Graph AlgorithmsIntermediate

Depth-First Search (DFS)

Explores a graph by going as deep as possible along each path before backtracking. Implemented using a stack or recursion, making it natural for recursive problems. Used for pathfinding, cycle detection, topological sorting, and maze generation.

#graph#traversal#recursive

Complexity Analysis

Time (Average)

O(V + E)

Expected case performance

Space

O(V)

Memory requirements

Time (Best)

O(V + E)

Best case performance

Time (Worst)

O(V + E)

Worst case performance

📚 CLRS Reference

Introduction to Algorithms•Chapter 22•Section 22.3

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Related Algorithms

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Breadth-First Search (BFS)

Intermediate

Explores a graph level by level, visiting all vertices at the current depth before moving deeper. Uses a queue and is ideal for finding shortest paths in unweighted graphs. Applications include maze solving, social network analysis, and finding connections between nodes.

Dijkstra's Algorithm

Advanced

Finds the shortest paths from a single source vertex to all other vertices in a weighted graph. Powers GPS navigation systems and network routing protocols. Works efficiently with non-negative edge weights using a greedy approach with a priority queue.

A* Search Algorithm

Advanced

A best-first search algorithm that finds the shortest path using heuristics. Combines Dijkstra's algorithm and greedy best-first search using f(n) = g(n) + h(n). Widely used in games, robotics, and GPS navigation for efficient pathfinding.

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