What is the difference between dijkstra's algorithm and Prim's algorithm in C?

Table of Contents

• 1. Dijkstra's Algorithm
  • Purpose:
  • Working Mechanism:
  • Time Complexity:
  • Example Use Case:
• 2. Prim's Algorithm
  • Purpose:
  • Working Mechanism:
  • Time Complexity:
  • Example Use Case:
• Key Differences Between Dijkstra's and Prim's Algorithm
• C Code Implementation Examples
  • Dijkstra’s Algorithm (Using Min-Heap)
  • Prim’s Algorithm (Using Min-Heap)
• Conclusion

1. Dijkstra's Algorithm

Purpose:

Dijkstra’s algorithm is used to find the shortest path from a single source to all other vertices in a weighted graph.

Working Mechanism:

• Starts from a single source vertex.
• Uses a priority queue (min-heap) to select the next vertex with the minimum distance.
• Updates the shortest distance of its adjacent vertices.
• Repeats the process until all vertices are processed.

Time Complexity:

• O(V²) (using an adjacency matrix and simple search).
• O((V + E) log V) (using a priority queue like a min-heap).

Example Use Case:

• Google Maps for shortest route calculations.
• Network Routing Protocols.

2. Prim's Algorithm

Purpose:

Prim’s algorithm is used to find the Minimum Spanning Tree (MST) of a weighted, connected graph.

Working Mechanism:

• Starts from any random vertex.
• Greedily selects the minimum-weight edge that connects a vertex inside the MST to a vertex outside the MST.
• Uses a priority queue (min-heap) to find the next minimum edge.
• Continues until all vertices are included in the MST.

Time Complexity:

• O(V²) (using an adjacency matrix).
• O((V + E) log V) (using a min-heap).

Example Use Case:

• Network Design (LAN, WAN).
• Electrical Circuit Design (minimum wiring cost).

Key Differences Between Dijkstra's and Prim's Algorithm

Feature	Dijkstra’s Algorithm	Prim’s Algorithm
Purpose	Finds the shortest path from a single source to all vertices.	Finds the Minimum Spanning Tree (MST) of a graph.
Graph Type	Works with directed and undirected graphs.	Works only with undirected graphs.
Selection Criteria	Selects the vertex with the minimum distance from the source.	Selects the minimum-weight edge to expand the MST.
Priority Queue	Stores vertices based on shortest distance.	Stores edges based on minimum weight.
Application	Shortest path in Google Maps, Network Routing.	Minimum cost connection in LAN, Power Grid.

C Code Implementation Examples

Dijkstra’s Algorithm (Using Min-Heap)

Prim’s Algorithm (Using Min-Heap)

Conclusion

• Use Dijkstra’s Algorithm when you need shortest path computations.
• Use Prim’s Algorithm when you need a Minimum Spanning Tree.
• Both use a greedy approach and priority queues for efficiency.