package Maths;

/**
 * Amicable numbers are two different numbers so related
 * that the sum of the proper divisors of each is equal to the other number.
 * (A proper divisor of a number is a positive factor of that number other than the number itself.
 * For example, the proper divisors of 6 are 1, 2, and 3.)
 * A pair of amicable numbers constitutes an aliquot sequence of period 2.
 * It is unknown if there are infinitely many pairs of amicable numbers.
 * *
 * <p>
 * * link: https://en.wikipedia.org/wiki/Amicable_numbers
 * * </p>
 * <p>
 * Simple Example : (220,284) 220 is divisible by {1,2,4,5,10,11,20,22,44,55,110 } <- Sum = 284
 * 284 is divisible by -> 1,2,4,71,142 and the Sum of that is. Yes right you probably expected it 220
 */

public class AmicableNumber {

    public static void main(String[] args) {

              AmicableNumber.findAllInRange(1,3000);
        /* Res -> Int Range of 1 till 3000there are 3Amicable_numbers These are  1: = ( 220,284)	2: = ( 1184,1210)
        3: = ( 2620,2924) So it worked	*/

    }

    /**
     * @param startValue
     * @param stopValue
     * @return
     */
    static void findAllInRange(int startValue, int stopValue) {

        /* the 2 for loops are to avoid to double check tuple. For example (200,100) and (100,200) is the same calculation
         * also to avoid is to check the number with it self. a number with itself is always a AmicableNumber
         * */
        StringBuilder res = new StringBuilder();
        int countofRes = 0;

        for (int i = startValue; i < stopValue; i++) {
            for (int j = i + 1; j <= stopValue; j++) {
                if (isAmicableNumber(i, j)) {
                    countofRes++;
                    res.append("" + countofRes + ": = ( " + i + "," + j + ")" + "\t");
                }
            }
        }
        res.insert(0, "Int Range of " + startValue + " till " + stopValue + " there are " + countofRes + " Amicable_numbers.These are \n ");
        System.out.println(res.toString());
    }

    /**
     * Check if {@code numberOne and numberTwo } are AmicableNumbers or not
     *
     * @param numberOne numberTwo
     * @return {@code true} if {@code numberOne numberTwo} isAmicableNumbers  otherwise false
     */
    static boolean isAmicableNumber(int numberOne, int numberTwo) {

        return ((recursiveCalcOfDividerSum(numberOne, numberOne) == numberTwo && numberOne == recursiveCalcOfDividerSum(numberTwo, numberTwo)));
    }

    /**
     * calculated in recursive calls the Sum of all the Dividers beside it self
     *
     * @param number div = the next to test dividely by using the modulo operator
     * @return sum of all the dividers
     */
    static int recursiveCalcOfDividerSum(int number, int div) {

        if (div == 1) {
            return 0;
        } else if (number % --div == 0) {
            return recursiveCalcOfDividerSum(number, div) + div;
        } else {
            return recursiveCalcOfDividerSum(number, div);
        }
    }






}