39 lines
939 B
C
39 lines
939 B
C
#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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// Using Stirling's approximation,
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// n! ~ sqrt(2*pi*n) * (n/e)^n
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// ln(n!) ~ 0.5*ln(2*pi*n) + n*ln(n) - n
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// So the number of digits of n! is around
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// log(n!) = ln(n!)/ln(10)
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// ~ (0.5*ln(2*pi*n) + n*ln(n) - n)/ln(10)
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int getFactorialDigits(double n) {
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return ceil((0.5*log(2.0*M_PI*n) + n*log(n) - n)/log(10.0));
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}
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int main (int argc, char* argv[]) {
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int len = getFactorialDigits(100.0);
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char* num = calloc (len, sizeof (char));
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num[0] = 1;
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for (int i = 1; i <= 100; i++) {
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int carry = 0;
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for (int j = 0; j < len; j++) {
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int new_carry = (carry + num[j] * i) / 10;
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num[j] = (carry + num[j] * i) % 10;
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carry = new_carry;
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}
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}
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int sum = 0;
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for (int i = 0; i < len; i++) {
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sum += num[i];
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printf("%d", num[i]);
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}
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free (num);
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printf("\n%d\n", sum);
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}
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