Special factorials: Difference between revisions

=={{header|C}}==

<lang c>#include <math.h>

#include <stdint.h>

#include <stdio.h>

/* n! = 1 * 2 * 3 * ... * n */

uint64_t factorial(int n) {

uint64_t result = 1;

int i;

for (i = 1; i <= n; i++) {

result *= i;

}

return result;

}

/* if(n!) = n */

int inverse_factorial(uint64_t f) {

int p = 1;

int i = 1;

if (f == 1) {

return 0;

}

while (p < f) {

p *= i;

i++;

}

if (p == f) {

return i - 1;

}

return -1;

}

/* sf(n) = 1! * 2! * 3! * ... . n! */

uint64_t super_factorial(int n) {

uint64_t result = 1;

int i;

for (i = 1; i <= n; i++) {

result *= factorial(i);

}

return result;

}

/* H(n) = 1^1 * 2^2 * 3^3 * ... * n^n */

uint64_t hyper_factorial(int n) {

uint64_t result = 1;

int i;

for (i = 1; i <= n; i++) {

result *= (uint64_t)powl(i, i);

}

return result;

}

/* af(n) = -1^(n-1)*1! + -1^(n-2)*2! + ... + -1^(0)*n! */

uint64_t alternating_factorial(int n) {

uint64_t result = 0;

int i;

for (i = 1; i <= n; i++) {

if ((n - i) % 2 == 0) {

result += factorial(i);

} else {

result -= factorial(i);

}

}

return result;

}

/* n$ = n ^ (n - 1) ^ ... ^ (2) ^ 1 */

uint64_t exponential_factorial(int n) {

uint64_t result = 0;

int i;

for (i = 1; i <= n; i++) {

result = (uint64_t)powl(i, (long double)result);

}

return result;

}

void test_factorial(int count, uint64_t(*func)(int), char *name) {

int i;

printf("First %d %s:\n", count, name);

for (i = 0; i < count ; i++) {

printf("%llu ", func(i));

}

printf("\n");

}

void test_inverse(uint64_t f) {

int n = inverse_factorial(f);

if (n < 0) {

printf("rf(%llu) = No Solution\n", f);

} else {

printf("rf(%llu) = %d\n", f, n);

}

}

int main() {

int i;

/* cannot display the 10th result correctly */

test_factorial(9, super_factorial, "super factorials");

printf("\n");

/* cannot display the 9th result correctly */

test_factorial(8, super_factorial, "hyper factorials");

printf("\n");

test_factorial(10, alternating_factorial, "alternating factorials");

printf("\n");

test_factorial(5, exponential_factorial, "exponential factorials");

printf("\n");

test_inverse(1);

test_inverse(2);

test_inverse(6);

test_inverse(24);

test_inverse(120);

test_inverse(720);

test_inverse(5040);

test_inverse(40320);

test_inverse(362880);

test_inverse(3628800);

test_inverse(119);

return 0;

}</lang>

{{out}}

<pre>First 9 super factorials:

1 1 2 12 288 34560 24883200 125411328000 5056584744960000

First 8 hyper factorials:

1 1 2 12 288 34560 24883200 125411328000

First 10 alternating factorials:

0 1 1 5 19 101 619 4421 35899 326981

First 5 exponential factorials:

0 1 2 9 262144

rf(1) = 0

rf(2) = 2

rf(6) = 3

rf(24) = 4

rf(120) = 5

rf(720) = 6

rf(5040) = 7

rf(40320) = 8

rf(362880) = 9

rf(3628800) = 10

rf(119) = No Solution</pre>