Week 25 of 43
Core DSA
WEEK 25 LEARNING MODULE
Binary Search & Search Space Reduction
Concludes Phase 1 with $O(\log n)$ Divide & Conquer search in sorted arrays, boundary invariants, lower/upper bounds, and Binary Search on the Answer Space.
5 Practice Problems3 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Master the Divide & Conquer search strategy to halve search spaces in $O(\log n)$ time.
- ✓Maintain loop invariants and safe midpoint calculation (`mid = left + (right - left) // 2`).
- ✓Implement exact match, first/last occurrence, and boundary search patterns.
- ✓Apply Binary Search on the Answer Space for optimization problems (Koko Eating Bananas).
Core Concepts
Binary Search Invariant
O(log n)Halving search range each step based on monotonic property of sorted array or predicate.
Midpoint Overflow Prevention
O(1)Using left + (right - left) // 2 instead of (left + right) // 2 to avoid integer overflow.
Binary Search on Answer Space
O(n log(max - min))Searching monotonic feasibility function f(k) across answer domain [min_val, max_val].
Algorithms Covered
Classic Binary Search ($O(\log n)$)First and Last Position SearchInteger Square Root via Binary Search2D Matrix Binary SearchBinary Search on Answer (Eating Speed Minimization)
Data Structures Applied
Sorted Arrays
“Believe you can and you're halfway there.”
— Theodore Roosevelt
Lecture Materials (1)
Curated Practice Problems (5)
LeetCode
W25