https://www.luogu.org/problemnew/show/P5120
题意:按资历顺序给出n头牛的到达时间和吃草持续时间,当有若干个牛都处于等待状态时,资历最大的优先吃草。
思路:暴力O(n^2)不行,考虑nlogn数据结构,用堆(优先队列)。将所有的牛按照到达时间排序排序,优先队列的优先级定义为资历顺序,排序后的牛入堆应该是顺序的,维护当前时间和当前牛指针,类似于单调队列那样,一头牛吃完草后,更新当前时间,把处于等待状态的牛入堆,每次堆顶就是要吃草的牛。
#include<bits/stdc++.h>
using namespace std;
#define maxn 100000+1000
int n,a[maxn],t[maxn],cur,ans,now;
int r[maxn];
struct HeapNode{
int idx;
bool operator < (HeapNode x)const{
return idx>x.idx;
}
};
priority_queue<HeapNode> Q;
bool cmp(int i,int j)
{
return a[i]<a[j];
}
int main()
{
// freopen("input.in","r",stdin);
scanf("%d",&n);
for(int i=1;i<=n;i++)scanf("%d%d",&a[i],&t[i]),r[i]=i;
sort(r+1,r+1+n,cmp);
for(int i=1;i<=n;i++)if(a[r[i]]==a[r[1]])Q.push((HeapNode){r[i]}),cur++;
now=a[r[1]];
while(!Q.empty())
{
HeapNode u=Q.top();Q.pop();
ans=max(ans,now-a[u.idx]);
now+=t[u.idx];
while(cur+1<=n&&a[r[cur+1]]<=now)
Q.push((HeapNode){r[cur+1]}),cur++;
if(cur+1<=n&&Q.empty())
{
now=a[r[cur+1]];
int pos=cur+1;
while(a[r[pos]]==a[r[cur+1]])
{
Q.push((HeapNode){r[cur+1]});
cur++;
}
}
}
cout<<ans<<endl;
return 0;
}