sim_probabilities.cpp

#include <stdlib.h>
#include <stdio.h>

// samples the height of one structure for a given maximum height (H)
int sample_height(int maxHeight) {
	int height = 0;
	while (rand() % 2 == 1 & height < maxHeight) {
		height++;
	}
	return height;
}

// returns a boolean if the round matches the criteria (equal or smaller set of structures) 
// for a numer of structure N and a maximum height (H)
bool simulate_round (int N, int H){
	int lastStrucHeight = H;
	int strucHeight;
	
	for (int i = 0; i < N; ++i) {
		strucHeight = sample_height(H);
		
		// compare the height of the current structure to the former
		// if larger, we can abort the inner for loop (the creation of the structures for this round) 
		if (strucHeight > lastStrucHeight) {
			return false;
		}
		lastStrucHeight = strucHeight;
	}
	return true;

}

// takes the number of simulation rounds, the number of structures per round, the maximum height
// and returns the chance of matching the criteria
double simulate(int nRounds, int N, int H) {
	int countSmallerEqual = 0; // initiate the count of matching 
	int countLarger = 0;
	bool allSmallerEqual;

	// simulate nRounds rounds
	for (int round = 0; round < nRounds; ++round){

		// get N structures
		allSmallerEqual = simulate_round(N, H);
		
		// add the result to our overall counters
		if (allSmallerEqual) {
			countSmallerEqual++;
		} else {
			countLarger++;
		}
	}

	// calculate the chance of matching the criteria
	double chance = (double) countSmallerEqual / nRounds;
	return chance;
}

// main function of the simulation
int main () {

	int nRounds = 1000000; // rounds of simulation (N = 3, H = 3, nRounds = 100mil takes roughly 8 seconds)
	int N = 2; // number of structures
	int H = 3; // max Height, beware, we start at 0 (see the declaration in sample_height())
	
	// Single run
	// double chance = simulate(nRounds, N, H); // simulate the chance with nRounds rounds, N structures, and H as the max height
	// printf("N = %3d & H = %2d | chance = %.6f\n", N, H, simulate(nRounds, N, H));
	// printf("-----------------------------------\n");

	// multiple runs of N = 2 to 20
	printf("Running %d simulations each:\n", nRounds);
	printf("-----------------------------------\n");
	for (int Nmult = 2; Nmult < 20; Nmult++) {
		printf("N = %3d & H = %2d | chance = %.6f\n", Nmult, H, simulate(nRounds, Nmult, H));
	
	}
}