Leetcode 1791: Find Center of Star Graph

Input: The input consists of a 2D integer array, 'edges', where each element [u, v] represents an edge between nodes u and v.

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

Constraints:

• 3 <= n <= 10^5

• edges.length == n - 1

• edges[i].length == 2

• 1 <= ui, vi <= n

• ui != vi

Output: Return the center of the star graph, which is the node that is connected to every other node.

Example: Output: 4

Constraints:

Goal: To identify the central node of the star graph from the given edges.

Steps:

• Check the first two edges and compare the nodes involved in them.

• The center node is the one that appears in both edges, as it connects to all other nodes.

Goal: The input graph will always form a valid star graph as per the given constraints.

Steps:

• The number of nodes (n) is between 3 and 10^5.

• There will always be n - 1 edges, ensuring the graph forms a valid star shape.

Assumptions:

• The given edges always represent a valid star graph with one center node.

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

• Explanation: Node 4 appears in all edges, so it is the center node.

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

• Explanation: Node 1 appears in all edges, so it is the center node.

Approach: To find the center of the star graph, we can use the fact that the center node will appear in multiple edges. By examining just the first two edges, we can easily determine the center node.

Observations:

• The center node is the one that connects to all other nodes.

• By checking only the first two edges, we can quickly identify the center node.

• Check which node appears in both edges and return it as the center.

Steps:

• Look at the first two edges from the input.

• Check if the first node of the first edge matches the first or second node of the second edge.

• The matching node will be the center node.

Empty Inputs:

• There will never be empty input as per the problem constraints.

Large Inputs:

• The solution should efficiently handle up to 10^5 nodes.

Special Values:

• The star graph is always valid, so we don’t need to check for invalid graphs.

Constraints:

• The input always represents a valid star graph with exactly one center node.

int findCenter(vector<vector<int>>& e) {
return e[0][0] == e[1][0] || e[0][0] == e[1][1] ? e[0][0] : e[0][1];
}

1 : Function Definition

int findCenter(vector<vector<int>>& e) {

Define the function `findCenter`, which takes a reference to a vector of vectors `e` representing the edges of the graph. The function returns the center of the star graph.

2 : Condition Check

return e[0][0] == e[1][0] || e[0][0] == e[1][1] ? e[0][0] : e[0][1];

Check if the first element of the first edge (`e[0][0]`) is equal to the first or second element of the second edge (`e[1][0]` or `e[1][1]`). If it matches, return that element as the center. Otherwise, return the second element of the first edge (`e[0][1]`).

Best Case: O(1), when the center is found after checking the first two edges.

Average Case: O(1), since we only need to check two edges to find the center.

Worst Case: O(1), as we are only checking the first two edges.

Description: The time complexity is constant since we only need to examine two edges.

Best Case: O(1), no additional space needed.

Worst Case: O(1), as no extra space is required.

Description: The space complexity is constant, as the solution does not require additional space that grows with input size.

Leetcode 1791: Find Center of Star Graph

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