4 Sum – All Distinct Quadruplets with given Sum in an Array

To find all unique quadruplets in an array that sum to a given target, various approaches can be employed. The naive approach involves generating all possible quadruplets using nested loops and checking their sums against the target. Though straightforward, this method has a time complexity of O(n^5), making it inefficient for larger arrays. A better approach uses hashing to identify the remaining two elements after generating pairs, ensuring distinct quadruplets while reducing time complexity to O(n^3).

The optimal approach involves sorting the array and employing the two-pointer technique. By generating pairs and finding the remaining two elements using pointers, this method efficiently identifies quadruplets with a time complexity of O(n^3) and O(1) space complexity. Duplicate quadruplets are avoided by skipping repeated elements in the outer and inner loops, as well as during pointer adjustments. This ensures a streamlined and efficient solution for finding unique quadruplets.

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