UVa1471 LIS变种 nlgn

//#include<bits/stdc++.h>#include<stdio.h>#include<algorithm>#include<queue>#include<string.h>#include<iostream>#include<math.h>#include<set>#include<map>#include<vector>#include<iomanip>using namespace std;#define ll long long#define pb push_backconst int maxn=2e5+9;int f[maxn];//以i开头的长度int g[maxn];//以i结尾的长度int d[maxn];const int inf=0x3f3f3f3f;int arr[maxn];int main(){int T;scanf("%d",&T);while(T--){int n;scanf("%d",&n);for(int i=1;i<=n;i++)scanf("%d",&arr[i]);f[1]=1;for(int i=2;i<=n;i++){if(arr[i]>arr[i-1])f[i]=f[i-1]+1;else f[i]=1;}g[n]=1;for(int i=n-1;i>=1;i--){if(arr[i]<arr[i+1])g[i]=g[i+1]+1;else g[i]=1;}int ans=0;for(int i=1;i<=n;i++)d[i]=inf;//长度i的头所需代价for(int i=1;i<=n;i++){int len=(lower_bound(d+1,d+1+i,arr[i])-(d+1))+g[i];ans=max(ans,len);d[f[i]]=min(arr[i],d[f[i]]);}printf("%d\n",ans);}}

d数组性质就是同样的长度存最小的开始点，维护数组前部的一个理想前半

长度增长1数值至少加1，d数组单调增，

所以可以边修改边用lowerbound