Find Center of Star Graph

To solve this coding challenge, you need to identify the center of a star graph. A star graph has one central node that is connected to all other nodes. Given that the input is a set of edges in a 2D array, where each edge connects two nodes, the central node will be the one that appears in every edge.

Since the graph is a star graph, examining any two edges is sufficient to determine the center. The center node will be the common node in the first two edges.

Steps to Solve:

1. Examine the First Two Edges:

Look at the first two edges in the array.

2. Identify the Common Node:

The center node will be the one that appears in both edges. There are only three nodes involved in the first two edges, and two of them will be the same. That repeated node is the center.

3. Return the Center Node:

Once identified, return the center node.

Pseudo Code:

                                        
FUNCTION findCenter(edges)
    // e[0] and e[1] are the first two edges in the edges array
    IF edges[0][0] EQUALS edges[1][0] OR edges[0][0] EQUALS edges[1][1] THEN
        RETURN edges[0][0]
    ELSE
        RETURN edges[0][1]
    END IF
END FUNCTION
                                    

Explanation:

• The function findCenter checks if the first node in the first edge (edges[0][0]) is also present in the second edge (edges[1]). It does this by comparing edges[0][0] with both nodes in the second edge (edges[1][0] and edges[1][1]).
• If edges[0][0] is found in the second edge, it is the center node, and the function returns edges[0][0].
• If edges[0][0] is not found in the second edge, then the second node in the first edge (edges[0][1]) must be the center, and the function returns edges[0][1].

This approach efficiently identifies the center of a star graph by leveraging the graph's structural properties, requiring only a constant number of comparisons.