Given an array and a target sum, the task is to find the count of quadruplets that add up to the target. The problem can be solved using three approaches: Naive (O(n^4)), Better (O(n^3)), and Efficient (O(n^2)) with hash maps. The Efficient approach uses a hash map to store the sum of pairs and count the matching quadruplets. The time complexity and space complexity vary based on the chosen approach.
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