How do I generate integer partitions?

Question

I have a list of numbers like 1,2,3 and I want to find all the combination patterns that sum up to a particular number like 5. For example:

Sum=5
Numbers:1,2         


        

Answer 1

    public static List<List<string>> Partition(int n, int max, string prefix)
    {

        if (n == 0)
        {
            _results.Add(prefix.Split(new char[] { ',' }).ToList());
        }

        for (int i = Math.Min(max, n); i >= 1; i--)
        {
            Partition(n - i, i, prefix + "," + i);
        }

        return _results;
    }

Answer 2

This is a slight modification of the change making problem. You should be able to find plenty of papers on this problem, and a dynamic programming solution would take no more than 20 lines of code.

http://en.wikipedia.org/wiki/Change-making_problem

Answer 3

This problem is known as a "doubly restricted integer partition." If the numbers "allowed" to sum to 5 were from a set V, then it is known as "multiply restricted integer partition." There is a paper by Riha and James: "Algorithm 29: Efficient algorithms for doubly and multiply restricted partitions" Computing Vol 16, No 1-2, pp 163-168 (1976). You should read that paper and implement their algorithm. Understanding how to do it will allow you to implement optimizations unique to your specific problem.

Answer 4

You can use following code .. it wiil give you a exact answer as you want..

void print(int n, int * a)

{
   int i ; 

   for (i = 0; i <= n; i++) 

   {

  printf("%d", a[i]); 

  }

 printf("\n"); 

}


void integerPartition(int n, int * a, int level)

{

   int first; 

  int i; 

  if (n < 1) 

 return ;    

 a[level] = n;

  print(level, a);

  first = (level == 0) ? 1 : a[level-1];

  for(i = first; i <= n / 2; i++)

   {

       a[level] = i; 

       integerPartition(n - i, a, level + 1);

   }

}

int main()

  {

   int n = 10;     

   int * a = (int * ) malloc(sizeof(int) * n); 

   integerPartition (n, a, 0); 

   return(0);

}

Answer 5

This might also help: Dynamic Programming: Combination Sum Problem

Answer 6

These are called the partitions of a number , and your problem seems to impose the constraint of which numbers you're allowed to use in the partition.