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Elite Computer Science Mastery
·
Module 1
Algorithmic Foundations and Complexity
1
Analyzing Algorithm Efficiency with Big O, Omega, and Theta Notations
Define Big O, Big Omega, and Big Theta notations and apply them to analyze the time complexity of iterative algorithms.
2
Space Complexity and Memory Trade-offs
Analyze space complexity and identify memory trade-offs in algorithm design.
3
Analyzing Algorithm Efficiency
Explain best, average, and worst-case complexity scenarios with concrete examples.
4
Analyzing Recursive Algorithms with Recurrence Relations
Use mathematical recurrence relations to derive the time complexity of recursive algorithms.
5
Sorting Algorithms: O(n^2) and O(n log n)
Implement and analyze O(n^2) sorting algorithms (bubble, insertion, selection) and advanced O(n log n) sorting algorithms (merge sort, quick sort).
6
Pivot Selection in Quick Sort: Average vs. Worst-Case Performance
Analyze pivot selection strategies in quick sort and its impact on average vs. worst-case performance.
7
Bitwise Operations for Low-Level Manipulation
Apply bitwise operations (AND, OR, XOR, NOT, shifts) to solve low-level manipulation problems.
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Linear Data Structures and Common Patterns