Given an array nums, return how many pairs of positions i < j hold equal values. This problem puts O(n)Linear Time O(n)Work proportional to the input size. and O(n²)Quadratic Time O(n²)Work proportional to the square of the input size. side by side. Checking every pair takes n(n − 1)/2 comparisons; remembering counts in a map turns the job into one pass. For 1000 values that is about 500,000 steps versus 1000; for a million values it is the difference between hours and a fraction of a second. The faster version trades extra memory for time — a very common bargain.