Find an Ancestor Shared by a Node Collection

### Problem Given binary-tree `root` and a nonempty list `nodes` of distinct `TreeNode` pointers, return the lowest existing tree node that is an ancestor of every listed node. A node is its own ancestor for this purpose. Preserve the node-pointer interface; the query supplies actual nodes belonging to this tree. ```cpp class Solution { public: TreeNode* lowestCommonAncestor(TreeNode* root, vector<TreeNode*> &nodes); }; ``` ### Examples **Example 1:** ```text Tree: root 9 has children 4 and 13; node 4 has children 2 and 6. nodes contains pointers to 2 and 6. Output: pointer to node 4 ``` **Example 2:** ```text Tree: root 7 has children 3 and 11. nodes contains only the pointer to 11. Output: pointer to node 11 Explanation: A single queried node is its own lowest common ancestor. ``` ### Constraints - The tree contains `1..10^4` nodes. - Values are unique integers in `[-10^9,10^9]`. - Each nodes entry exists in the tree, and query pointers are distinct. - For this practice version, `1 <= nodes.length <= N`, where `N` is the tree's node count. ### Practice Assumptions The query list is nonempty for this practice version. The returned pointer must identify an existing `TreeNode`, not merely its value. ```hint Inspect the structure Does a proposed pointer identify an existing node that meets the ancestor condition for the entire nonempty query? ``` ### Reasoning checkpoints - Show that the returned existing node is an ancestor of every requested node. - Prove that no proper descendant has that property, respecting the nonempty query and node identities. ### Optional extensions What preprocessing would make repeated collection-LCA queries more efficient?