HDU 5643 King's Game （约瑟夫环问题的变形 递推）

大体题意：

有n 个人，进行比赛，第一轮比赛 从1开始报数，报到1的出局，第二轮报2，，，，  问最后谁没出局？

思路：

一看就是约瑟夫环问题的变型了。

在简单记录一下思考的过程吧：

n 个人 编号为0，1，2，，，，，n-1.

假设这一局k-1 出局了。

那么重新编号：

k  k+1 k+2,,,, n-1  0 1   k-2

0  1     2                           n-2

这n -2 个人进行比赛。

那么我们给他变回去即可！

怎么变呢？ 显然是(x + k) % n = f[n]

但是这里k 是变化的，当i 为2 时  只有两个人  显然报数是 n-i+1.

详细见代码:

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
int f[5007];
int main(){
    int T;
    scanf("%d",&T);
    while(T--){
        int n;
        scanf("%d",&n);
        f[1] = 0;
        for (int i = 2; i <= n; ++i){
            f[i] = (f[i-1] + n-i+1) % i;
        }
        printf("%d\n",f[n]+1);
    }
    return 0;
}

King's Game

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 703    Accepted Submission(s): 390

Problem Description

In order to remember history, King plans to play losephus problem in the parade gap.He calls  n(1≤n≤5000)  soldiers, counterclockwise in a circle, in label  1,2,3...n .

The first round, the first person with label  1  counts off, and the man who report number  1  is out.

The second round, the next person of the person who is out in the last round counts off, and the man who report number  2  is out.

The third round, the next person of the person who is out in the last round counts off, and the person who report number  3  is out.



The N - 1 round, the next person of the person who is out in the last round counts off, and the person who report number  n−1  is out.

And the last man is survivor. Do you know the label of the survivor?

 

Input

The first line contains a number  T(0<T≤5000) , the number of the testcases.

For each test case, there are only one line, containing one integer  n , representing the number of players.

 

Output

Output exactly  T  lines. For each test case, print the label of the survivor.

 

Sample Input

  

   2
2
3
  

 

Sample Output

  

   2
2

Hint:
For test case #1：the man who report number $1$ is the man with label $1$, so the man with label $2$ is survivor.

For test case #1：the man who report number $1$ is the man with label $1$, so the man with label 1 is out. Again the the man with label 2 counts $1$,  the man with label $3$ counts $2$, so the man who report number $2$ is the man with label $3$. At last the man with label $2$ is survivor.
  

 

Source

BestCoder Round #75

 

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