// CSIT 121
// Dr. Straight
// Problem: Choose a poynomial p(x) with nonnegative-integer coefficients and at least two terms.
// Input p(1) and p(p(1)).
// Output the degree of p(x) and its coefficients.

// Program written by (Your Name)

#include <iostream>
#include <iomanip>
#include <cmath>
using namespace std;

int degree(int z2,int z1)
//Computes the degree of p(x).
{
	return floor(log(z2)/log(z1));
}

void coefficients(int n,int b)
//Computes and outputs the coefficients of p(x).
//Essentially, this computes the base-b representation of n.
{
	int i, d, q = n, r;
	d = degree(n,b);
	for (i = 0; i <= d; i = i + 1)
	{
		r = q % b;
		cout << setw(10) << r << endl;
		q = (q - r)/b;
	}
}

int main()
{
	//Variables used:
	int y1; //y1 = p(1)
	int y2; //y2 = p(p(1))
	int d; //degree of p(x)

	//Prompt the user for p(1) and p(p(1)).
	cout << "Choose a polynomial p(x) with nonnegative integer coefficients and" << endl;
	cout << "at least two terms." << endl;
	cout << "Enter p(1) (enter 0 or a negative integer to quit): ";
	cin >> y1;
	While (y1 > 0)
	{
		cout << "Enter p(p(1)): ";
		cin >> y2;
		cout << "The Great Mathemagician will now compute your polynomial." << endl;
		d = degree(y2,y1);
		cout << "The degree of your polynomial is " << d << endl;
		cout << "The coefficients of your polynomial, in order of increasing" << endl;
		cout << "term-power, are as follows:" << endl;
		coefficients(y2,y1);
		cout << endl;
		cout << "Choose another polynomial p(x)." << endl;
		cout << "Enter p(1) (0 or a negative integer to quit): ";
		cin >> y1;
	}
	system("pause");
	return 0;
}