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,编号为1到n,围成一个圆圈。从1开始逆时针每次数k个人,从n开始顺时针每次数m个人。数到的人出列,有可能是同一个人。出列后排队按照逆时针先,顺时针后。直到所有人都被数出来。
这道题数据不大,就直接用数组来模拟了。约瑟夫问题的延伸。如果说数据很大的话,可以用链表来做,不过这个链表还得是双向链表,也挺麻烦的。
#include<iostream> #include<cstdio> #include<cstring> #include<cmath> using namespace std; int a[25]; int main () { int n,k,m,t,i,j,posk,posm; while(cin>>n>>k>>m) { if (n==0) break; t=0; memset(a,0,sizeof(a)); posk=0; posm=n+1; while(t<n) { i=j=0; while(i<k) { posk++; if (posk>n) posk=0; if (!a[posk] && posk!=0) i++; } while(j<m) { posm--; if (posm<1) posm=n+1; if (!a[posm] && posm!=n+1) j++; } if (posk==posm) { t++; printf("%3d",posk); } else { t+=2; printf("%3d%3d",posk,posm); } if (t!=n) cout<<","; else cout<<endl; a[posk]=a[posm]=1; } } }