Graph AlgorithmsAdvanced

Dijkstra's Algorithm

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.

#graph#shortest-path#greedy#weighted

Complexity Analysis

Time (Average)

O((V + E) log V)

Expected case performance

Space

O(V)

Memory requirements

Time (Best)

O((V + E) log V)

Best case performance

Time (Worst)

O((V + E) log V)

Worst case performance

📚 CLRS Reference

Introduction to Algorithms•Chapter 24•Section 24.3

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Real-time Statistics

Algorithm Performance Metrics

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Algorithm Visualization

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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.

Depth-First Search (DFS)

Intermediate

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.

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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