Quadratic algorithm for 4-SUM

Question

The 4-SUM is as follows:

Given an array of N distinct integers find 4 integers a, b, c, d such that a+b+c+d = 0.

I could come up

Answer 1

There is also a O(N²) algorithm for this problem using O(N²) extra memory.

1. Generate all the pairwise sums in O(N²) and store the pair (a_i, a_j) in a hash table and use the absolute value of their sum as the key of the hash table (a_i and a_j are two distinct numbers of the input array)

2. Iterate over the table and find a key which has both negative and positive sum with four distinctive elements and return is as the answer

There is an alternative if you prefer not using hash table. Since your numbers are integers, you can sort the list of all the sum in a linear time of the elements in the sum list using something like a Radix sort (there are O(N²) elements in the sum list).