Maximize sum without choosing adjacent elements

## Problem You are given an integer array `nums` where `nums[i]` is the value in position `i`. Select a subset of indices such that **no two selected indices are adjacent** (i.e., you cannot select both `i` and `i+1`). Return the **maximum possible sum** of the selected values. ### Input - `nums`: array of integers (can include `0`) ### Output - An integer: the maximum achievable sum under the non-adjacent constraint. ### Constraints (reasonable interview assumptions) - `1 <= nums.length <= 2 * 10^5` - `0 <= nums[i] <= 10^9` - Time target: `O(n)` - Space target: `O(1)` or `O(n)` ### Examples - `nums = [2, 7, 9, 3, 1]` → `12` (pick `2 + 9 + 1`) - `nums = [1, 2, 3, 1]` → `4` (pick `1 + 3`)