Two Pointers

You have an array and you need to find two numbers that add up to a target, or check whether a word reads the same backwards, or push all the zeros to the end. The reflex is a nested loop: for each element, walk the rest of the array. That works, but it is quadratic. On ten thousand elements it is fifty million steps, and it gets worse fast.

The two pointers technique replaces that nested loop with two indices that walk the array intelligently. Instead of comparing every pair, you move the pointers based on what you learn, so each element is visited a small, constant number of times. That drops the work from n squared down to n. The catch is that it only works when the data has some structure you can lean on, usually that it is sorted, or that you can split the array into a part you have finished and a part you have not.

There are two shapes to recognize. In the first, the pointers start at opposite ends and move toward each other. In the second, both start at the front and one races ahead of the other. This unit walks through both, and more importantly, teaches you to feel which one a problem is asking for, and when two pointers is the wrong tool entirely.