Question

What I’m trying to accomplish is making a function to the following:

Imagine that I have between 1-9 squares. Those squares have a number assigned to them globally, not individually. They are like a set, and that set has this number.

E.g.: | _ | _ | _ | 19

What I’m trying to do is a function that gives me the possible combinations depending on number of squares and the number associated with them. For the example above: 9, 8, 2 is one of the possible combinations. However I just want the numbers that are in those combinations, not the combinations themselves. Plus they have to be unique (shouldn’t be 9, 9, 1). Oh and those numbers range from 1-9 only.

How can I achieve this in C? If you are wondering this is for a puzzle game.

Thanks in advance!

Answer 1

For future reference, in combinatorics we say “order doesn’t matter” to mean “I only want the set of numbers, not a specific ordering”

//Sets the given digit array to contain the "first" set of numbers which sum to sum
void firstCombination(int digits[], int numDigits, int sum) { 
    reset(digits, 0, 1, numDigits, sum);
}

//Modifies the digit array to contain the "next" set of numbers with the same sum.
//Returns false when no more combinations left
int nextCombination(int digits[], int numDigits) {
    int i;
    int foundDiffering = 0;
    int remaining = 0;
    for (i = numDigits - 1; i > 0; i--) {
        remaining += digits[i];
        if (digits[i] - digits[i - 1] > 1) {
            if (foundDiffering || digits[i] - digits[i - 1] > 2) {
                digits[i - 1]++;
                remaining--;
                break;
            } else
                foundDiffering = 1;
        }
    }
    if (i == 0)
        return 0;
    else {
        reset(digits, i, digits[i - 1] + 1, numDigits - i, remaining);
        return 1;
    }
}

//Helper method for firstCombination and nextCombination
void reset(int digits[], int off, int lowestValue, int numDigits, int sum) {
    int i;
    int remaining = sum;
    for (i = 0; i < numDigits; i++) {
        digits[i + off] = lowestValue;
        remaining -= lowestValue;
        lowestValue++;
    }
    int currentDigit = 9;
    for (i = numDigits + off - 1; i >= off; i--) {
        if (remaining >= currentDigit - digits[i]) {
            remaining -= currentDigit - digits[i];
            digits[i] = currentDigit;
            currentDigit--;
        } else {
            digits[i] += remaining;
            break;
        }
    }
}