Different Ways to Add Parentheses Coding Problem

Different Ways to Add Parentheses is a recursive problem that tests how well you can break an expression into subproblems and combine results correctly. You are given a string representing a mathematical expression made up of numbers and operators like +, -, and *. Your task is to compute all possible results that can be obtained by adding parentheses in different valid ways. The key detail is that parentheses can change the order of evaluation. You are not asked to return one result or the maximum result. You must return every possible outcome produced by all valid parenthesizations. For example, the expression 2-1-1 can evaluate to 0 or 2, depending on how parentheses are placed. This problem often appears in interviews because it checks whether you understand recursion, divide-and-conquer thinking, and how to manage repeated subexpressions. Why this problem is harder than it looks At first glance, it seems like you could try all possible parentheses placements directly. But the numb