Problem Description
You are given a 0-indexed integer array nums. Return the sum of the squares of the distinct counts of all subarrays of nums. A subarray is a contiguous non-empty sequence of elements within an array.
Key Insights
- A subarray is defined by its starting and ending indices, and the distinct count can change as the subarray expands or contracts.
- To efficiently calculate the distinct counts for all subarrays, we can utilize a sliding window approach with a hash table (or dictionary) to track the frequency of elements.
- For each subarray, we can compute the distinct count by maintaining the current count of unique elements as we expand the subarray.
Space and Time Complexity
Time Complexity: O(n^2)
Space Complexity: O(n)
Solution
To solve this problem, we can use a nested loop to generate all possible subarrays. For each subarray, we maintain a hash table to track the frequency of each element. By using a sliding window approach, we can efficiently update the distinct count as we expand the subarray. The sum of the squares of the distinct counts is then accumulated and returned.