Connected Components
Given n nodes (0-indexed) and a list of undirected edges, return the number of connected components in the graph.
Input: first line is n, second line is edges as a,b pairs separated by semicolons (empty if no edges).
Example:
5 0,1;1,2;3,4
2
- The input
5represents the number of nodes in the graph, and the edges are given as0,1;1,2;3,4, which can be split into pairs:(0,1),(1,2), and(3,4). - These edges form two connected components: one containing nodes
0,1, and2, and another containing nodes3and4. - Node
4is connected to node3, but there are no edges connecting the first group of nodes (0,1,2) to the second group (3,4), resulting in 2 separate components. - The final output is the number of these connected components, which is 2.
Constraints:
- 1 <= n <= 2000
- 0 <= edges <= 5000
Background Knowledge
The problem of finding connected components in a graph is a fundamental concept in graph theory. A graph is a non-linear data structure consisting of nodes (also known as vertices) and edges that connect these nodes. In the context of this problem, we are dealing with an undirected graph, where edges do not have a direction and can be traversed in both ways. The key concept here is that of a connected component, which is a subgraph in which there is a path between any two nodes.
To understand this problem, it's essential to be familiar with graph traversal techniques, such as Depth-First Search (DFS) and Breadth-First Search (BFS). These techniques allow us to explore the nodes and edges of a graph in a systematic way. In the case of DFS, we start at a given node and explore as far as possible along each branch before backtracking. BFS, on the other hand, involves exploring all the nodes at a given depth level before moving on to the next level.
The concept of connectedness is also crucial. A graph is said to be connected if there is a path between every pair of nodes. If a graph is not connected, it can be divided into connected components, each of which is a connected subgraph. The problem requires us to find the number of these connected components in a given graph.
Continue the full explanation
You're reading the free preview. Unlock the complete walkthrough, the code editor, test runner and reference solution with Premium.
Editor locked
The code editor is locked for Pro problems. It is only available for free problems. Please upgrade to gain access to the code editor for all problems.