Eddy ' s digital RootsTime
limit:2000/1000 MS (java/others) Memory limit:65536/32768 K (java/others)
Total submission (s): 5125 Accepted Submission (s): 2861
Problem DescriptionThe Digital root of a positive integer is found by summing the digits of the integer. If The resulting value is a, digit then, digit is the digital root. If The resulting value contains or more digits, those digits was summed and the process is repeated. This was continued as long as necessary to obtain a and 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 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 are that:give you the n,want your to find the N^n ' s digital Roots.
Inputthe input file would contain a list of positive integers n, one per line. The end of the input would be indicated by an integer value of zero. Notice:for each integer in the input n (n<10000).
Outputoutput N^n ' s digital root on a separate line of the output.
Sample Input
240
Sample Output
44
Authoreddy
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#include <stdio.h>int _pow (int a,int b) {if (b==0) return 1;if (b==1) return a%9;int Res=_pow (A,B/2); res= Res*res%9;if (b&1) Res=res*a%9;return res%9;} int main () {int n;while (~scanf ("%d", &n), n) {int T=_pow (n,n), if (t) printf ("%d\n", T), elseprintf ("9\n");} return 0;}
nine theorem of remainder: the sum of the numbers on each digit of a number = nine of its number (nine remainder is 9)
mathematics is simply too strong, incredibly still have this theorem!!
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Hdoj-1163-eddy ' s digital Roots "nine remainder theorem"
