Cycle detection in graphs in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a cycle in a graph?

A cycle is a path in a graph where the first and last vertices are the same, and no edges or vertices are repeated except the starting/ending vertex.

beginner

Why is cycle detection important in graphs?

Detecting cycles helps identify problems like infinite loops, deadlocks, or inconsistencies in networks, scheduling, and dependency management.

intermediate

Name two common methods to detect cycles in graphs.

Depth-First Search (DFS) with recursion stack and Union-Find (Disjoint Set) are two common methods to detect cycles.

intermediate

How does DFS help detect cycles in a directed graph?

DFS tracks nodes in the current path using a recursion stack. If it revisits a node in this stack, a cycle exists.

intermediate

What is the difference in cycle detection between directed and undirected graphs?

In undirected graphs, a cycle is detected if a visited node is found again and it is not the parent node. In directed graphs, cycles are detected by revisiting nodes in the current recursion path.

What does a cycle in a graph mean?

A A path with no edges

B A path that starts and ends at the same vertex without repeating edges or vertices

C A path that never returns to the starting vertex

D A path that visits every vertex exactly once

A cycle is a path that starts and ends at the same vertex without repeating edges or vertices except the start/end vertex.

Which algorithm uses a recursion stack to detect cycles in directed graphs?

A Depth-First Search

B Breadth-First Search

C Dijkstra's Algorithm

D Kruskal's Algorithm

Depth-First Search uses a recursion stack to track nodes in the current path and detect cycles in directed graphs.

In an undirected graph, a cycle is detected if a visited node is found again and it is not the ____.

A child node

B root node

C parent node

D leaf node

In undirected graphs, revisiting a visited node that is not the parent indicates a cycle.

Which data structure is commonly used in cycle detection with Union-Find method?

A Linked List

B Queue

C Stack

D Disjoint Set

Union-Find uses Disjoint Set data structure to detect cycles by checking if two vertices belong to the same set.

Why is cycle detection important in dependency management?

A To avoid infinite loops and conflicts

B To speed up processing

C To reduce memory usage

D To increase network speed

Cycle detection prevents infinite loops and conflicts in dependencies, ensuring proper order and consistency.

Explain how Depth-First Search can be used to detect cycles in a directed graph.

Think about how DFS keeps track of nodes it is currently exploring.

Describe the difference between cycle detection in directed and undirected graphs.

Consider how edge direction affects revisiting nodes.