Contains Duplicate - Implementation

Here is the optimal hash set solution:

function containsDuplicate(nums)
    seen := empty hash set
    for each num in nums
        if num in seen then
            return true
        add num to seen
    return false

Time: $O(n)$ since hash set operations are $O(1)$ average. Space: $O(n)$ for the set. This is the best time complexity possible since you must examine each element at least once.