Compute the next lexicographic permutation

## Problem Given an integer array `nums` representing a permutation of its elements, modify the array **in-place** to produce the **next lexicographically greater** permutation. - If such a permutation exists, rearrange `nums` into that next greater ordering. - If no greater permutation exists (i.e., `nums` is in non-increasing order), rearrange `nums` into the **lowest possible order** (sorted ascending). ## Input - `nums`: an array of integers (may contain duplicates). ## Output - No return value; update `nums` in-place. ## Requirements - Use **O(1)** extra space. - Aim for **O(n)** time. ## Examples 1. `nums = [1,2,3]` → after update: `[1,3,2]` 2. `nums = [3,2,1]` → after update: `[1,2,3]` 3. `nums = [1,1,5]` → after update: `[1,5,1]` ## Notes / Edge Cases to consider - Array length `n` can be 0, 1, or larger. - Duplicates may exist. - Strictly increasing, strictly decreasing, and “plateau” patterns (e.g., `[2,2,1]`).