What are the core concepts covered in Dijkstra's Shortest Path & Disjoint Set (Union-Find)?

Dijkstra's greedy shortest path algorithm with Min-Heap in O((V + E) log V); Disjoint Set Union (DSU) with path compression and union by rank; Kruskal's algorithm for Minimum Spanning Trees (MST)

Advanced 24 min readModule: Module 10: Shortest Path & Minimum Spanning Trees (Dijkstra, Prim)

Dijkstra's Shortest Path & Disjoint Set (Union-Find)

Find shortest paths on weighted graphs with Dijkstra's algorithm and detect cycles with Union-Find.

What You Will Learn in This Lesson

Dijkstra's greedy shortest path algorithm with Min-Heap in O((V + E) log V)
Disjoint Set Union (DSU) with path compression and union by rank
Kruskal's algorithm for Minimum Spanning Trees (MST)

Introduction & Core Concept

Dijkstra's algorithm finds the shortest path between nodes in a graph with non-negative edge weights (like highway travel times).

WHY DOES THIS MATTER IN THE REAL WORLD?

Dijkstra's algorithm powers Google Maps routing, internet network packet routing (OSPF), and airline flight schedulers.

Dijkstra Shortest Path Concept

javascript

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// Dijkstra computes min distance from source to all destinations
console.log("Dijkstra Algorithm computes optimal weighted paths in O(E log V).");

Line-by-Line Technical Breakdown

1Union-Find with path compression achieves nearly constant O(α(n)) inverse Ackermann time.

Try It Yourself (Interactive Editor)

Modify the code in real-time and click Run to test live browser output and console logs.

Intelligent Code Runner & Live Sandbox[JAVASCRIPT]

JAVASCRIPT SOURCE EDITOR

Interactive Live Code

>Dijkstra Algorithm computes optimal weighted paths in O(E log V).

Industry Best Practices & Professional Standards

Use Dijkstra when edges are weighted positively; use Bellman-Ford if negative weights exist.

Lesson Summary & Core Takeaways

Dijkstra and Union-Find solve complex routing and network connectivity problems.