Week 30 of 43
Advanced DSA
WEEK 30 LEARNING MODULE
Depth-First Search (DFS) & Graph Traversals
Covers graph DFS traversal using recursion and explicit stacks, visited set tracking, connected component counting, flood fill, and 2D grid graph traversal.
5 Practice Problems4 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Master Depth-First Search (DFS) on graphs using recursion and explicit stacks.
- ✓Maintain a `visited` set to prevent infinite loops in cyclic graphs.
- ✓Model 2D grid matrices as implicit graphs with 4-directional or 8-directional neighbor transitions.
- ✓Count connected components (Number of Islands, Number of Provinces) and solve Flood Fill.
- ✓Analyze DFS complexities: $O(V + E)$ time and $O(V)$ space.
Core Concepts
Graph DFS Paradigm
O(V + E) time, O(V) spaceTraversing as deep as possible along each branch before backtracking.
Visited Set Management
O(1) lookupTracking visited vertices to avoid cycles and redundant processing.
Implicit 2D Grid Graphs
O(R * C)Treating matrix cells as vertices with edges between adjacent cells (r±1, c) and (r, c±1).
Connected Components Counting
O(V + E)Iterating over all vertices, triggering a new DFS whenever an unvisited vertex is encountered.
Algorithms Covered
Graph DFS ($O(V + E)$)Flood Fill AlgorithmNumber of Islands (Grid DFS)Max Area of IslandCycle Detection in Undirected Graphs
Data Structures Applied
GraphsCall StackVisited Hash Set
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— Maori Proverb