UVA 133 The Dole Queue

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本文解析了 UVA133:The Dole Queue 的问题背景及算法实现，通过设定特定规则从申请者中选择人员进行再培训。提供了完整的 C 语言代码实现，并详细说明了输入输出格式。

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UVA 133 The Dole Queue

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
tex2html_wrap_inline34 4 tex2html_wrap_inline34 8, tex2html_wrap_inline34 9 tex2html_wrap_inline34 5, tex2html_wrap_inline34 3 tex2html_wrap_inline34 1, tex2html_wrap_inline34 2 tex2html_wrap_inline34 6, tex2html_wrap_inline50 10, tex2html_wrap_inline34 7
where tex2html_wrap_inline50 represents a space.

#include<stdio.h>
int num[25],n,a,b;
int run(int number,int turn,int running)
{
    while(running--)
    {
        do
        {
            number=(number+turn+(n-1))%n+1;//解决了求余后值为0的情况
        }
        while(num[number]==0);
    }
    return number;
}
int main (void)
{
    while(~scanf("%d%d%d",&n,&a,&b)&&n)
    {
        for(int i=1; i<=n; i++)
        {
            num[i]=i;
        }
        int rest=n;
        int p1=n;
        int p2=1;
        while(rest)
        {
            p1=run(p1,1,a);//顺时针走
            p2=run(p2,-1,b);//逆时针走
            printf("%3d",p1);
            rest--;
            if(p1!=p2)
            {
                printf("%3d",p2);rest--;
            }
            num[p1]=num[p2]=0;
            if(rest) printf(",");
        }
        printf("\n");
    }
    return 0;
}