Eddy's digital Roots HDU杭电1163 【一个比较实用的定理】
来源:互联网 发布:淘宝详情页的尺寸 编辑:程序博客网 时间:2024/05/30 07:12
Problem Description
The digital root of a positive integer is found by summing the digits of the integer. If the resulting value is a single digit then that digit is the digital root. If the resulting value contains two or more digits, those digits are summed and the process is repeated. This is continued as long as necessary to obtain a single digit.
For example, consider the positive integer 24. Adding the 2 and the 4 yields a value of 6. Since 6 is a single digit, 6 is the digital root of 24. Now consider the positive integer 39. Adding the 3 and the 9 yields 12. Since 12 is not a single digit, the process must be repeated. Adding the 1 and the 2 yeilds 3, a single digit and also the digital root of 39.
The Eddy's easy problem is that : give you the n,want you to find the n^n's digital Roots.
For example, consider the positive integer 24. Adding the 2 and the 4 yields a value of 6. Since 6 is a single digit, 6 is the digital root of 24. Now consider the positive integer 39. Adding the 3 and the 9 yields 12. Since 12 is not a single digit, the process must be repeated. Adding the 1 and the 2 yeilds 3, a single digit and also the digital root of 39.
The Eddy's easy problem is that : give you the n,want you to find the n^n's digital Roots.
Input
The input file will contain a list of positive integers n, one per line. The end of the input will be indicated by an integer value of zero. Notice:For each integer in the input n(n<10000).
Output
Output n^n's digital root on a separate line of the output.
Sample Input
240
Sample Output
44
#include<stdio.h>int main(){int n;int pos;while(scanf("%d",&n),n){int res=1;for(int i=1;i<=n;++i){res*=n;res=res%9==0?9:res%9;}printf("%d\n",res);}return 0;}/*因为ab*ab=(10*a+b)*(10*a+b)=100*a*a+10*2*a*b+b*b=a*a+2*a*b+b*b=(a+b)*(a+b)abc*abc=(100*a+10*b+c)*(100*a+10*b+c)=10000*a*a+2000*a*b+100*b*b+200*a*c+20*b*c+c*c=a*a+2*a*b+b*b+2*a*c+2*b*c+c*c=(a+b)^2+2*c*(a+b)+c*c= (a+b+c)*(a+b+c)所以((a+b+c)*(a+b+c))%9=((abc)%9*(abc)%9)%9 同余定理 */
0 0
- Eddy's digital Roots HDU杭电1163 【一个比较实用的定理】
- 杭电 HDU 1163 Eddy's digital Roots
- 杭电1163 Eddy's digital Roots
- 杭电 1163 Eddy's digital Roots
- Hdu-1163 Eddy's digital Roots(九余数定理)
- hdu 1163 Eddy's digital Roots(九余数定理)
- HDU 1163 Eddy's digital Roots(九余数定理)
- Hdu 1163 Eddy's digital Roots(九余数定理)
- HDU 1163 Eddy's digital Roots(九余数定理)
- [数学 九余数定理] HDU 1163 Eddy's digital Roots
- 杭电1163--Eddy's digital Roots (九余数定理)
- HDU-1163Eddy's digital Roots,九余定理的另一种写法!
- hdu 1163 Eddy's digital Roots
- hdu 1163 Eddy's digital Roots
- HDU 1163 Eddy's digital Roots
- HDU 1163 Eddy's digital Roots
- HDU 1163 Eddy's digital Roots
- 数论---HDU 1163 Eddy's digital Roots
- JS之reduce
- Activity跳转Flag详解
- 系统性能调优
- Android之HttpClient的使用方法
- hdu5402 Travelling Salesman Problem
- Eddy's digital Roots HDU杭电1163 【一个比较实用的定理】
- HTTP协议总结
- C语言之文件操作08——总结
- 差分约束系统详解
- POJ 2367 Genealogical tree 【拓扑 基础题】
- 如何有效地记忆与学习
- uva 1175 Ladies' Choice (稳定婚姻问题)
- Android 笔记1
- jQuery转义