Week 28 of 43
Advanced DSA
WEEK 28 LEARNING MODULE
Advanced Recursion: Backtracking & Divide and Conquer
Covers combinatorial search, State-Space tree exploration, feasibility pruning (Choose-Explore-Unchoose), Subsets, Permutations, Combinations, and N-Queens.
5 Practice Problems3 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Master Backtracking pattern: Choose $\to$ Explore (Recurse) $\to$ Un-choose (Backtrack).
- ✓Apply State-Space tree pruning to avoid exploring infeasible subtrees.
- ✓Generate combinatorial outputs: Subsets ($O(2^n)$), Permutations ($O(n!)$), and Combinations ($O(\binom{n}{k})$).
- ✓Solve constraint satisfaction problems (N-Queens) with diagonal and column conflict tracking.
Core Concepts
Backtracking Paradigm
Exponential / FactorialSystematic depth-first search of solution spaces that abandons invalid candidate paths immediately upon constraint violation.
State-Space Tree Pruning
Using boolean flags or bitmasks to skip invalid choices before making recursive calls.
Combinatorial Generation
O(2^n) or O(n!)Constructing subsets (power set) and permutations systematically via recursion.
Algorithms Covered
Subsets Generation ($O(2^n)$)Permutations Generation ($O(n!)$)Combinations GenerationN-Queens Puzzle SolverDivide & Conquer Sorting
Data Structures Applied
Recursion TreeState ListsHash Sets
“The bad news is time flies. The good news is you’re the pilot.”
— Michael Altshuler