How do you approach Number of Connected Components in an Undirected Graph?

Start with n components and union each edge.

What are common mistakes on Number of Connected Components in an Undirected Graph?

Building the adjacency list in one direction on an undirected graph. Assuming the graph is connected. Most inputs allow several components, and one traversal from node 0 misses the rest. Ignoring self-loops and parallel edges when the constraints allow them.

gitGood.dev

← Back to problems

Number of Connected Components in an Undirected Graph

MediumAlgorithms

Description

You have a graph of n nodes labeled 0 to n - 1. You are given n and a list of edges where edges[i] = [a, b] is an undirected edge.

Return the number of connected components in the graph.

Example 1

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

Output: 2

Explanation: {0,1,2} and {3,4}.

Example 2

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

Output: 1

Explanation: All nodes form one chain.

Constraints

- 1 <= n <= 2000 - 0 <= edges.length <= n * (n - 1) / 2 - There are no self-loops or repeated edges

Number of Connected Components in an Undirected Graph: approach, complexity and pitfalls

A medium graphs problem, graded against 7 test cases (5 of them hidden).

The pattern: Graphs

Nodes and edges - traversal, connectivity, cycles, and shortest paths.

Reach for it when you see: Explicit edges, a grid treated as a graph, or dependencies between items.

If you are stuck

Show the 2-step hint ladder

Start with n components and union each edge.
Every successful union (two different roots) reduces the component count by one.

The optimal approach

Show the approach: The approach

Union-Find with a running counter. Begin with `count = n`. Each edge that joins two distinct sets decrements the count. The final count is the number of components.

Time: O((n + e)·α(n)). Space: O(n).

The full reference solution in every supported language stays in the editor above - reveal it there once you have had a real attempt.

What the tests check

Read off this problem's own test suite, so these are the cases a submission actually has to survive.

Empty input. At least one case passes an empty collection. Make sure your loop bounds and any "first element" read survive a length of zero.
Zero. Zero appears in the input, which is the value most likely to break a truthiness check used in place of an explicit comparison.

Common Graphs mistakes

These apply to the pattern as a whole, not just this problem.

Building the adjacency list in one direction on an undirected graph.
Assuming the graph is connected. Most inputs allow several components, and one traversal from node 0 misses the rest.
Ignoring self-loops and parallel edges when the constraints allow them.