Consider a sorted array of size n. What would be the time complexity for the best-known algorithm to find a and b
such that |a-b| = k, k is a positive integer? Describe your solution.
The best-known algorithm to find two elements a and b in a sorted array such that |a-b| = k is the two-pointer technique. This technique involves using two pointers to traverse the array from both ends towards the middle, while comparing the absolute difference between the values at the two pointers.
Here is the step-by-step process of the two-pointer technique:
1. Initialize two pointers, left = 0 and right = n-1, where n is the size of the array.
2. While left < right, compare the absolute difference between the values at the left and right pointers with k.
3. If the absolute difference is equal to k, return the values at the left and right pointers as a and b.
4. If the absolute difference is less than k, increment the left pointer to move towards higher values.
5. If the absolute difference is greater than k, decrement the right pointer to move towards lower values.
6. Repeat steps 2-5 until the left pointer crosses the right pointer.
The time complexity of the two-pointer technique is O(n), where n is the size of the sorted array. This is because both pointers traverse the array at most once from opposite ends until they meet or cross each other in the middle. Therefore, the time complexity of finding two elements a and b in a sorted array such that |a-b| = k using the two-pointer technique is O(n).