Find if Path Exists in Graph
Given n nodes, undirected edges, and two nodes source and destination, return True if a path exists between them.
Input: first line = n, second = edges as u:v comma-separated (or 'none'), third = source destination.
Example:
3 0:1,1:2,2:0 0 2
True
- The graph is constructed with n=3 nodes and undirected edges between nodes 0 and 1, 1 and 2, and 2 and 0.
- The edges create a cycle: 0↔1↔2↔0, allowing for a path between any two nodes.
- A path exists from the
sourcenode 0 to thedestinationnode 2, as they are directly connected through node 1 and also through the cycle 0↔2. - The function returns
Truebecause a path is found between thesourceanddestinationnodes.
Constraints:
- 1 <= n <= 2 * 10^5
- 0 <= edges.length <= 2 * 10^5
Background Knowledge
The problem "Find if Path Exists in Graph" involves working with graphs, which are non-linear data structures consisting of nodes (also known as vertices) and edges that connect these nodes. In this case, we're dealing with an undirected graph, meaning that the edges do not have a direction and can be traversed in both ways. The problem requires finding a path between two given nodes, source and destination, in this graph.
To solve this problem, it's essential to understand the basics of graph traversal algorithms, which are methods for visiting each node in a graph. The two primary graph traversal algorithms are Breadth-First Search (BFS) and Depth-First Search (DFS). BFS explores all the nodes at a given depth level before moving on to the next level, while DFS goes as deep as possible along each branch before backtracking. Both algorithms can be used to find a path between two nodes in a graph.
Understanding the representation of graphs is also crucial. Graphs can be represented using adjacency matrices or adjacency lists. An adjacency matrix is a matrix where the entry at row i and column j represents the weight of the edge between nodes i and j. An adjacency list, on the other hand, is a list of edges, where each edge is represented as a pair of nodes. In this problem, the graph is represented using an adjacency list, where the edges are given as u:v pairs.
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