Introduction to Stack Pattern

You are given a string of brackets. Decide whether every bracket is closed by the right partner, in the right order.

{[()]}   is balanced
{[(])}   is not

One approach is to scan the string again and again, deleting any adjacent matching pair each time, until nothing changes. If the string becomes empty it was balanced. That works, and it can cost O(N²) because each pass may remove only one pair.

Look at what the question actually needs. When a closing bracket arrives, only one opening bracket can possibly match it: the most recent one that is still open