Uva133 The Dole Queue (simulation of Joseph's ring), uva133dole
Link to the question: Ah, Haha, I chose my train of thought: It is equivalent to simulating the Joseph ring, but it is done at the same time in the clockwise direction. Then, you can write a function in the clockwise direction, it is only the opposite of the variable marked in the direction .. There is also a wonderful use for (pos + flag + N-1) % n + 1... Question:
In a serious attempt to downsize (reduce) the dole queue, The New National Green Labor 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 labor 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 shoshould 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 shocould not be a trailing comma ).
Sample input
10 4 30 0 0
Sample output
4 8, 9 5, 3 1, 2 6, 10, 7
Where Represents a space.
Code:
#include<cstdio>#include<cstring>const int maxn=25+10;bool vis[maxn];int n,k,m;int Move(int pos,int flag,int step){ for(int i=1;i<=step;i++) { do { pos=(pos+flag+n-1)%n+1; }while(vis[pos]); } return pos;}int main(){ int left,p1,p2; while(~scanf("%d%d%d",&n,&k,&m)) { if(n==0&&k==0&&m==0) return 0; memset(vis,false,sizeof(vis)); p1=n; p2=1; left=n; while(left) { p1=Move(p1,1,k); p2=Move(p2,-1,m); printf("%3d",p1); left--; if(p1!=p2) { printf("%3d",p2); left--; } vis[p1]=vis[p2]=1; if(left) printf(","); else printf("\n"); } } return 0;}
Sample output
4 8, 9 5, 3 1, 2 6, 10, 7