1791 - Find Center of Star Graph

Problem

There is an undirected star graph consisting of n nodes labeled from 1 to n. A star graph is a graph where there is one center node and exactly n - 1 edges that connect the center node with every other node.

You are given a 2D integer array edges where each edges[i] = [ui, vi] indicates that there is an edge between the nodes ui and vi. Return the center of the given star graph.

Input: edges = [[1,2],[2,3],[4,2]]
Output: 2
Explanation: As shown in the figure above, node 2 is connected to every other node, so 2 is the center.

Approach

Since the graph is guaranteed to be a star, the center is present in every edges[i]. So we just have to find the common element between edges[0] and edges[1].

Code

class Solution {
public:
    int findCenter(vector<vector<int>>& edges) {
        if (edges[0][0] == edges[1][0] || edges[0][0] == edges[1][1])
            return edges[0][0];
        return edges[0][1];
    }
};

Complexity

• time: O(1) — two edges and four comparisons, regardless of n
• space: O(1)