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【数论】 大数的各个位数和直到取到个位
2012年3月11日dlut周赛1002
LOVELY-POINT
TimeLimit: 1 Second MemoryLimit: 32 Megabyte
Totalsubmit: 154 Accepted: 42
Description
Lolihunter loves Lolita,To tell while lolita is batter,he makes the lovely-point of a Lolita which is found by summing the digits of the fascination of the Lolita. If the resulting value is a single digit then that digit is the Lolita’s lovely-point. If the resulting value contains two or more digits, those digits are summed and the process is repeated. This is continued as much as necessary times to obtain a single digit.
The fascination of a Lolita is n^n.n is a positive integer which is her age.
For example, consider the her age n=4. 4*4*4*4=256. Adding the 2 ，the 5,and the 6 yields a value of 13. Since 13 is not a single digit, the process must be repeated. Adding the 1 and the 3 yeilds 4, the lovely-point of the Lolita is 4.
The fascination of a Lolita is n^n.n is a positive integer which is her age.
For example, consider the her age n=4. 4*4*4*4=256. Adding the 2 ，the 5,and the 6 yields a value of 13. Since 13 is not a single digit, the process must be repeated. Adding the 1 and the 3 yeilds 4, the lovely-point of the Lolita is 4.
Input
The input file will contain a list of positive integers, one per line(0<=n<=10000). The end of the input will be indicated by an integer value of zero.
Output
For each integer in the input, output its digital sum on a separate line of the output.
Sample Input
4
3
0
Sample Output
4
9
接触到的第一道数论题，开始以为是大数运算问题，其实可以步步求余来简化。
那么本题的关键在于一个%9
我们看这样的例子abc-->表示为100*a +10*b +c 那么进行各个位的数值相加运算后是什么结果呢？
我们认为是（100*a +10*b +c ）%9的余数，因为（100*a +10*b +c ）可以写成（99*a +9*b）+（a+b+c），推广之~那么我们步步对9求余，如果能被9整除则结果为9，否则继续求余。
#include <iostream>#include <cstring>#include <cstdio>#include <stack>using namespace std;int main(){ //freopen("in.txt","r",stdin); int n; while(cin >> n) { int flag=0; if (n==0)break; int temp=n; for(int i=0;i<temp-1;i++) { if(n%9==0) { flag=1; break; } n%=9; n=n*temp; } if(flag==1)cout << 9 << endl; else { if(n>9)n%=9; cout << n << endl; } } return 0;}
【数论】 大数的各个位数和直到取到个位
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