HDU 1013.Digital Roots模拟或数论8月16
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Digital Roots
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.
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.
Input
The input file will contain a list of positive integers, one per line. The end of the input will be indicated by an integer value of zero.
Output
For each integer in the input, output its digital root on a separate line of the output.
Sample Input
24 39 0
Sample Output
6 3
#include<cstdio> #include<cstring> void zuo(int x){ int sum=0; while(x){ sum+=(x%10); x/=10; } if(sum<10) printf("%d\n",sum); else zuo(sum); } int main(){ char s[1010]; while(scanf("%s",s)&&s[0]!=‘0‘){ int x=0; for(int i=0;i<strlen(s);i++) x+=(s[i]-‘0‘); zuo(x); } return 0; }另一种解法。数论的知识。
数字本身: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 12 22 23 24 25 26 27 28 29 30············
各个位数和: 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3·············
你会发现。每9个是一个循环。所以仅仅要对9取余就ok了。代码例如以下:
#include<cstdio> #include<cstring> int main(){ char s[1010]; while(scanf("%s",s)&&s[0]!=‘0‘){ int x=0; for(int i=0;i<strlen(s);i++) x+=(s[i]-‘0‘); x=x%9; if(x==0) printf("9\n"); else printf("%d\n",x); } return 0; }
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(HDU)1013 --Digital Roots(数字根)