Summary of Prim's algorithm in 2 minutes

Summary of "Prim's Algorithm in 2 Minutes"

Main Ideas and Concepts:

• Prim's Algorithm Purpose: Prim's Algorithm is used to find a Minimum Spanning Tree (MST) in a graph, which is a connected graph with the minimum total edge weight and no cycles.
• Greedy Approach: The algorithm follows a greedy strategy by always selecting the smallest edge that connects an unvisited node to the growing MST.

Step-by-Step Methodology:

1. Initialize:
   • Create an empty list called visited to track nodes that have been added to the MST.
2. Start Node:
   • Choose an arbitrary starting node (e.g., node A) and add it to the visited list.
3. Examine Reachable Nodes:
   • Look at all vertices connected to the current node (A) using edges (shown with blue edges).
4. Select Smallest Edge:
   • From the current node, choose the smallest edge that connects to an unvisited node. For example, from A to B.
5. Update Visited List:
   • Add the newly connected node (B) to the visited list.
6. Repeat:
   • Continue the process of examining reachable nodes and selecting the smallest edge connecting to an unvisited node:
   • If multiple edges have the same weight, you can choose any of them.
   • Avoid edges that connect nodes already in the MST.
7. Completion:
   • Repeat until all nodes are included in the MST.
   • If all edge weights are distinct, the resulting MST will be unique.
8. Calculate Total Weight:
   • Sum the weights of the edges in the MST to find the total edge weight.

Time Complexity:

The time complexity of Prim's Algorithm can vary based on the data structures used for implementation.

Featured Speakers or Sources:

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