约瑟夫问题专题

 

UVa 1452 - Jump(约瑟夫环变形)

分类： 动态规划2013-08-10 16:25 538人阅读 评论(0) 收藏 举报

目录(?)[-]

1. 题意
2. 思路
3. 代码
   1. 来自CODE的代码片 uvaa-1452-Jumpcpp

本文出自   http://blog.csdn.net/shuangde800

题目点击打开链接

题意

把1～n按逆时针顺序排成一个圆圈，从1开始没k个数字删除掉一个，知道所有数字都删完。

求最后删除的3个数。

思路

我们已经知道了，怎么可以推出最后一个被删除的编号（可参考百度百科）

http://baike.baidu.com/view/213217.htm

f(1) = 0, 表示最后还剩下一个时，这个编号为0

f(n) = (f(n-1) + m) % n

那么保存最后第1,2,3个数，一直推到第一个即可。

代码

<a target=_blank id="L1" href="http://blog.csdn.net/shuangde800/article/details/9745849#L1" rel="#L1" style="color: rgb(102, 102, 102); text-decoration: none;">  1</a><a target=_blank id="L2" href="http://blog.csdn.net/shuangde800/article/details/9745849#L2" rel="#L2" style="color: rgb(102, 102, 102); text-decoration: none;">  2</a><a target=_blank id="L3" href="http://blog.csdn.net/shuangde800/article/details/9745849#L3" rel="#L3" style="color: rgb(102, 102, 102); text-decoration: none;">  3</a><a target=_blank id="L4" href="http://blog.csdn.net/shuangde800/article/details/9745849#L4" rel="#L4" style="color: rgb(102, 102, 102); text-decoration: none;">  4</a><a target=_blank id="L5" href="http://blog.csdn.net/shuangde800/article/details/9745849#L5" rel="#L5" style="color: rgb(102, 102, 102); text-decoration: none;">  5</a><a target=_blank id="L6" href="http://blog.csdn.net/shuangde800/article/details/9745849#L6" rel="#L6" style="color: rgb(102, 102, 102); text-decoration: none;">  6</a><a target=_blank id="L7" href="http://blog.csdn.net/shuangde800/article/details/9745849#L7" rel="#L7" style="color: rgb(102, 102, 102); text-decoration: none;">  7</a><a target=_blank id="L8" href="http://blog.csdn.net/shuangde800/article/details/9745849#L8" rel="#L8" style="color: rgb(102, 102, 102); text-decoration: none;">  8</a><a target=_blank id="L9" href="http://blog.csdn.net/shuangde800/article/details/9745849#L9" rel="#L9" style="color: rgb(102, 102, 102); text-decoration: none;">  9</a><a target=_blank id="L10" href="http://blog.csdn.net/shuangde800/article/details/9745849#L10" rel="#L10" style="color: rgb(102, 102, 102); text-decoration: none;"> 10</a><a target=_blank id="L11" href="http://blog.csdn.net/shuangde800/article/details/9745849#L11" rel="#L11" style="color: rgb(102, 102, 102); text-decoration: none;"> 11</a><a target=_blank id="L12" href="http://blog.csdn.net/shuangde800/article/details/9745849#L12" rel="#L12" style="color: rgb(102, 102, 102); text-decoration: none;"> 12</a><a target=_blank id="L13" href="http://blog.csdn.net/shuangde800/article/details/9745849#L13" rel="#L13" style="color: rgb(102, 102, 102); text-decoration: none;"> 13</a><a target=_blank id="L14" href="http://blog.csdn.net/shuangde800/article/details/9745849#L14" rel="#L14" style="color: rgb(102, 102, 102); text-decoration: none;"> 14</a><a target=_blank id="L15" href="http://blog.csdn.net/shuangde800/article/details/9745849#L15" rel="#L15" style="color: rgb(102, 102, 102); text-decoration: none;"> 15</a><a target=_blank id="L16" href="http://blog.csdn.net/shuangde800/article/details/9745849#L16" rel="#L16" style="color: rgb(102, 102, 102); text-decoration: none;"> 16</a><a target=_blank id="L17" href="http://blog.csdn.net/shuangde800/article/details/9745849#L17" rel="#L17" style="color: rgb(102, 102, 102); text-decoration: none;"> 17</a><a target=_blank id="L18" href="http://blog.csdn.net/shuangde800/article/details/9745849#L18" rel="#L18" style="color: rgb(102, 102, 102); text-decoration: none;"> 18</a><a target=_blank id="L19" href="http://blog.csdn.net/shuangde800/article/details/9745849#L19" rel="#L19" style="color: rgb(102, 102, 102); 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/**==========================================
 *   This is a solution for ACM/ICPC problem
 * 
 *   @source:  uva-1452 Jump
 *   @author: shuangde
 *   @blog: blog.csdn.net/shuangde800
 *   @email: [e-mail]
 *===========================================*/
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<vector>
#include<queue>
#include<cmath>
#include<cstring>
using namespace std;
typedef long long int64;
const int INF = 0x3f3f3f3f;
const double PI  = acos(-1.0);
const int MAXN = 110;
int n, m;
int main(){
    int T;
    scanf("%d", &T);
    while(T--){
        
        scanf("%d%d", &n, &m);
        int ans1 = 0, ans2, ans3;
        for(int i=2; i<=n; ++i){
            ans1 = (ans1+m) % i;
            if(i==2){
                // 当剩下最后2个数时，编号为0，1, 推出倒数第二个删除的数当前值
                ans2 = !ans1;
            }else if(i==3){
                // 当剩下最后3个数时，编号为0，1，2, 推出倒数第三个删除的数当前值
                ans2 = (ans2+m) % i;
                bool vis[3];
                memset(vis, 0, sizeof(vis));
                vis[ans1] = vis[ans2] = true;
                for(int j=0; j<3; ++j)if(!vis[j]){
                    ans3 = j; break; 
                }
            }else{
                ans2 = (ans2+m) % i;
                ans3 = (ans3+m) % i;
            }
        }
        ans1 = (ans1+1)%n; 
        ans2 = (ans2+1)%n;
        ans3 = (ans3+1)%n;
        printf("%d %d %d\n", ans3?ans3:n, ans2?ans2:n, ans1?ans1:n);
    }
    return 0;
}

 来自CODE的代码片

uvaa-1452-Jump.cpp