Using two pointers to iterate through an array for efficient searching and subarray processing.
The two-pointers technique is an algorithmic pattern that uses two pointers to iterate over a data structure, typically an array, until they meet or satisfy a certain condition. This method is often used to optimize solutions from O(n^2) to O(n) or from O(n log n) to O(n) when the array is sorted. There are several variations of this pattern. One common approach is to have the pointers start at opposite ends of a sorted array. Let's say `left` is at index 0 and `right` is at `n-1`. They move towards each other based on some condition. This is frequently used for problems like 'find a pair with a given sum' in a sorted array. If `arr[left] + arr[right]` is less than the target sum, we increment `left` to get a larger sum. If it's greater, we decrement `right` to get a smaller sum. Another variation is the fast and slow pointer, where both pointers start at the beginning but one moves faster than the other. This is famously used for cycle detection in linked lists but can also be applied to arrays. The two-pointers technique is simple yet incredibly powerful, applicable to a wide range of problems including reversing an array, sorting an array of 0s, 1s, and 2s (Dutch National Flag problem), and finding triplets that sum to zero.