Prim's Algorithm | MST Step-by-Step Dry Run | DSA Graph Theory Explained
Welcome to this power-packed 7-minute video on Prim’s Algorithm – one of the most fundamental and frequently asked concepts in Graph Theory and Data Structures & Algorithms (DSA). Whether you're a university student, preparing for interviews, or revising for your DSA exams, this short but focused video will help you grasp Prim's Algorithm clearly and confidently.
In this video, we focus on:
The logic and working of Prim's Algorithm
A step-by-step dry run on a weighted undirected graph
Selection of minimum-weight edges at each stage
Understanding how the Minimum Spanning Tree (MST) is built
Time and space complexity breakdown
Practical uses of MST and how Prim’s differs from Kruskal’s
💡 What Is a Minimum Spanning Tree (MST)?
A Minimum Spanning Tree is a subset of edges in a connected, weighted, undirected graph that:
Connects all the vertices together (spanning)
Has no cycles (tree)
Has the minimum possible total edge weight
MSTs are useful in real-world applications like:
Network design (telecommunication, computer, electrical)
Road/path optimization
Cluster analysis
Approximation algorithms
🌿 Prim’s Algorithm – Key Characteristics:
Type: Greedy Algorithm
Graph Type: Connected, Undirected, Weighted
Strategy: Build MST starting from a node, expanding by minimum weight edges to unvisited nodes
🔍 How Prim’s Algorithm Works – Step-by-Step Overview:
Start from any vertex (often node 0)
Initialize MST Set (to track visited vertices)
Track the minimum weight edge connecting a visited node to an unvisited node
Pick the smallest such edge and add the new vertex to the MST
Repeat the process until all vertices are included in the MST
📊 Dry Run Example (Explained in Video):
We take a simple graph with nodes and weighted edges and manually perform:
Iteration 1: Select minimum edge from source
Iteration 2-N: Add vertex with lowest cost edge to MST
Update edge values dynamically
Build the final MST and calculate total cost
Each iteration shows how the MST is expanded and how decisions are made based on minimum edge weights. This visual + verbal explanation makes it easy to grasp the core logic.
🧠 Time & Space Complexity:
Implementation Type Time Complexity Space Complexity
Using Adjacency Matrix O(V²) O(V²)
Using Min Heap + Adjacency List O(E log V) O(V + E)
Where:
V = number of vertices
E = number of edges
✅ Why This Video Is Different:
✔️ No long theory — direct, to-the-point explanation
✔️ Focused on iterations and dry run rather than abstract code
✔️ Perfect for last-minute revision, viva prep, or exams
✔️ Ideal for beginners and non-coders who want visual understanding
✔️ Concepts explained in simple, clear language
🎓 Who Should Watch This?
BS Computer Science, Software Engineering, and IT students
DSA crash course learners
Competitive programmers
Anyone preparing for technical interviews (FAANG, Microsoft, TCS, Wipro, etc.)
Students from Punjab University, FAST, NUST, UET, or any institution studying DSA
📚 Prim’s vs Kruskal’s – Quick Difference Recap:
Feature Prim's Algorithm Kruskal’s Algorithm
Approach Grows one tree Merges multiple components
Starts With Any node Sorted edge list
Data Structure Used Priority Queue/Min Heap Union-Find (Disjoint Sets)
Cycle Detection Not needed Required (Union-Find)
Graph Type Dense graphs preferred Sparse graphs preferred
🧩 Real-Life Use Cases:
Designing the most cost-efficient telecommunication networks
Connecting multiple cities with minimal road cost
Building network backbones (Internet routers, electrical circuits)
GIS and geographical mapping systems
Computer graphics (mesh generation)
🔔 Stay Connected & Learn More!
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📌 Related DSA Topics You Should Watch Next:
▶️ Kruskal’s Algorithm – MST using Union-Find
▶️ Dijkstra’s Algorithm – Single Source Shortest Path
▶️ Graph Representations: Adjacency Matrix & List
▶️ BFS & DFS Traversal Techniques
▶️ Disjoint Set (Union-Find) with Path Compression
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