Collect Binary-Tree Nodes at an Exact Distance from a Target

### Problem Given a binary-tree root, a pointer `target` to a node in that tree, and `k`, return the values of every node exactly `k` edges from the target. Edges may be followed toward a parent or a child. Return the values in any order. The native interface uses a `TreeNode*` target; value notation in examples identifies that existing node. ```cpp class Solution { public: vector<int> distanceK(TreeNode* root, TreeNode* target, int k); }; ``` ### Examples **Example 1:** ```text Input: root = [8,3,10,1,6,9,12], target = node with value 3, k = 1 Output: [8,1,6] Explanation: Its parent and two children are each one edge away. Any ordering is valid. ``` **Example 2:** ```text Input: root = [4,2,7], target = node with value 4, k = 0 Output: [4] Explanation: The target itself is the only node at distance zero. ``` ### Constraints - The tree contains `1` to `500` nodes. - `0 <= Node.val <= 500`; all node values are unique. - The target identifies a node in the tree. - `0 <= k <= 1000` ### Contract considerations Example arrays describe level-order tree shape with null placeholders; the callable receives the original pointers. Preserve the supplied TreeNode definition. ```hint Read the boundary condition How can a search leave the target subtree without changing the tree? ``` ### What a Strong Answer Covers Example arrays describe level-order tree shape with null placeholders; the callable receives the original pointers. Preserve the supplied TreeNode definition. ### Follow-up Questions Optional practice extension, separate from the original task: How would the search cost change when many distance queries share the same tree?