Identify the Hub of a Guaranteed Star

### Problem `edges` describes a valid undirected star on vertices labeled `1..n`: one center is connected to every other vertex, with no other edges. Return the center vertex label. ```cpp class Solution { public: int findCenter(vector<vector<int>>& edges); }; ``` ### Examples **Example 1:** ```text edges = [[3,1],[2,3]] Output: 3 Explanation: Vertex 3 is shared by both edges. ``` **Example 2:** ```text edges = [[4,2],[4,1],[3,4],[5,4]] Output: 4 Explanation: Every edge has endpoint 4. ``` ### Constraints - `3 <= n <= 10^5` and `edges.length == n-1`. - Every edge has two distinct endpoints in `[1,n]`. - The input is guaranteed to be a valid star. ### Clarifying Questions The validity guarantee means general graph-center computation and validation are unnecessary. At least two edges exist. ```hint Inspect the structure Which facts follow from the guaranteed star, and which label is the requested output? ``` ### Reasoning checkpoints - Use only consequences justified by the guaranteed-star input. - Show that the returned label is the unique center, regardless of endpoint or edge order. ### Optional extensions If the star guarantee were removed, how would you check for a universal vertex?