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Floyd-Warshall Algorithm

Floyd-Warshall algorithm ek dynamic programming based graph algorithm hai jo ek weighted graph me…

Overview

Floyd-Warshall Algorithm — Quick Facts

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Property: Detail

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Topic: Floyd-Warshall Algorithm

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Category: Graph Algorithm / Dynamic…

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Also Known As: Floyd's Algorithm,…

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Infobox

🧮 | Property | Detail | |---|---| | Topic | Floyd-Warshall Algorithm | | Category | Graph…

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1. Parichay (Introduction)

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All-pairs: Sab nodes ke beech…

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Dynamic programming: Subproblems…

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Dense graphs ke liye: Sparse…

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Simple implementation: Triple…

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2. Algorithm Kaise Kaam Karta Hai

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Algorithm sochta hai: "Kya node…

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Har step me ek naya intermediate…

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V iterations ke baad, sab possible…

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3. Core Formula

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$dist[i][j]$: Current shortest…

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$dist[i][k]$: Shortest distance…

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$dist[k][j]$: Shortest distance…

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Agar $i → k → j$ ka path shorter…

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4. Example Walkthrough

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Edge A→B: weight 3

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Edge A→C: weight 8

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Edge B→C: weight 2

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Edge C→D: weight 1

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5. Negative Edges & Cycles

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Floyd-Warshall negative edge…

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Dijkstra nahi kar sakta (Dijkstra…

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Example: edge weight = -2…

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Algorithm complete hone ke baad…

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6. Time & Space Complexity

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Dense graphs (edges close to V²)

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Small to medium graphs (V <…

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Jab sab pairs ka answer chahiye

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Very large sparse graphs

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7. Applications

💡 | # | Application | How Floyd-Warshall Used | |---|---|---| | 1 | Network Routing |…

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8. Comparison with Other Algorithms

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Sab pairs chahiye + dense graph:…

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Ek source, non-negative edges:…

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Ek source, negative edges…

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Sab pairs + sparse graph: V times…

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9. Example Graph

📊 `mermaid graph LR A((A)) -->|3| B((B)) A -->|8| C((C)) B -->|2| C B -->|7| D((D)) C…

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10. Fayde aur Challenges

🔬 Fayde (Benefits) | # | Benefit | Description | |---|---|---| | 1 | All-Pairs | Ek run me…

Comparison

8. Comparison with Other Algorithms

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1: Problem

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2: Time

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3: Negative Edges

Diagram

Visual Flow

📊 Diagram visualization — details in narration

Quiz — Question 1

Floyd-Warshall Algorithm ka sabse sahi definition kya hai?

Quick Quiz

Quiz — Question 2

Floyd-Warshall Algorithm ka 'Topic' kya hai?

Complete! 🎉

Floyd-Warshall Algorithm Complete!

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