Question

I’ve got this – possibly trivial – loop/combinations problem similar to binary combinations. I don’t know how to approach it efficiently. Consider this scenario, I need unique loop to pass through all these combinations in a sequence:

Round  ABC

01.    000 <- values of A=0, B=0, C=0
02.    001
03.    010
04.    011
05.    100
06.    101
07.    110
08.    111

09.    002
10.    012
11.    102
12.    112
13.    020
14.    021
15.    120
16.    121 <- values of A=1, B=2, C=1
17.    022
18.    122
19.    220
20.    221
21.    222

Except there are 12 letters (A-L), and also the “bit” size is not just 0,1 or 2 but any integer number (from 0 possibly up-to 1000 or 1024, not to make it crazy). I know it’s a huge load of combinations, but I’ll just scrap just top few that also fulfill my other conditions. So no need to worry about computational madness.

Disclaimer: The order has to be exactly as shown above. NOT a multiple FOR loops going first 0-1024 for C, then B.

Thanks in advance, I just can’t seem to find the way to “algorithm it”.

Update: Added whole sequence for combinations of ABC/012

regards,
Kate

Explanation:

I’ve encountered this problem when trying to tackle problem of analyzing sum of money for its combination of coins/notes:

For example $5001 to find out x optimal combinations.

10x $500 + 1x $1
50x $100 + 1x $1
..

Now letters (A,B,C..) correspond to a number of possible values of banknotes or coins ($1, $5,.. $100). While base correspond to a number of pieces of that banknotes/coins (for example $5001/$5000 = 1piece max.)

Answer 1

if I guess your sequence right, you will have it easier to generate it recursively

here an approach in Java, which should generate a sequence that matches your scenario.
I hope it helps you (maybe I add more explanation later):

public static void init() {
    // define constants
    final int length = 3;
    final char maxValue = '3';

    // define buffer
    final char[] array = new char[length]; java.util.Arrays.fill(array, '0');
    final boolean[] alreadySet = new boolean[length]; java.util.Arrays.fill(alreadySet, false);

    // fill first digit, then let the recursion take place
    for(char c = '1'; c <= (char)(maxValue); c++) {
        // iterate from lowest to highest digit
        for(int i = array.length-1; i >= 0; i--) {
            // set value
            array[i] = c;
            alreadySet[i] = true;
            // print value
            System.out.println(new String(array));
            // call recursion
            recursive(array, c, i, alreadySet, length);
            // unset value
            alreadySet[i] = false;
            array[i] = '0';
        }
    }
}

public static void recursive(char[] array, char lastValue, int lastIndex, boolean[] alreadySet, int leftToSet) {
    // if we didn't set all digits
    if(leftToSet > 0) {
        // iterate from lowest to highest digit
        for(int i = array.length-1; i >= 0; i--) {
            // missing all digits already set
            if(!alreadySet[i]) {
                // count from 1 to lastValue-1
                for(char c = '1'; c < lastValue; c++) {
                    // set value
                    array[i] = c;
                    alreadySet[i] = true;
                    // print value
                    System.out.println(new String(array));
                    // call recursion
                    recursive(array, c, i, alreadySet, leftToSet-1);
                    // unset value
                    alreadySet[i] = false;
                    array[i] = '0';
                }
            }
        }

        char c = lastValue;
        // iterate from lowest to highest digit
        for(int i = array.length-1; i > lastIndex; i--) {
            // missing all digits already set
            if(!alreadySet[i]) {
                // set value
                array[i] = c;
                alreadySet[i] = true;
                // print value
                System.out.println(new String(array));
                // call recursion
                recursive(array, c, i, alreadySet, leftToSet-1);
                // unset value
                alreadySet[i] = false;
                array[i] = '0';
            }
        }
    }
}