Subset Sum

Given a set of non-negative integers, and a value sum, determine if there is a subset of the given set with sum equal to given sum.

The previous post talks about recursive approach which has exponential complexity

Lets see a dynamic programming approach which has polynomial complexity.

// Returns true if there is a subset of set[] with sun equal to given sum
	public static boolean isSubsetSumDynamic(int set[], int n, int sum)
	{
	    // The value of subset[i][j] will be true if there is a subset of set[0..j-1]
	    //  with sum equal to i
	    boolean subset[][] = new boolean[sum+1][n+1];
	 
	    // If sum is 0, then answer is true
	    for (int i = 0; i <= n; i++)
	      subset[0][i] = true;
	 
	    // If sum is not 0 and set is empty, then answer is false
	    for (int i = 1; i <= sum; i++)
	      subset[i][0] = false;
	 
	     // Fill the subset table in bottom up manner
	     for (int i = 1; i <= sum; i++)
	     {
	       for (int j = 1; j <= n; j++)
	       {
	         subset[i][j] = subset[i][j-1];
	         if (i >= set[j-1])
	           subset[i][j] = subset[i][j] || subset[i - set[j-1]][j-1];
	       }
	     }
	     return subset[sum][n];
	}