And Then There Was One
来源:互联网 发布:淘宝店铺文案范文 编辑:程序博客网 时间:2024/06/05 19:30
Description
Let's play a stone removing game.
Initially, n stones are arranged on a circle and numbered 1,..., n clockwise (Figure 1). You are also given two numbers k and m . From this state, remove stones one by one following the rules explained below, until only one remains. In step 1, remove stone m . In step 2, locate the k -th next stone clockwise from m and remove it. In subsequent steps, start from the slot of the stone removed in the last step, make k hops clockwise on the remaining stones and remove the one you reach. In other words, skip (k - 1) remaining stones clockwise and remove the next one. Repeat this until only one stone is left and answer its number.
For example, the answer for the case n = 8 , k = 5 , m = 3 is 1, as shown in Figure 1.
Initial state: Eight stones are arranged on a circle.
Step 1: Stone 3 is removed since m = 3 .
Step 2: You start from the slot that was occupied by stone 3. You skip four stones 4, 5, 6 and 7 (since k = 5 ), and remove the next one, which is 8.
Step 3: You skip stones 1, 2, 4 and 5, and thus remove 6. Note that you only count stones that are still on the circle and ignore those already removed. Stone 3 is ignored in this case.
Steps 4-7: You continue until only one stone is left. Notice that in later steps when only a few stones remain, the same stone may be skipped multiple times. For example, stones 1 and 4 are skipped twice in step 7.
Final State: Finally, only one stone, 1, is on the circle. This is the final state, so the answer is 1.
Input
The input consists of multiple datasets each of which is formatted as follows.
n k m
The last dataset is followed by a line containing three zeros. Numbers in a line are separated by a single space. A dataset satisfies the following conditions.
The number of datasets is less than 100.
Output
For each dataset, output a line containing the stone number left in the final state. No extra characters such as spaces should appear in the output.
Sample Input
8 5 3 100 9999 98 10000 10000 10000 0 0 0
Sample Output
1 93 2019
题意:将石头排序,将石头m拿掉,从石头m开始,每经过K的石头,拿掉第k个...求最后剩下哪一个...
思路:约瑟夫环问题变型..
原型是从第一个石头开始的...
1.将石头编号改为从0到n-1,mod n,再加1,可得到结果..
2.递推公式 f[i]=(f[i-1]+k)%i,f[1]=0; f[i]表示第i个人时胜利者的编号...
最后一步应该分开来算..因为石头不是从1 开始算起的,而是第m个石头..
f[n]=(f[n-1]+m)%n;
CODE:
#include<stdio.h>#include<iostream>using namespace std;int f[10005];int main(){ int n,k,m; while(~scanf("%d%d%d",&n,&k,&m),n,k,m) { f[1]=0; for(int i=2;i<n;i++) f[i]=(f[i-1]+k)%i; f[n]=(f[n-1]+m)%n+1; printf("%d\n",f[n]); } return 0;}
- And Then There Was One
- And Then There Was One
- POJ 3517 And Then There Was One
- POJ 3157 And Then There Was One
- pku3517 And Then There Was One
- And Then There Was One----约瑟夫环
- POJ-3517-And Then There Was One
- uva 1394 - And Then There Was One
- UVA 1394 And Then There Was One
- UVALive 3882 And Then There Was One
- UVALive 3882 And Then There Was One
- UVa 1394: And Then There Was One
- UVa:1394 And Then There Was One
- LA-3882 And Then There Was One
- POJ 3517 And Then There Was One
- POJ 3517 And Then There Was One
- Sicily 1499. And Then There Was One
- UVA - 1394 And Then There Was One
- Intel 平台编程总结----计时机制
- 颜色迁移之一——基础知识(色彩空间及其转换)
- Windows 中GDI、设备描述表和位图
- Python之easy_install安装出错
- const
- And Then There Was One
- Intel 平台编程总结---自顶向下的软件优化策略
- LeetCode:Maximum Subarray
- 【Leetcode】Pascal's Triangle
- gzip
- 单调队列+DP
- hadoop常见错误及处理方法
- 悲催的实习面试经历
- 55个常用技巧