Scoring Subsequences

合集 - 刷题集(97)
1.妖梦拼木棒2.[USACO1.2]回文平方数 Palindromic Squares3.[COCI2012-2013#1] LJUBOMORA4.火柴棒等式5.Kieszonkowe6.[COCI2014-2015#5] TRAKTOR7.硬币翻转8.[蓝桥杯 2020 省 AB1] 走方格9.P2097 资料分发10.[AHOI2005]约数研究11.[NOIP2004 普及组] 火星人12.我焯,原神(这真是个题)13.滑雪 OJ365114.CV的人有福啦!YTU贪心训练2(部分注释)15.砝码称重16.警钟长鸣-----找零钱17.[USACO09OCT]Barn Echoes G18.【CSGRound2】光骓者的荣耀19.初见蓝桥杯20.[蓝桥杯 2022 省 B] 扫雷21.开餐馆22.P9241 [蓝桥杯 2023 省 B] 飞机降落23.P7083 [NWRRC2013] Energy Tycoon24.高精度25.P7954 [COCI2014-2015#6] PAPRIKA26.(输出路径搜索)[USACO06OCT] Cows on Skates G27.畜栏保留问题28.(贪心+搜索+剪枝)P8801 [蓝桥杯 2022 国 B] 最大数字29.蓝桥杯 入门----普及-30.[NOIP2016 提高组] 玩具谜题31.[NOIP2002 提高组] 字串变换(无向图查重)32.[NOIP2000 提高组] 单词接龙33.POJ 硬币34.动态规划学习 1(最长上升子序列问题)35.动态规划学习 2(背包问题及其变形)36. 切割回文37.[NOIP2001 提高组] 数的划分(剪枝)38.字符串转换数字,sscanf和sprintf大法39.[CTSC1997] 选课(树状DP)40. k 倍区间(同余定理,组合数)41.[蓝桥杯 2018 省 AB] 全球变暖42.马的遍历(对bfs的更深一层探讨)43.找零钱44.Pasha Maximizes45.Newspaper Headline46.Balanced Ternary String47.(数论)素数,质数48.(数论) 约数49.Helping the Nature50.(博弈论)Even Number Addicts51.Present52.Mr. Kitayuta's Colorful Graph(二维并查集,弱化版)53.Edgy Trees(dfs,并查集,快速幂,树形结构,红黑树)54.并查集55.再谈 前缀和,差分,离散化56.Best Cow Fences(前缀和+特殊二分)57.二分58.同类型,类背包动态规划,选地dp59.Primes on Interval(欧拉筛+二分+滑动窗口)60.字符串(KMP , Trie树 , STL)61.Codeforces1 #879 div.262.Add Modulo 10(数论,思维,数学,规律)63.期末考试YTU4035: Shmily(数学,等差数列)64.[POI2006] OKR-Periods of Words65.Getting Zero(Bfs)66.快速幂67.Dreaming of Freedom(数论,贪心)
68.Scoring Subsequences
69.Dolce Vita70.Cake Assembly Line71.Constructive Problem72.Forever Winter73.Maximum Sum(前缀和)74.Contrast Value(数学规律)75.Lamps(STL+双端队列)76.Long Long77.Sum in Binary Tree78.Apple Tree(树状搜索,树形DP)79.Strong Password(贪心思想)80.Come Together81.Notepad82.Hamiltonian Wall83.7.17作业84.逛画展(双指针)85.#88586.树状数组87.Subsequence Addition88.7.22作业89.Diverse Substrings90.Tracking Segments(二分,区间前缀)91.最大食物链计数92.线段树193.[TJOI2007] 线段(状态机)94.#87895.测试196.李白打酒97.砍竹子
收起
Scoring Subsequences
time limit per test
2.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The score of a sequence [s1,s2,…,sd][1,2,…,] is defined as s1⋅s2⋅…⋅sdd!1⋅2⋅…⋅!, where d!=1⋅2⋅…⋅d!=1⋅2⋅…⋅. In particular, the score of an empty sequence is 11.

For a sequence [s1,s2,…,sd][1,2,…,], let m be the maximum score among all its subsequences. Its cost is defined as the maximum length of a subsequence with a score of m.

