Week 31 of 43
Advanced DSA
WEEK 31 LEARNING MODULE
Breadth-First Search (BFS) & Shortest Path in Unweighted Graphs
Covers level-order BFS exploration using FIFO queues, shortest path guarantees in unweighted graphs, multi-source BFS, and state-space transitions.
5 Practice Problems3 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Master Breadth-First Search (BFS) using a FIFO queue (`collections.deque`).
- ✓Understand why BFS guarantees the shortest path (minimum edge count) in unweighted graphs.
- ✓Implement Multi-Source BFS: enqueuing multiple starting nodes simultaneously (Rotting Oranges, 01 Matrix).
- ✓Solve state-space shortest path puzzles (Word Ladder, Open the Lock) in $O(V + E)$ time.
Core Concepts
Graph BFS Paradigm
O(V + E)Exploring all neighbor vertices at the current depth before moving to nodes at the next depth level.
Shortest Path Guarantee in Unweighted Graphs
O(V + E)The first time a target vertex is dequeued in BFS is guaranteed to be the shortest path from the source.
Multi-Source BFS
O(V + E)Initializing the queue with all initial source nodes at distance 0 to find distance to closest source.
Algorithms Covered
Graph BFS ($O(V + E)$)Unweighted Shortest PathMulti-Source BFS (Rotting Oranges)Bidirectional / State BFS (Word Ladder, Open the Lock)
Data Structures Applied
GraphsFIFO Queue (`collections.deque`)Visited Hash Set
“Exploration is really the essence of the human spirit.”
— Frank Borman