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Sum of divisors

2024-08-01 14:09:28   221人阅读

Problem Description
mmm is learning division, she‘s so proud of herself that she can figure out the sum of all the divisors of numbers no larger than 100 within one day!
But her teacher said "What if I ask you to give not only the sum but the square-sums of all the divisors of numbers within hexadecimal number 100?" mmm get stuck and she‘s asking for your help.
Attention, because mmm has misunderstood teacher‘s words, you have to solve a problem that is a little bit different.
Here‘s the problem, given n, you are to calculate the square sums of the digits of all the divisors of n, under the base m.
 
Input
Multiple test cases, each test cases is one line with two integers.
n and m.(n, m would be given in 10-based)
1≤n≤109
2≤m≤16
There are less then 10 test cases.
 
Output
Output the answer base m.
 
Sample Input
10 2
30 5
 
Sample Output
110
112
 
Hint
Use A, B, C...... for 10, 11, 12......Test case 1: divisors are 1, 2, 5, 10 which means 1, 10, 101, 1010 under base 2, the square sum of digits is 1^2+ (1^2 + 0^2) + (1^2 + 0^2 + 1^2) + .... = 6 = 110 under base 2.
 
 1 #include <stdio.h> 2  3 int change(int number,int m); 4  5 int main(){ 6     int n; 7     int m; 8     int i; 9     int j;10     int length;11     int sum;12     int temp;13     char s[100];        14     15     while(scanf("%d%d",&n,&m)!=EOF){16         sum=0;17         for(i=1;i*i<=n;i++){  //这里i*i<=n，如果i从1到n则超时 18             if(n%i==0){19                 temp=change(i,m);    20                 sum+=temp;21                 22                 if(i!=n/i){  //如果i和n/i相等则算一次 23                     temp=change(n/i,m);24                     sum+=temp;25                 }26             }27         }28         29         i=0;30         while(sum){31             temp=sum%m;32             33             if(temp<=9)34                 s[i]=temp+‘0‘;35                 36             else if(temp==10)37                 s[i]=‘A‘;38                 39             else if(temp==11)40                 s[i]=‘B‘;41                 42             else if(temp==12)43                 s[i]=‘C‘;44                 45             else if(temp==13)46                 s[i]=‘D‘;47                 48             else if(temp==14)49                 s[i]=‘E‘;50                 51             else if(temp==15)52                 s[i]=‘F‘;53                 54             i++;55             sum/=m;56         }57         58         length=i;59         60         for(i=length-1;i>=0;i--)61             printf("%c",s[i]);62         63         printf("\n");64     }65     66     return 0;67 } 68 69 int change(int number,int m){70     int temp;71     int result;72     73     result=0;74     while(number){75         temp=number%m;76         result+=temp*temp;77         number/=m;78     }79     return result;80 }

 

Sum of divisors


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