Sorry, the solution above is not correct. for example, if you have a set [-7, -5, -4, 0, 1, 2, 3, 4], the algorithm is not right. Am I missing anything?

It's correct. When i=7 (assume that index starting from 1) and left = 0, right = 8 we get right answer -7 + 3 + 4 Pseudo algo: For each i = 1..length do left = 0, right = length While lefti do if values[left] + values[i] + values[right] == 0 >> Got solution here if values[left] + values[i] + values[right] > 0 # means that right border should be moved right-- else # moving left border left++

cant we generate permutations of three numbers and use it to get the answer?

Sort. Fix one element i of array and move to it from left and right of array depending on value of values[left]+values[i]+values[right] Complexity O(N^2)