UVa133
The Dole Queue |
In a serious attempt to downsize (reduce) the dole queue, The New National Green Labour Rhinoceros Party has decided on the following strategy. Every day all dole applicants will be placed in a large circle, facing inwards. Someone is arbitrarily chosen as number 1, and the rest are numbered counter-clockwise up to N (who will be standing on 1's left). Starting from 1 and moving counter-clockwise, one labour official counts off k applicants, while another official starts from N and moves clockwise, counting m applicants. The two who are chosen are then sent off for retraining; if both officials pick the same person she (he) is sent off to become a politician. Each official then starts counting again at the next available person and the process continues until no-one is left. Note that the two victims (sorry, trainees) leave the ring simultaneously, so it is possible for one official to count a person already selected by the other official.
Input
Write a program that will successively read in (in that order) the three numbers (N, k and m; k, m > 0, 0 < N < 20) and determine the order in which the applicants are sent off for retraining. Each set of three numbers will be on a separate line and the end of data will be signalled by three zeroes (0 0 0).
Output
For each triplet, output a single line of numbers specifying the order in which people are chosen. Each number should be in a field of 3 characters. For pairs of numbers list the person chosen by the counter-clockwise official first. Separate successive pairs (or singletons) by commas (but there should not be a trailing comma).
Sample input
10 4 3 0 0 0
Sample output
4
8,
9
5,
3
1,
2
6,
10,
7
where represents a space.
题意:
有N个人围成一圈、给其中任意一人编号为1,顺时针依次从1到N给剩余的每个人编号。N号应该就在1号的旁边。现在每回合不断选走一个或者两个人,知道没有人剩下,规则是这样的:首先从1号开始每次顺时针地数k个人(包括1号)并选定第k个人,然后从N号开始逆时针地数m个人(包括N号)并选定第m个人,如果前面选定的那个人与后面选定的那个人重合,则选走那一个人,否则选走分别选定的两个人。每次都是顺时针数k个人和逆时针数m个人,只不过都从分别选定的那个人的下一个人开始数起。按顺序输出每次被选走的人。
输入:
多组数据,每组给出N,k,m。以0,0,0作为输入的结束。
输出:
每组数据按顺序输出每次出圈人的编号,次与次之间有逗号间隔,整数都要占3个空格的位置并右顶格。
分析:
模拟题。每次遍历整个环形数列,如果已经选走则将它置为零。
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
1 #include <cstdio> 2 #include <iostream> 3 #include <cstring> 4 #include <cmath> 5 #include <algorithm> 6 using namespace std; 7 const int MAX_N = 20; 8 int n,k,m; 9 int arr[MAX_N + 1]; 10 int main(){ 11 while(scanf("%d%d%d",&n,&k,&m) == 3){ 12 if(!n && !k && !m) break; 13 int size = n; 14 int p = 0,q = n - 1; 15 for(int i = 0 ; i < n ; i++) arr[i] = i + 1; 16 while(size > 0){ 17 for(int i = 1 ; i <= k - 1 ; i++){ 18 p = (p + 1) % n; 19 if(!arr[p]) i--; 20 } 21 for(int j = 1 ; j <= m - 1 ; j++){ 22 q = (q - 1 + n) % n; 23 if(!arr[q]) j--; 24 } 25 printf("%3d",arr[p]); 26 arr[p] = 0; 27 size--; 28 if(arr[q]){ 29 printf("%3d",arr[q]); 30 arr[q] = 0; 31 size--; 32 } 33 for(int i = 0 ; i < n ; i++){ 34 p = (p + 1) % n; 35 if(arr[p]) break; 36 } 37 for(int j = 0 ; j < n ; j++){ 38 q = (q - 1 + n) % n; 39 if(arr[q]) break; 40 } 41 printf("%c",size == 0 ? '\n' : ','); 42 } 43 } 44 return 0; 45 }