What is the optimal time complexity of solving Number of Connected Components?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Number of Connected Components?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Number of Connected Components?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Number of Connected Components?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Number of Connected Components

Learn how to solve the 'Number of Connected Components' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

You have a graph of n nodes. You are given an integer n and an array edges where edges[i] = [ai, bi] indicates that there is an undirected edge between ai and bi in the graph.

Return the number of connected components in the graph.

Write a function countComponents(n: int, edges: List[List[int]]) -> int.

Constraints

•1 <= n <= 2000
•0 <= len(edges) <= 5000
•edges[i].length == 2
•0 <= ai, bi < n

Examples

Example 1

Input

n = 5, edges = [[0,1],[1,2],[3,4]]

Output

Explanation

Nodes 0, 1, 2 form one component, and nodes 3, 4 form another component.

Example 2

Input

n = 5, edges = [[0,1],[1,2],[2,3],[3,4]]

Output

Explanation

All nodes are connected in a single path.

Need a Hint?

Represent graph node connections as an adjacency list/matrix, then use standard BFS or DFS graph traversal.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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