#1791

Easy

auto_awesomeGraph-driven solution strategy

LeetCode Problem Workspace

Find Center of Star Graph

Find the center node of a star graph, where one node connects to all others.

Problem Statement

Given an undirected star graph with n nodes, labeled 1 to n, there is one center node connected to all other nodes. You are given a 2D array representing the edges, where each edge connects two nodes. The task is to find the center node of the star graph.

In this problem, the center is the only node that appears in more than one edge. The challenge is to identify this node efficiently using the given edges, ensuring your solution is optimal for the given constraints.

Examples

Example 1

Input: edges = [[1,2],[2,3],[4,2]]

Output: 2

As shown in the figure above, node 2 is connected to every other node, so 2 is the center.

Example 2

Input: edges = [[1,2],[5,1],[1,3],[1,4]]

Output: 1

Example details omitted.

Constraints

3 <= n <= 105
edges.length == n - 1
edges[i].length == 2
1 <= ui, vi <= n
ui != vi
The given edges represent a valid star graph.

Solution Approach

Identify the Node with Multiple Edges

Since the center node is the only one that has more than one connection, you can simply check the first two edges in the list. If the first node in both edges is the same, it's the center.

Efficient Check Using First Two Edges

Instead of checking all edges, which could take time, you only need to focus on the first two edges. This allows you to solve the problem in constant time, O(1), since you know the center must appear in at least two edges.

Return the Center Node

Once the center node is identified based on the edges, return it as the result. The star graph property ensures that you only need a constant amount of work to find the center.

Complexity Analysis

Metric	Value
Time	O(1)
Space	O(1)

This solution runs in O(1) time and uses O(1) space, as the center is determined by analyzing only a constant number of edges, regardless of the size of the graph.

What Interviewers Usually Probe

Look for recognition of the graph structure and the center node's properties.
Test if the candidate can propose an efficient solution with minimal edge checking.
Evaluate the candidate's ability to leverage graph patterns for an O(1) solution.

Common Pitfalls or Variants

Common pitfalls

Focusing on complex graph traversal methods when the problem can be solved with simple edge checks.
Overcomplicating the solution by analyzing all nodes or edges when only two edges are needed.
Misunderstanding the star graph's structure and attempting to identify the center through unnecessary computations.

Follow-up variants

What if the graph had a different structure, like a tree or cyclic graph?
How would you solve this if the graph were directed?
How would your approach change if there were more than one center node?

FAQ

What is the center node in the Find Center of Star Graph problem?

The center node is the only node with more than one edge connecting it to other nodes, and it appears in multiple edges.

How do you identify the center node efficiently in a star graph?

By examining the first two edges, you can immediately identify the node that appears in both edges, which is the center.

What time complexity does the solution to this problem have?

The solution has a time complexity of O(1), as it only requires checking two edges to determine the center node.

Can you solve the Find Center of Star Graph problem without checking all edges?

Yes, since the center node appears in multiple edges, you only need to examine the first two edges for an immediate solution.

What pattern is commonly used to solve the Find Center of Star Graph problem?

This problem relies on a graph-driven solution where recognizing the star graph structure allows for an O(1) solution.

terminal

Solution

Solution 1: Directly Compare the Points of the First Two Edges

The characteristic of the center point is that it is connected to all other points. Therefore, as long as we compare the points of the first two edges, if there are the same points, then this point is the center point.

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class Solution:
    def findCenter(self, edges: List[List[int]]) -> int:
        return edges[0][0] if edges[0][0] in edges[1] else edges[0][1]

Continue Practicing

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