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POJ---2010(Moo University - Financial Aid,优先队列)

热度:83   发布时间:2024-01-22 02:03:50.0

题意:

一共C个学生,学校要录N(奇数)个,每个学生的分数和需要的aid给出,学校最多能提供F资金,求录取的学生中分数中位数最大。

题解:

方法1:对所有的学生按照分数进行从小到大排序,左边从第N/2+1个学生开始,到第C-N/2个学生结束,算出每个学生以他的分数为中位数,左边需要的最小总aid,需要用到优先队列!

同样地,对右边也进行计算,以每个学生自身为中位数,右边需要的最小总aid

最后从右往左扫描,算出以每个学生为中位数,左右需要的总aid<=F即可!

 

 

方法2:二分。对于每个mid看是否满足左右两边的score=N/2,并且aid<=F


#include<iostream>
#include<cstdio>
#include<algorithm>
#include<queue>
#include<string>
#include<cstring>using namespace std;struct node{int score,aid,left,right;};
bool cmp(struct node x1,struct node x2)
{return x1.score<x2.score;
}
struct node a[100000+5];int main()
{   memset(a,0,sizeof(a));int N,C,F;cin>>N>>C>>F;for(int i=1; i<=C; i++)scanf("%d%d",&a[i].score,&a[i].aid);sort(a+1,a+C+1,cmp);priority_queue<int>q;int sum=0;if(N>1){   //前N/2个肯定不能当中位数for(int i=1; i<=N/2; i++){q.push(a[i].aid);sum+=a[i].aid;}//从N/2+1开始,计算分数比他小的N/2个最少需要多少aidfor(int i=N/2+1; i<=C-N/2; i++){a[i].left=sum;if(a[i].aid<q.top()){sum=sum-q.top()+a[i].aid;q.pop();q.push(a[i].aid);}}while(q.size())q.pop();sum=0;//右边同理;for(int i=C; i>C-N/2; i--){q.push(a[i].aid);sum+=a[i].aid;}for(int i=C-N/2; i>=N/2+1; i--){a[i].right=sum;if(a[i].aid<q.top()){sum=sum-q.top()+a[i].aid;q.pop();q.push(a[i].aid);}}}int ans=-1;for(int i=C-N/2; i>N/2; i--){int total=a[i].left+a[i].right+a[i].aid;if(total<=F){ans=a[i].score;break;}}cout<<ans<<endl;}

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<queue>
#include<string>
#include<cstring>
using namespace std;
const int maxn=100000+5;struct node{int rank_by_score,score,aid;};node cow_score[maxn],cow_aid[maxn];bool less_by_score(struct node a,struct node b)
{return a.score<b.score;
}bool less_by_aid(struct node a,struct node b)
{return a.aid<b.aid;
}int main()
{int N,C,F;cin>>N>>C>>F;for(int i=1;i<=C;i++)scanf("%d%d",&cow_score[i].score,&cow_score[i].aid);sort(cow_score+1,cow_score+1+C,less_by_score);for(int i=1;i<=C;i++)cow_score[i].rank_by_score=i;memcpy(cow_aid,cow_score,sizeof(node)*(C+1));sort(cow_aid+1,cow_aid+C+1,less_by_aid);int lb=1,ub=C,ans=-1;while(ub-lb>1){int mid=(lb+ub)>>1;int left=0,right=0,total_aid=cow_score[mid].aid;for(int i=1;i<=C;i++)//按照aid从小到大 扫描{   //每次去找mid 左右两边 aid总和最小的。如果能找到符合条件的,则left,right最后应该都为N/2;//如果扫描一遍 left,right 都小于N/2,那么就是没有符合题意的解了。if(cow_aid[i].rank_by_score<mid && total_aid+cow_aid[i].aid<=F && left< N/2 ){total_aid+=cow_aid[i].aid;left++;}else if(cow_aid[i].rank_by_score>mid && total_aid+cow_aid[i].aid<=F && right< N/2 ){total_aid+=cow_aid[i].aid;right++;}}if(left<N/2 && right< N/2)//从小的aid开始选,都选不够N个{ans=-1;break;}else if(left < N/2)//放大lb=mid;else if(right<N/2)//缩小ub=mid;else{ans=cow_score[mid].score;lb=mid;//求最大}}cout<<ans<<endl;
}




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