You are given **two coding problems**. ## Problem 1: Longest balanced subarray (0/1) Given an integer array `nums` of length `n` where each element is either `0` or `1`, return the **maximum length** of a contiguous subarray that contains an **equal number of `0`s and `1`s**. **Input:** `nums: int[]` (each `nums[i] ∈ {0,1}`) **Output:** `int` = maximum length **Constraints (typical):** `1 ≤ n ≤ 2e5` --- ## Problem 2: Longest increasing downward path in a binary tree (return the path) Given the root of a binary tree where each node has an integer value, find a **downward path** (must follow parent → child pointers) such that for every adjacent pair on the path: - `child.value > parent.value` (strictly increasing) Return the **entire path** (e.g., as a list/array of node values in order from start to end) that has the **maximum length**. If multiple longest paths exist, you may return **any one** of them. **Input:** `root: TreeNode` with fields `val`, `left`, `right` **Output:** `int[]` (or `List<int>`) representing the node values along the chosen maximum-length increasing path **Constraints (typical):** up to `2e5` nodes.