Asymptotic Analysis: Big-O, Big-Omega & Amortized Complexity
Establish rigorous algorithmic foundations. Master Big-O upper bounds, Omega lower bounds, Theta tight bounds, space complexity, and amortized array expansion.
Basic algebraic equations and logarithmic functions
Ability to prove upper, lower, and tight complexity bounds using Big-O, Big-Omega, Big-Theta, and the Master Theorem.
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Every lesson builds on the one before it. Open any lesson to read the explanation, run the examples, and try the practice challenges.
- 06.01Asymptotic Notation: Upper Bounds, Lower Bounds & Tight Bounds4 min
Deconstruct asymptotic notation. Contrast Big-O, Big-Omega, and Big-Theta, understand dominant terms, and eliminate hardware-specific constants.
- 06.02Auxiliary Space Complexity & Recursion Call Stack Footprint4 min
Analyze memory scaling. Differentiate between total space and auxiliary space, calculate recursion call stack depth, and optimize for in-place algorithms.
- 06.03Amortized Complexity: The Accounting Method & Dynamic Array Resizing4 min
Master amortized analysis. Understand why ArrayList.add() is O(1) amortized despite occasional O(N) resizing, and model costs using the Aggregate and Banker's methods.
- 06.04Recurrence Relations, Recursion Trees, and the Master Theorem4 min
Formulate mathematical recurrence relations for divide-and-conquer algorithms and solve them rigorously using recursion trees and the Master Theorem.
Ready to move on?
Solve recurrence relations and prove amortized bounds for dynamic array doubling.
Open the module self-check