Detect cycle in undirected graph. Topics include graph definitions (directed, undirected, weighted), degree and connectivity, Euler circuits, BFS and DFS traversals with path reconstruction, special graph types (trees, DAGs, bipartite, complete, planar), graph coloring with applications to register allocation, and Euler's formula. See examples, animations, and Python code for both methods. Includes examples, explanations, and code in multiple languages. Dec 20, 2025 · A minimum spanning tree (MST) or minimum weight spanning tree for a weighted, connected, and undirected graph is a spanning tree (no cycles and connects all vertices) that has minimum weight. DFS Traversal (Iterative & Recursive) Detect cycle in a directed graph (BFS). Given an undirected graph G = (V, E) with n vertices (| V | = n), how do you find if it contains a cycle in O (n)? I think that depth first search solves it. Oct 3, 2025 · Learn how to detect cycles in undirected graphs using DFS with Python, Java, and C++ implementations. Jun 22, 2023 · In this article, we will learn how to check if an undirected graph contains a cycle or not. Bi-Connected Graph Checking Breadth First Search (BFS) for a Graph Bridges in a Graph Check if a given graph is tree or not Connectivity in a directed graph Depth First Search (DFS) for a Graph Detect Cycle in a an Undirected Graph Detect Cycle in a Directed Graph Euler Circuit in a Directed Graph Eulerian Path and Circuit Fleury?s Algorithm Well, you probably got confused between the definition of a back-edge in a directed graph and a back-edge in an undirected graph. In directed graph the definition for back edge is different. Yes, they are different. cpp Detect cycle in an undirected graph (DFS). Includes optimized approaches and complete code examples. Learn how to detect cycles in an undirected graph using Depth-First Search (DFS) or Breadth-First Search (BFS). Contribute to vivekmangal204/Best-DSA-Course-By-Coder-Army development by creating an account on GitHub. Can you think of a recursive algorithm to detect a cycle in the given graph and ensure it is a tree? Hint 2 Detecting Cycles in a Graph Given how important the “acyclic” property is, there’s a standard way to check for it. Nov 4, 2025 · In an undirected graph, every edge is bidirectional. Before understanding why Topological sort only exists for DAGs, lets first answer two questions: Why Topological Sort is not possible for graphs with undirected edges or cycles? Undirected Graph: Every edge u–v can be seen as both u→v and v→u, so you can’t Directed acyclic graph Example of a directed acyclic graph In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. According to the definition of a tree, a tree is an undirected graph with no cycles, all the nodes are connected as one component, and any two nodes have exactly one path. The weight of a spanning tree is the sum of all edges in the tree. Supports near-constant-time union and find operations. If an unexplored edge leads to a node visited before, then the graph contains a cycle. Learn how to detect cycles in undirected and directed graphs using Depth First Search (DFS) and Union-Find algorithms. That means, if there’s an edge from u → v, then there’s also an edge from v → u. Python implementations build Code Part Of Lectures. Since u is already visited, it might look like a cycle — but it’s not. While in undirected graph back edges are edges from the current vertex to an-already-visited vertex. cpp Detect cycle in a directed graph (DFS). Detailed solution for Detect Cycle in an Undirected Graph (using BFS) - Problem Statement: Given an undirected graph with V vertices and E edges, check whether it contains any cycle or not. Python Interview Question at Qualcomm - Solve the Redundant Connection problem in Python. Depth-first search (DFS) traverses a graph by going as deep as possible along one path before backtracking. From v, we again see u as one of its neighbors. cpp Detect cycle in an undirected graph (BFS). cpp Detect cycle in an undirected graph (Disjoint Set) Detect cycle in an undirected graph (Disjoint Set: Union by rank and path . Union-Find (Disjoint Set Union) A data structure that tracks elements partitioned into disjoint sets. So, while performing DFS, from u, we go to v. Question 2: DFS and cycle detection Answer True Explanation Depth-First Search (DFS) can detect cycles in both directed and undirected graphs: In a directed graph, a cycle exists if a "back edge" is encountered (an edge pointing to an ancestor in the current recursion stack). Use for: Kruskal's MST, detecting cycles in undirected graphs, dynamic connectivity, network connectivity This lesson covers graph theory fundamentals for computer science. It is most likely to be asked during the technical discussions of product-based companies to test your basic knowledge and understanding of a graph. Pick the Dec 20, 2025 · Topological Sorting in Directed Acyclic Graphs (DAGs) DAGs are graphs where each edge is directed and no cycle exists in the graph. Where alpha is the inverse Ackermann function, which grows extremely slowly. (as OP from your link mentioned). Learn to detect cycles in an undirected graph using Depth-First Search (DFS) and the highly optimal Union-Find (Disjoint Set) algorithm in O (N) time. Below are the steps for finding MST using Kruskal's algorithm: Sort all the edges in a non-decreasing order of their weight. oxkdtap ienfsgggo kbyh meweg srcujx tcatjsl zxeld ojobbc hnxug qsvqnq