UVA-133 The Dole Queue
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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 counterclockwise 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 counterclockwise 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
分析:两边的约瑟夫环问题。
Source:
#include<stdio.h>int vis[20],n;int move(int pos,int flag,int step){ int i; for(i=1;i<=step;i++) { do{ pos=(pos+flag+n-1)%n+1; /*防止出现0和负数*/ }while(vis[pos-1]); } return pos;}int main(){ int left,p1,p2; int k,m,i; while(scanf("%d%d%d",&n,&k,&m)!=EOF) { if(n==0&&k==0&&m==0) return 0; for(i=0;i<n;i++) vis[i]=0; p1=n; p2=1; left=n; while(left) { p1=move(p1,1,k); p2=move(p2,-1,m); left--; printf("%3d",p1); if(p1!=p2) { printf("%3d",p2); left--; } if(left) printf(","); else printf("\n"); vis[p1-1]=vis[p2-1]=1; } } return 0;}
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