To solve this problem, we need to find the center of a star graph given its edges. A star graph is defined as a graph where there is one center node connected to all other nodes via edges. The key insight here is that the center node will always be present in the first two edges of the graph (since it is connected to all other nodes).

Approach

The center node of a star graph is the node that appears in all edges. However, to find it efficiently, we can leverage the fact that the center node must be present in the first two edges. This is because:

1. The first edge connects the center node to some other node.
2. The second edge also connects the center node to another node. Thus, the center node is the common node between the first two edges. We can check if the first node of the first edge is present in the second edge; if not, the second node of the first edge must be the center.

Solution Code

def findCenter(edges):
    return edges[0][0] if edges[0][0] in edges[1] else edges[0][1]

Explanation

Let’s break down the solution:

1. First Edge: The first edge in the list (edges[0]) consists of two nodes, say a and b.
2. Second Edge: The second edge (edges[1]) consists of two nodes, say c and d.
3. Check Common Node:
   • If a (from the first edge) is present in the second edge (edges[1]), then a is the center node.
   • If a is not present in the second edge, then b must be the center node (since the center node must be present in both edges).

This approach runs in O(1) time complexity (since we only check a fixed number of nodes) and uses O(1) space complexity (no additional data structures are needed). This is optimal for the given problem constraints.

Example:

• For edges [[1,2], [2,3], [4,2]], the first edge is [1, 2] and the second edge is [2,3]. The first node of the first edge (1) is not present in the second edge, so we return the second node of the first edge (2), which is the center.
• For edges [[5,3], [3,4], [3,1]], the first edge is [5, 3] and the second edge is [3, 4]. The first node of the first edge (5) is not present in the second edge, so we return 3 (second node of first edge), which is the center.

This solution works for all valid star graphs and is both efficient and concise. ✨✨✨

作者声明:本文包含人工智能生成内容。