Subset Sum Problem

 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.

Examples: set[] = {3, 34, 4, 12, 5, 2}, sum = 9
Output:  True  //There is a subset (4, 5) with sum 9.

Let isSubSetSum(int set[], int n, int sum) be the function to find whether there is a subset of set[] with sum equal to sum. n is the number of elements in set[].

The isSubsetSum problem can be divided into two subproblems

…a) Include the last element, recur for n = n-1, sum = sum – set[n-1]

…b) Exclude the last element, recur for n = n-1.

If any of the above subproblems return true, then return true.

Following is the recursive formula for isSubsetSum() problem.

isSubsetSum(set, n, sum) = isSubsetSum(set, n-1, sum) ||
                           isSubsetSum(arr, n-1, sum-set[n-1])
Base Cases:
isSubsetSum(set, n, sum) = false, if sum > 0 and n == 0
isSubsetSum(set, n, sum) = true, if sum == 0

Sol:

public static boolean subSetSum(int[] a, int n, int sum) {
    if(sum == 0) {
	return true;
    }		
    if(n == 0 && sum != 0) {
        return false;
    }		
    if(a[n]>sum) {
	subSetSum(a, n-1, sum);
    }		
    return subSetSum(a, n-1, sum-a[n]) || subSetSum(a, n-1, sum);
}