Maximize sum with no adjacent elements

Given an array of non-negative integers `nums`, choose a subset of elements such that **no two chosen elements are adjacent in the original array**. Return the **maximum possible sum** of the chosen elements. ### Input - `nums`: array of integers, `0 <= nums[i]` ### Output - An integer: the maximum sum achievable without choosing adjacent elements. ### Constraints (typical interview constraints) - `1 <= n <= 10^5` - `0 <= nums[i] <= 10^9` ### Examples - `nums = [1,2,3,1]` → `4` (choose `1` and `3`) - `nums = [2,7,9,3,1]` → `12` (choose `2, 9, 1`)