You are given a non-decreasing sequence [a1,a2,…,an][1,2,…,] of integers of length n. In other words, the condition a1≤a2≤…≤an1≤2≤…≤ is satisfied. For each k=1,2,…,n=1,2,…,, find the cost of the sequence [a1,a2,…,ak][1,2,…,].

A sequence x is a subsequence of a sequence y if x can be obtained from y by deletion of several (possibly, zero or all) elements.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1≤t≤1041≤≤104). The description of the test cases follows.

The first line of each test case contains an integer n (1≤n≤1051≤≤105) — the length of the given sequence.

The second line of each test case contains n integers a1,a2,…,an1,2,…, (1≤ai≤n1≤≤) — the given sequence. It is guaranteed that its elements are in non-decreasing order.

It is guaranteed that the sum of n over all test cases does not exceed 5⋅1055⋅105.

Output

For each test case, output n integers — the costs of sequences [a1,a2,…,ak][1,2,…,] in ascending order of k.

Example
input
Copy
3
3
1 2 3
2
1 1
5
5 5 5 5 5
output
Copy
1 1 2 
1 1 
1 2 3 4 5
Note

In the first test case:

  • The maximum score among the subsequences of [1][1] is 11. The subsequences [1][1] and [][] (the empty sequence) are the only ones with this score. Thus, the cost of [1][1] is 11.
  • The maximum score among the subsequences of [1,2][1,2] is 22. The only subsequence with this score is [2][2]. Thus, the cost of [1,2][1,2] is 11.
  • The maximum score among the subsequences of [1,2,3][1,2,3] is 33. The subsequences [2,3][2,3] and [3][3] are the only ones with this score. Thus, the cost of [1,2,3][1,2,3] is 22.
Therefore, the answer to this case is 112112, which are the costs of [1],[1,2][1],[1,2] and [1,2,3][1,2,3] in this order.
复制代码
#include <bits/stdc++.h>
//#define int long long
using namespace std;
const int N=1e5+10,mod=1e9+7;
string s;
int n,t,a[N],f[N],res,num,ans;
bool vis[N];
int op(int u)
{
    if(u==1||u==0) return 1;
    return u*op(u-1);
}
int main()
{
    std::ios::sync_with_stdio(false),cin.tie(0),cout.tie(0);
    cin>>t;
    while(t--){
        cin>>n;
        res=0;
        for(int i=1;i<=n;i++){
            cin>>a[i];
            int l=1,r=i;
        //如果当前的数小于长度,那就肯定到不了最大值,所以求最小的当前值能让序列价值达到最大
        //二分即可
            while(l<r){
                int mid=l+r>>1;
                if(a[mid]>=i-mid+1) r=mid;
                else l=mid+1;
            }
            cout<<i-l+1<<" ";
        }
        cout<<endl;
    }
    return 0;
}
复制代码

 


__EOF__

本文作者：Sakurajimamai
本文链接：https://www.cnblogs.com/o-Sakurajimamai-o/p/17500718.html
关于博主：评论和私信会在第一时间回复。或者直接私信我。
版权声明：本博客所有文章除特别声明外，均采用 BY-NC-SA 许可协议。转载请注明出处！
声援博主：如果您觉得文章对您有帮助，可以点击文章右下角【推荐】一下。您的鼓励是博主的最大动力！
posted @   o-Sakurajimamai-o  阅读(24)  评论(0)  编辑  收藏  举报
相关博文：
·  Subsequence Addition
·  Maximum Sum(前缀和)
·  Scoring Subsequences
·  [LeetCode] 2542. Maximum Subsequence Score
·  1007 Maximum Subsequence Sum（25分）
阅读排行：
· winform 绘制太阳，地球，月球 运作规律
· AI与.NET技术实操系列（五）：向量存储与相似性搜索在 .NET 中的实现
· 超详细：普通电脑也行Windows部署deepseek R1训练数据并当服务器共享给他人
· 【硬核科普】Trae如何「偷看」你的代码？零基础破解AI编程运行原理
· 上周热点回顾（3.3-3.9）
-- --
点击右上角即可分享
微信分享提示