Graph AlgorithmsIntermediate

Prim's MST Algorithm

Greedy algorithm that grows a minimum spanning tree by repeatedly adding the cheapest edge connecting the tree to a new vertex. Uses a priority queue for efficiency with O(E log V) time. Preferred for dense graphs and real-time applications like network broadcasting and circuit design.

#graph#minimum-spanning-tree#greedy#priority-queue

Complexity Analysis

Time (Average)

O(E log V)

Expected case performance

Space

O(V)

Memory requirements

Time (Best)

O(E log V)

Best case performance

Time (Worst)

O(E log V)

Worst case performance

📚 CLRS Reference

Introduction to Algorithms•Chapter 23•Section 23.2

Implementation

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.

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.

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