During the power crisis in New Zealand this winter (caused by a shortage of rain and hence low levels in the hydro dams), a contingency scheme was developed to turn off the power to areas of the country in a systematic, totally fair, manner. The country was divided up into N regions (Auckland was region number 1, and Wellington number 13). A number, m, would be picked ‘at random’, and the power would first be turned off in region 1 (clearly the fairest starting point) and then in every m’th region after that, wrapping around to 1 after N, and ignoring regions already turned off. For example, if N = 17 and m = 5, power would be turned off to the regions in the order:1,6,11,16,5,12,2,9,17,10,4,15,14,3,8,13,7.
The problem is that it is clearly fairest to turn off Wellington last (after all, that is where the Electricity headquarters are), so for a given N, the ‘random’ number m needs to be carefully chosen so that region 13 is the last region selected.
Write a program that will read in the number of regions and then determine the smallest number m that will ensure that Wellington (region 13) can function while the rest of the country is blacked out.
Input
Input will consist of a series of lines, each line containing the number of regions (N) with 13 ≤ N < 100. The file will be terminated by a line consisting of a single ‘0’.
Output
Output will consist of a series of lines, one for each line of the input. Each line will consist of the number m according to the above scheme.
Sample Input
17
0
Sample Output
7
问题链接：UVA151 Power Crisis
问题简述：
电厂按照约瑟夫环的规则断电，步长为m，最后停在13号，求m。
问题分析：
这个问题是约瑟夫环问题，用暴力法来解决。在此之前需要做数学的推导，占个位置以后解释。
程序说明：（略）
题记：（略）
参考链接：（略）
/* UVA151 Power Crisis */
#include <iostream>
#include <stdio.h>
using namespace std;
int main()
{
int n;
while(~scanf("%d", &n) && n) {
for(int i = 1; i < n; i++) {
int k = 0;
for(int j = 1; j < n; j++)
k = (k + i) % j;
if(k == 11) {
printf("%d\n", i);
break;
}
}
}
return 0;
}