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

// Problem #1 (tail recursive)

void findlargest(const apvector<int> &vector, int position, int &largest) {
	if (position == vector.length()) return;
	else if (vector[position] > largest) largest = vector[position];
	findlargest(vector, position+1, largest);
}

// Problem #1 embedded recursive (this will look weird)

int findlargest(const apvector<int> &vector, int position) {
	if (position == vector.length()) return 0; // we assume 0 is the smallest possible value
	
	/* ok, this will look very very weird.  If we assume that findlargest should return the
	   largest value in the vector starting at a given position, then we can get away with 
	   saying we want to return which ever is larger: the item we're looking at now, or the 
	   largest remaining value in the apvector, which is what we're saying with the following
	   code */
	else if (vector[position] > findlargest(vector, position+1)) return vector[position];
		else return findlargest(vector, position+1);
}

// Problem #2

// this should be a lot easier now

int numseries(int position) {
	if (position > 0 && position <= 3) return 1;
	else return 2 * numseries(position - 1) + numseries(position - 2) 
		- numseries(position - 3);
}

// Problem #3 (saving the world from your teacher...)

int sl(const apvector<int> &v, const int cutoff, int pos) {
	if (pos == v.length()) return 0;
	else if (v[pos] < cutoff) return v[pos]+sl(v,cutoff,pos+1);
	else return sl(v,cutoff, pos+1);
}

int sumlower(const apvector<int> &v, const int cutoff) {
	return sl(v, cutoff, 0);
}