v]]++;
que.push(v);
}
}
} int pre[MAXN];
int cur[MAXN];
int ISAP(){
bfs();
memset(pre,-,sizeof(pre));
memcpy(cur,head,sizeof(head));
int u=pre[vs]=vs,flow=,aug=INF;
gap[]=NV;
while(level[vs]<NV){
bool flag=false;
for(int &i=cur[u]; i!=-; i=edge[i].next){
int v=edge[i].v;
if(edge[i].cap!=edge[i].flow && level[u]==level[v]+){
flag=true;
pre[v]=u;
u=v;
//aug=(aug==-1?edge[i].cap:min(aug,edge[i].cap));
aug=min(aug,edge[i].cap-edge[i].flow);
if(v==vt){
flow+=aug;
for(u=pre[v]; v!=vs; v=u,u=pre[u]){
edge[cur[u]].flow+=aug;
edge[cur[u]^].flow-=aug;
}
//aug=-1;
aug=INF;
}
break;
}
}
if(flag) continue;
int minlevel=NV;
for(int i=head[u]; i!=-; i=edge[i].next){
int v=edge[i].v;
if(edge[i].cap!=edge[i].flow && level[v]<minlevel){
minlevel=level[v];
cur[u]=i;
}
}
if(--gap[level[u]]==) break;
level[u]=minlevel+;
gap[level[u]]++;
u=pre[u];
}
return flow;
} int n,b,happy[][],cap[];
bool isok(int mm,int mx){
vs=; vt=n+b+; NV=vt+; NE=;
memset(head,-,sizeof(head));
for(int i=; i<=n; ++i) addEdge(vs,i,);
for(int i=; i<=n; ++i){
for(int j=; j<=b; ++j){
if(mm<=happy[i][j] && happy[i][j]<=mx) addEdge(i,j+n,);
}
}
for(int i=; i<=b; ++i) addEdge(i+n,vt,cap[i]);
return ISAP()==n;
}
int main(){
int a;
scanf("%d%d",&n,&b);
for(int i=; i<=n; ++i){
for(int j=; j<=b; ++j){
scanf("%d",&a);
happy[i][a]=j;
}
}
for(int i=; i<=b; ++i) scanf("%d",cap+i);
int res=INF;
for(int i=; i<=b; ++i){
for(int j=i; j<=b; ++j){
if(isok(i,j)) res=min(res,j-i);
}
}
printf("%d",res+);
return ;
}