Java – divides integers into sums and products

This is what I need to do: write an algorithm to decompose a given integer into sum products, but each subsequent number must be greater than the previous one, that is:

6 = 1+5;
6 = 1+2+3;
6 = 1*2+4;
6 = 2+4;
6 = 2*3;

A basic partition integer algorithm does not work because it returns numbers in a different order

I'm not asking for the final code, I'm just asking for some tips and suggestions, so I can do it myself Thank you in advance!

Solution

public class Perms {

public class Perms {

/**
 * @param args
 */
public static int x;
public static void main(String[] args) {
    // TODO Auto-generated method stub

    x = 6;
    rec(x,new int[1000],new String[1000],0);
}

public static void rec(int n,int all[],String operator[],int size)
{
       if (n==0)
       {
          if (size==1)return;
          System.out.print(x + " =");
          for (int i=0;i<size;i++)
          {
             System.out.print(" " + all[i]);
             if (i!=size-1)
                 System.out.print(" " + operator[i]);
          }
          System.out.println();
          return;
       }
       int i=1;
       if (size>0)
          i = all[size-1]+1;
       for ( ;i<=n;i++)
       {
          operator[size] = "+";
          all[size] = i;
          rec(n-i,all,operator,size+1);
       }

       i=1;
       if (size>0)
          i = all[size-1]+1;
       for (;i<=n;i++)
       {
          float r = n/(float)i;
          if (r == (int)r)
          {
             operator[size] = "*";
             all[size] = i;
             rec(n/i,size+1);
          }
       }
    }
}

Output:

6 = 1 + 2 + 3
6 = 1 + 5
6 = 2 + 4
6 = 1 * 2 + 4
6 = 1 * 6
6 = 1 * 2 * 3
6 = 2 * 3

Note: operations have priority (evaluation operations from right to left)

Example: 20 = 2 * 3 7 = (2 * (3 7)) = 2 * 10 = 20

It's easy to add these parentheses But the output will look ugly Just notice that it's better