Question

I am writing a program to try to solve a math problem. I need to generate a unique list of all of the numbers that add up to another number. For example, all of the unqiue combinations of 4 numbers that add up to 5 are:

5 0 0 0
4 1 0 0 
3 2 0 0
3 1 1 0
2 2 1 0
2 1 1 1

This is easy to brute force in perl but I am working in C and would like to find a more elegant solution.

In perl I would generate every possible combination of numbers 0-N in each column, discard the ones that don’t add up to the target number, then sort the numbers in each row and remove the duplicate rows.

I’ve been trying all morning to write this in C but can’t seem to come up with a satisfactory solution. I need it to work up to a maximum N of about 25. Do you guys have any ideas?

Here is an example of the kind of thing I have been trying (this produces duplicate combinations):

// target is the number each row should sum to.
// Don't worry about overflows, I am only using small values for target
void example(int target)
{

  int row[4];

  for (int a=target; a>=0; a--) {
    row[0] = a;

    for (int b=target-a; b>=0; b--) {
      row[1] = b;

      for (int c=target-(a+b); c>=0; c--) {
        row[2] = c;

        row[3] = target-(a+b+c);

        printf ("%2d %2d %2d %2d   sum: %d\n", row[0],row[1],row[2],row[3],
                                          row[0]+row[1]+row[2]+row[3]);
      }
    }
  }
}

Answer 1

This is called a partition problem and approaches are discussed here, here and here.