Week 10 of 43
Foundation
WEEK 10 LEARNING MODULE
Asymptotic Analysis: Time & Space Complexity
Establishes formal theoretical principles for analyzing algorithm efficiency using Big-O notation, time-space trade-offs, and memory complexity.
4 Practice Problems3 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Understand asymptotic growth rates: $O(1)$, $O(\log n)$, $O(n)$, $O(n \log n)$, $O(n^2)$, $O(2^n)$, $O(n!)$.
- ✓Calculate both Time and Auxiliary Space complexities for iterative and recursive algorithms.
- ✓Analyze time vs. space trade-offs when optimizing brute-force solutions.
- ✓Solve array and string problems with optimal in-place index manipulation.
Core Concepts
Big-O Notation & Asymptotic Bounds
O(1) to O(n!)Mathematical framework describing the limiting behavior of execution time or memory as input size grows.
Time vs. Space Trade-offs
Balancing auxiliary memory usage (e.g. hash tables) to reduce algorithmic time complexity.
In-place Array Index Negation
O(n) time, O(1) spaceUsing element values as indices and negating values in-place to find duplicates in O(n) time and O(1) space.
Algorithms Covered
In-place Duplicate FindingMonotonic Array VerificationCharacter Frequency Balancing
Data Structures Applied
ArraysHash Tables
“The first principle is that you must not fool yourself — and you are the easiest person to fool.”
— Richard Feynman