5th Jan - Count Pairs With Sum Less Than Target

To find the count of pairs whose sum is strictly less than a given target, several approaches can be used, such as a naive approach, binary search, or the two-pointer technique. In the naive approach, we generate all possible pairs using two nested loops, but this has a time complexity of O(n^2). A better approach uses binary search after sorting the array, with a time complexity of O(2*nlogn), which significantly reduces the search time. The expected approach, however, is the two-pointer technique, which sorts the array and uses two pointers—one at the beginning and one at the end of the array—to efficiently count pairs in O(nlogn + n) time. The two-pointer technique works by comparing the sum of the elements at the left and right pointers. If the sum is less than the target, all elements between the left and right pointers will form valid pairs with the left element. The count is updated accordingly, and the left pointer is incremented. If the sum is greater than or equal to the target, the right pointer is decremented. This technique provides an optimized solution with a linear time complexity after sorting, making it the most efficient approach for counting pairs with a sum less than a given target.