Subset Sum - Implementation

Here's the full solution:

function subsetSumExists(arr, target)
    n := length of arr
    for mask := 0 to (1 << n) - 1
        sum := 0
        for i := 0 to n - 1
            if (mask >> i) & 1 = 1 then
                sum := sum + arr[i]
        if sum = target then
            return true
    return false

Time: $O(2^n \cdot n)$. For each of $2^n$ masks, you check $n$ bits. Space: $O(1)$ extra. This is your first complete bitmask solution. The pattern is simple: iterate masks, extract bits, compute answer.