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Number of Connected Components

Detailed guide and Python implementation for the 'Number of Connected Components' problem.

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
2
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
1
Explanation

All nodes are connected in a single path.

Need a Hint?
Consider using Graphs-specific data structures like sets or heaps.
Edge Cases to Watch
  • Empty input structures
  • Single element inputs
  • Large numerical bounds

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