C++ 3sum complexity

Question

I was trying to solve the 3 sum problem in cpp.

Given an array S of n integers, are there elements a, b, c in S such that a + b + c = 0? Find all unique triplets in the

Answer 1

The source of extra complexity is the third loop, which brings time complexity of your code to O(n³).

Key observation here is that once you have two numbers, the third number is fixed, so you do not need to loop around to find it: use hash table to see if it's there or not in O(1). For example, if your first loop looks at value 56 and your second loop looks at value -96, the third value must be 40 in order to yield zero total.

If the range of numbers is reasonably small (say, -10000..10000) you can use an array instead.

This would bring time complexity to O(n²), which should be a noticeable improvement on timing.