Problem Description
You may heard of the Joseph Problem, the story comes from a Jewish historian living in 1st century. He and his 40 comrade soldiers were trapped in a cave, the exit of which was blocked by Romans.
They chose suicide over capture and decided that they would form a circle and start killing themselves using a step of three.
Josephus states that by luck or maybe by the hand of God, he and another man remained the last and gave up to the Romans.
Now the problem is much easier: we have N men stand in a line and labeled from 1 to N, for each round, we choose the first man, the k+1-th one, the 2*k+1-th one and so on, until the end of the line.
These poor guys will be kicked out of the line and we will execute them immediately (may be head chop, or just shoot them, whatever), and then we start the next round with the remaining guys.
The little difference between the Romans and us is, in our version of story, NO ONE SURVIVES. Your goal is to find out the death sequence of the man.
For example, we have N = 7 prisoners, and we decided to kill every k=2 people in the line. At the beginning, the line looks like this:
1 2 3 4 5 6 7
after the first round, 1 3 5 7 will be executed, we have
2 4 6
and then, we will kill 2 6 in the second round. At last 4 will be executed. So, you need to output 1 3 5 7 2 6 4. Easy, right?
But the output maybe too large, we will give you Q queries, each one contains a number m, you need to tell me the m-th number in the death sequence.
 Input
Multiple cases. The first line contains a number T, means the number of test case.
For every case, there will be three integers N (1<=N<=3000000), K(1<=K), and Q(1<=Q<=1000000), which indicate the number of prisoners, the step length of killing,
and the number of query. Next Q lines, each line contains one number m(1<=m<=n).
 Output
For each query m, output the m-th number in the death sequence.
Sample Input
1 7 2 7 1 2 3 4 5 6 7
 
将约瑟夫环拉成一条直线,一开始一共n个人,每次从第一个人开始(杀掉第一个)从前向后依次每隔k个人杀一个人,最后大家都被干掉了,然后就形成了一个死亡序列
有m次询问,问你在死亡序列中的第x个人编号是多少.
 
思路:
如果我们把他们的下标从0开始,那么第一批死的人下标肯定满足i%k==0
继续想,杀掉一批人以后活着的人会向前补空位,加上第i个人在这轮没有被杀,那么他下轮的位置就会在i-i/k-1.
换句话说第i个人会比第i-i/k-1多活一轮
然后我们发现我们花O(n)的时间就能递推出每个人是在第几轮的第几个死的.
我们开一个pair 保存每个人是 第几轮 和第几个
我们再对轮数取个前缀和.就能知道他在总队列里面是第几个了
一开始想到补空位的想法了,但是没有深想,利用递推的思路,其实在线性时间内就可以求出答案了
代码如下:
 #include <bits/stdc++.h>

 using namespace std;
const int maxn=3e6+;
int cnt[maxn];
int ans[maxn];//最后的答案
int n,k,q;
pair<int,int> dp[maxn];
int main()
{
//freopen("de.txt","r",stdin);
int t;
scanf("%d",&t);
while (t--){
scanf("%d%d%d",&n,&k,&q);
memset(cnt,,sizeof cnt);
for (int i=;i<n;++i){
dp[i].first=i%k?(dp[i-i/k-].first+):;
dp[i].second=cnt[dp[i].first]++;//求出来第i人的轮数,相应轮数cnt++
}
for (int i=;i<maxn;++i){
if (cnt[i]==)
break;
cnt[i]+=cnt[i-];//处理前缀和,即第i轮之前一共杀死多少人
}
for (int i=;i<n;++i){
ans[(dp[i].first?cnt[dp[i].first-]:)+dp[i].second]=i;
}
for (int i=;i<q;++i){
int x;
scanf("%d",&x);
printf("%d\n",ans[x-]+);
}
}
return ;
}

hdu 5860 Death Sequence(递推+脑洞)的更多相关文章

  1. HDU 5860 Death Sequence(递推)

    HDU 5860 Death Sequence(递推) 题目链接http://acm.split.hdu.edu.cn/showproblem.php?pid=5860 Description You ...

