/*
 * -----------------------------------------------------
 * CS2S03/SE2S03, September 2011
 * Assignment 1, Question 2
 * File: PE0107.cpp
 * -----------------------------------------------------
 * This program generates and displays the list of
 * perfect numbers in the range of 1 to 9999.
 * -----------------------------------------------------
 */

#include "genlib.h"
#include "simpio.h"
#include <iostream>
#include <iomanip>
#include <cmath>

/*
 * Constants
 * -----------------------------------------------------
 * LOWER_LIMIT -- Starting value for the range
 * UPPER_LIMIT -- Final value for the range
 */
const int LOWER_LIMIT = 1;
const int UPPER_LIMIT = 9999;

/* Private function prototypes */

bool IsPerfect(int n);

/* Main program */

int main() {
    for (int i = LOWER_LIMIT; i <= UPPER_LIMIT; i++) {
        if (IsPerfect(i))
            cout << setw(4) << i << " " << "is a perfect number." << endl;
    }

    return 0;
}

/*
 * Function: IsPerfect
 * Usage: if (IsPerfect(n)) ...
 * ------------------------------------------------------------
 * This function returns true if integer n is a perfect number,
 * that is, n equals the sum of its proper divisors.
 */

bool IsPerfect(int n) {
    if (n < 1) return false;

    int sum = 0;                //sum of divisors
    int q;                      //quotient
    int ubound = sqrt(n);       //upper bound for the potential divisors
    if (ubound > n - 1)         //divisors must be proper
        ubound = n - 1;
								
    for (int divisor = 1; divisor <= ubound; divisor++) {
        if ((n % divisor == 0)) {		//found a divisor
            sum += divisor;
            q = n / divisor;
            if ((q > divisor) && (q < n)) {    //the other proper divisor
                sum += q;
            }
        }
    }

    return (n == sum);
}