Detect Cycle in a Directed Graph
Detecting cycles in a directed graph is a common problem with wide-ranging applications in various domains such as network analysis, scheduling, and resource allocation. The algorithmic approach involves traversing the graph using depth-first search (DFS) and identifying back edges. If a back edge is encountered during the traversal, it indicates the presence of a cycle.
Algorithm Steps:
- Initialize arrays for visited vertices and recursion stack.
- Start DFS from each unvisited vertex.
- Mark the current vertex as visited and add it to the recursion stack.
- For each adjacent vertex:
- If the vertex is not visited, recursively call DFS.
- If the vertex is in the recursion stack, a cycle is detected.
- Remove the current vertex from the recursion stack upon backtracking.
Applications:
- Task scheduling in project management.
- Resource allocation in computer systems.
Graph-Based Algorithms for GATE Exam [2024]
Ever wondered how computers figure out the best path in a maze or create efficient networks like a pro? That’s where Graph-Based Algorithms come into play! Think of them as your digital navigation toolkit. As you prepare for GATE 2024, let these algorithms be your allies, unraveling the intricacies of graphs and leading you to success.
Table of Content
- Depth First Search or DFS for a Graph
- Detect Cycle in a Directed Graph
- Topological Sorting
- Bellman–Ford Algorithm
- Floyd Warshall Algorithm
- Shortest path with exactly k edges in a directed and weighted graph
- Biconnected graph
- Articulation Points (or Cut Vertices) in a Graph
- Check if a graph is strongly connected (Kosaraju’s Theorem)
- Bridges in a graph
- Transitive closure of a graph
- Previously Asked GATE Questions on Graph-Based Algorithms
A Graph is a non-linear data structure consisting of vertices and edges. The vertices are sometimes also referred to as nodes and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph is composed of a set of vertices( V ) and a set of edges( E ). The graph is denoted by G(E, V).
In this comprehensive guide, we will explore key graph algorithms, providing detailed algorithm steps with its applications, which are relevance for the GATE Exam.