#include <iomanip.h>
#include <apstring.h>
#include <apvector.h>
#include <apmatrix.h>

// problem #1
// precondition: num is >= 1
int factorial(int num) {
	if (num == 1) return 1;
	else return num * factorial(num - 1);
}

// problem #2
// precondition: num is >= 1, high starts off at num, and low starts off at 1
int squarert(int num, int high, int low) {
	int midpt;
	if (high==low) return high; // if there is no exact match, return what's close
	midpt = (high+low)/2;
	if (midpt * midpt == num) return midpt; // perfect match
	else if (midpt * midpt > num) // guess is too high
		return squarert(num, midpt-1, low); // we know our guess is beyond what the highest # could be
	else return squarert(num, high, midpt+1); // else our guess is too low
}

// problem #3
// precondition: counter starts at vector.length() - 1
int sumapvector(const apvector<int> &vector, int counter) {
	if (counter < 0) return 0; // indexes below 0 aren't possible, so the answer should be nothing
	return vector[counter] + sumapvector(vector, counter - 1);
}