  2. HDU 5860 Death Sequence(死亡序列)

    p.MsoNormal { margin: 0pt; margin-bottom: .0001pt; text-align: justify; font-family: Calibri; font-s ...

  3. HDU 5950 Recursive sequence 递推转矩阵

    Recursive sequence Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Other ...

  4. hdu 5950 Recursive sequence 递推式 矩阵快速幂

    题目链接 题意 给定\(c_0,c_1,求c_n(c_0,c_1,n\lt 2^{31})\),递推公式为 \[c_i=c_{i-1}+2c_{i-2}+i^4\] 思路 参考 将递推式改写\[\be ...

  5. 2016 Multi-University Training Contest 10 || hdu 5860 Death Sequence(递推+单线约瑟夫问题)

    题目链接:http://acm.split.hdu.edu.cn/showproblem.php?pid=5860 题目大意:给你n个人排成一列编号,每次杀第一个人第i×k+1个人一直杀到没的杀.然后 ...

  6. HDU 5860 Death Sequence

    用线段树可以算出序列.然后o(1)询问. #pragma comment(linker, "/STACK:1024000000,1024000000") #include<c ...

  7. HDU 2085 核反应堆 --- 简单递推

    HDU 2085 核反应堆 /* HDU 2085 核反应堆 --- 简单递推 */ #include <cstdio> ; long long a[N], b[N]; //a表示高能质点 ...

  8. hdu-5496 Beauty of Sequence(递推)

    题目链接: Beauty of Sequence Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java ...

  9. hdu 2604 Queuing(dp递推)

    昨晚搞的第二道矩阵快速幂,一开始我还想直接套个矩阵上去(原谅哥模板题做多了),后来看清楚题意后觉得有点像之前做的数位dp的水题,于是就用数位dp的方法去分析,推了好一会总算推出它的递推关系式了(还是菜 ...

随机推荐

  1. Vue的使用总结(2)

    1.Vue 中 class 和 style 的绑定 在 Vue 中,可以通过数据绑定来操作元素的 class 列表和内联样式,操作 class 和 style 是用 v-bind 来绑定的.在将 v- ...

  2. 【BZOJ2555】SubString(后缀自动机,LCT)

    题意:给你一个字符串init,要求你支持两个操作 (1):在当前字符串的后面插入一个字符串 (2):询问字符串s在当前字符串中出现了几次?(作为连续子串) 你必须在线支持这些操作. 长度 <= ...

  3. IGServer for Java

    Eclipse和JavaEE: DCServer是哪个? 查看服务器文件夹: Env_Var变量没有定义:JRE_HOME.JDK_HOME 这是Tomcat报错的提示,但是既然JAVA_HOME都有 ...

  4. [BZOJ3379] Turning in Homework

    中文题目:提交作业 原文题目:Turning in Homework 传送门:http://www.lydsy.com/JudgeOnline/problem.php?id=3379 哎,今天竟然没有 ...

  5. 7 November in 614

    每日总结不能少!让自己的头脑好好清醒清醒,才不会犯那些所谓的低级错误! Contest A. ssoj3045 A 先生砍香蕉树 根据数据范围 \(m\le 1000,b\le 10000\),显然本 ...

  6. codeforces 559D Randomizer

    题意简述: 在一个格点图中 给定一个凸$n$边形(每个定点均在格点上),随机选择其中一些点构成一个子多边形, 求子多边形的内部点个数的期望. ----------------------------- ...

  7. 【HTTP】http请求url参数包含+号,被解析为空格

    项目技术:Angular 6 问题现象:接口传参的时候,使用 httpClient.post 方法提交数据,字段中包含+号被解析成空格,提交数据错误 解决过程: 1.http请求中包含+号,会被自动解 ...

  8. spring aop思想

  9. c#生成html静态文件时出现空白行,怎么去掉utf-8中的bom

    public static void UTF8RemoveBOM(string filepath) { UTF8RemoveBOM(filepath, filepath); }   public st ...

  10. nginx 日志统计接口每个小时访问量

    指定时间段增量统计nginx日志不同接口的访问量: #!/bin/bash#此脚本用于统计nginx日志当前时间15分钟之内不同接口(URL)的访问量统计LOG=/usr/local/nginx/lo ...