Find the number of digit(s) of the factorial of an integer in a certain base

问题

My solution was pretty fast but not enough. I need more faster. How can I reduce my time? Input Number: n (0 ≤ n ≤ 1000000) Base should be: base (2 ≤ base ≤ 1000)

Input 5! in 10 base. Output is: 3
Input 22! in 3 base. Output is: 45

Time Limit: 2 second(s), and Memory Limit: 32 MB

Here is my code in c language:

#include<stdio.h>
#include<math.h>
int factorialDigitExtended ( int n, int base ) {
    double x = 0;
    for ( int i = 1; i <= n; i++ ) {
        x += log10 ( i ) / log10(base);
    }
    int res = ( (int) x ) + 1;
    return res;
}

int main(){
    int i, t, n, b;
    for(i=1; i<= t; i++){
        scanf("%d %d", &n, &b);
        printf("Case %d: %d\n", i, factorialDigitExtended(n, b));
    }
    return 0;
}

回答1:

Like I mentioned in the comment above this might be target specific behavior. A few things I would look at:

Only calculate constant values once:

int factorialDigitExtended ( int n, int base ) {
    double x = 0;
    double lbase = log10(base);
    for ( int i = 1; i <= n; i++ ) {
        x += log10 ( i ) / lbase;
    }
    int res = ( (int) x ) + 1;
    return res;
}

Division may be expensive:

int factorialDigitExtended ( int n, int base ) {
    double x = 0;
    double lbase = 1 / log10(base);
    for ( int i = 1; i <= n; i++ ) {
        x += log10 ( i ) * lbase;
    }
    int res = ( (int) x ) + 1;
    return res;
}

Don't repeat the same multiplication n times:

int factorialDigitExtended ( int n, int base ) {
    double x = 0;
    double lbase = 1 / log10(base);
    for ( int i = 1; i <= n; i++ ) {
        x += log10 ( i );
    }
    x *= lbase;
    int res = ( (int) x ) + 1;
    return res;
}

0 compare might be cheaper:

int factorialDigitExtended ( int n, int base ) {
    double x = 0;
    double lbase = 1 / log10(base);
    for ( int i = n; i > 0; --i ) {
        x += log10 ( i );
    }
    x *= lbase;
    int res = ( (int) x ) + 1;
    return res;
}

Btw (int) x might fail at some points due to precision problems.

There might also be processor specific logarithm instructions.

来源：https://stackoverflow.com/questions/40909278/find-the-number-of-digits-of-the-factorial-of-an-integer-in-a-certain-base

标签

base

factorial