Design an algorithm to find all pairs of integers within an array which sum to a specified value (assume for simplicity that the array has distinct elements). For example, for the array A[2 5 3 6 4] and sum = 8, it prints (2,6) and (3,5). Provide a brute-force solution. What is the worst-case running time of this solution and why using only informal justification. Then try to find a better solution, and show how its worst-case running time is better.

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Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.