#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <assert.h>
#include <stdint.h>

uint64_t _pow(uint64_t n1, uint64_t n2) {
    uint64_t result = 1;
    for(int i = 0; i < n2; i++) {
        result *= n1;
    }
    return result;
}

void _iterate_noops_helper(uint64_t n, int depth, uint64_t* a_num_invocations) {
    *a_num_invocations += 1;
    if(depth > 0) {
        for(uint64_t i = 0; i < n; i++) {
            _iterate_noops_helper(n, depth - 1, a_num_invocations);
        }
    }
}

int iterate_noops(uint64_t n) {
    uint64_t num_invocations = 0;
    _iterate_noops_helper(n, n, &num_invocations);
    return num_invocations;
}

int main(int argc, char* argv[]) {
    for(int n = 5; n < 10; n++) {
        printf("___________________________\n");
        printf("n == %d\n", n);
        uint64_t num_invocations = iterate_noops(n);
        printf("num_invocations == %lu\n", num_invocations);
        printf("%d ^ %d == %lu\n", n, n, _pow(n, n));
        printf("num_invocations / (%d ^ %d) == %.06f\n", n, n, (1.0 * num_invocations / _pow(n, n)));
    }

    return EXIT_SUCCESS;
}
/* vim: set tabstop=4 shiftwidth=4 fileencoding=utf-8 noexpandtab: */