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Overview

Copyright (c) A|iens. All rights reserved. — Quick Facts

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Property: Detail

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Full Name: Prim's Algorithm…

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Type: Greedy Algorithm / Graph Algorithm

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Problem Solved: Minimum Spanning Tree (MST)

Topic 1

Infobox

📚 | Property | Detail | |---|---| | Full Name | Prim's Algorithm (Jarník-Prim-Dijkstra…

Topic 2

1. Minimum Spanning Tree — Foundation

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Saare V vertices include karta hai

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Exactly V - 1 edges hoti hain

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Connected hai (har vertex…

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Acyclic hai (koi cycle nahi)

Topic 3

2. Algorithm Steps

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Agar v MST me nahi hai (inMST[v] =…

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key[v] = w(u,v) update karo

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parent[v] = u set karo

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Priority queue me v ki key update…

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3. Step-by-Step Walkthrough Example

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A-B: 4, A-C: 2

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B-C: 1, B-D: 5

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C-D: 8, C-E: 10

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D-E: 2, D-F: 6

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4. Algorithm Execution Visualization (Mermaid Diagram)

🔑 `mermaid flowchart TD subgraph Step_1["Step 1: Start at A"] A1((A<br/>key=0)) ---|4|…

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5. Time Complexity Analysis

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Main loop V times chalta hai.

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Har iteration me minimum key find…

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Har iteration me neighbors check…

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Total: V × (V + V) = O(V²).

Topic 7

6. Data Structures Used

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Simple array: O(V) extract-min,…

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Binary heap: O(log V) extract-min,…

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Indexed binary heap: Binary heap…

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Fibonacci heap: O(log V) amortized…

Topic 8

7. Prim's vs Kruskal's Algorithm

🚀 Dono MST find karte hain, lekin approach fundamentally different hai: | Aspect | Prim's…

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8. Prim's vs Dijkstra's Algorithm

📚 Prim's aur Dijkstra's structurally bahut similar dikhte hain — dono priority queue use…

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9. Cut Property — Why Prim's Works

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Har step me MST vertices S aur…

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Prim's hamesha sabse light…

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Cut property guarantee karta hai…

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Isliye har step me correct edge…

Topic 11

10. Real-World Applications

🎯 | Application | How MST/Prim's Helps | Example | |---|---|---| | Network Design (Telecom)…

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11. Variants and Optimizations

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Lazy: Jab edge discover hoti hai,…

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Eager: Decrease-key operation se…

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12. Interview Patterns and Problems

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Dense graph (complete graph,…

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Sparse graph ya edge list given →…

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"MST from specific vertex" →…

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Prim's aur Dijkstra's ka code…

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13. Historical Context

✨ | Year | Milestone | Significance | |---|---|---| | 1926 | Borůvka's algorithm published…

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14. Common Mistakes

🌟 1. Directed graph par Prim's lagana — Prim's sirf undirected graphs ke liye hai. Directed…

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15. Best Practices

🚀 1. Graph type pehle verify karo — Confirm ki graph undirected, weighted, aur connected…

Topic 17

16. Glossary

📚 | Term | Definition | |---|---| | Prim's Algorithm | Greedy algorithm jo MST find karta…

Topic 18

19. Disclaimer

💡 Yeh article Aliens Wiki ka part hai aur educational/reference purposes ke liye likha gaya…

Comparison

7. Prim's vs Kruskal's Algorithm

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Approach: Vertex-centric: grow one tree…

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Process: Expand MST by adding nearest…

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Data Structure: Priority queue…

Comparison

8. Prim's vs Dijkstra's Algorithm

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Problem: Minimum Spanning Tree

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Key Value: Minimum edge weight…

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Comparison: w(u,v) < key[v] ?

Diagram

Visual Flow

📊 Diagram visualization — details in narration

Quiz — Question 1

Quick Quiz

Quiz — Question 2

Complete! 🎉

Aliens Wiki · HIEN · Cinematic Knowledge

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➡️

Copyright (c) A|iens. All rights reserved.

Copyright (c) A|iens. All rights reserved. — Quick Facts

Property: Detail

Full Name: Prim's Algorithm…

Type: Greedy Algorithm / Graph Algorithm

Problem Solved: Minimum Spanning Tree (MST)

Infobox

1. Minimum Spanning Tree — Foundation

Saare V vertices include karta hai

Exactly V - 1 edges hoti hain

Connected hai (har vertex…

Acyclic hai (koi cycle nahi)

2. Algorithm Steps

Agar v MST me nahi hai (inMST[v] =…

key[v] = w(u,v) update karo

parent[v] = u set karo

Priority queue me v ki key update…

3. Step-by-Step Walkthrough Example

A-B: 4, A-C: 2

B-C: 1, B-D: 5

C-D: 8, C-E: 10

D-E: 2, D-F: 6

4. Algorithm Execution Visualization (Mermaid Diagram)

5. Time Complexity Analysis

Main loop V times chalta hai.

Har iteration me minimum key find…

Har iteration me neighbors check…

Total: V × (V + V) = O(V²).

6. Data Structures Used

Simple array: O(V) extract-min,…

Binary heap: O(log V) extract-min,…

Indexed binary heap: Binary heap…

Fibonacci heap: O(log V) amortized…

7. Prim's vs Kruskal's Algorithm

8. Prim's vs Dijkstra's Algorithm

9. Cut Property — Why Prim's Works

Har step me MST vertices S aur…

Prim's hamesha sabse light…

Cut property guarantee karta hai…

Isliye har step me correct edge…

10. Real-World Applications

11. Variants and Optimizations

Lazy: Jab edge discover hoti hai,…

Eager: Decrease-key operation se…

12. Interview Patterns and Problems

Dense graph (complete graph,…

Sparse graph ya edge list given →…

"MST from specific vertex" →…

Prim's aur Dijkstra's ka code…

13. Historical Context

14. Common Mistakes

15. Best Practices

16. Glossary

19. Disclaimer

7. Prim's vs Kruskal's Algorithm

Approach: Vertex-centric: grow one tree…

Process: Expand MST by adding nearest…

Data Structure: Priority queue…

8. Prim's vs Dijkstra's Algorithm

Problem: Minimum Spanning Tree

Key Value: Minimum edge weight…

Comparison: w(u,v) < key[v] ?

Visual Flow

See Also

Kruskals_algorithm

Dijkstras_algorithm

Minimum_spanning_tree

Graph

Greedy_algorithm

Priority_queue

Quiz — Question 1

Quiz — Question 2

Copyright (c) A|iens. All rights reserved. Complete!

Copyright (c) A|iens. All rights reserved. Complete

Kruskals_algorithm