This Curriculum covers algorithm design strategies, mathematical analysis, time and space complexity, growth rates, searching, sorting, graph algorithms, and pattern algorithms, with each unit standing as a complete, self-contained lesson while also fitting into a cohesive full course.

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Curriculum Structure & Coverage

1. Foundations of Algorithms

✏️ Introduction to Algorithms

✏️ Algorithm definition and characteristics

✏️ Algorithm analysis and design concepts

✏️ Time and space complexity

✏️ Python as a tool for algorithm implementation

2. Core Algorithm Analysis

✏️ Time complexity analysis

✏️ Space complexity analysis

✏️ Best, average, and worst-case analysis

✏️ Asymptotic notations

3. Orders of Growth & Runtime Analysis

✏️ Limits and growth rate comparison

✏️ Orders of growth

✏️ Ranking functions by efficiency

✏️ Runtime analysis of loops and algorithms

✏️ Mathematical comparison of algorithm performance

4. Mathematical Analysis of Algorithms

✏️ Mathematical analysis of recursive algorithms

✏️ Recurrence relation

✏️ Forward and backward substitution

✏️ Operation counting

✏️ Analysis of classic recursive problems

5. Algorithm Design Strategies

✏️ Brute Force strategy

✏️ Exhaustive Search strategy

✏️ Baseline algorithm design techniques

✏️ Use of brute force as a comparison yardstick

6. Brute Force & Exhaustive Search Algorithms

✏️ Selection Sort

✏️ Bubble Sort

✏️ Linear (Sequential) Search

✏️ Brute-force string matching

✏️ Exhaustive search for optimization problems

7. GCD Algorithms & Numerical Methods

✏️ Euclid’s Algorithm

✏️ Middle-school GCD algorithm

✏️ Algorithm efficiency comparison

✏️ Numerical methods

✏️ Newton–Raphson method

8. Complete Algorithm Analysis I

✏️ Integrated analysis of foundational algorithms

✏️ Combined time complexity and design principles

✏️ Application of asymptotic analysis

✏️ End-to-end algorithm evaluation

9. Complete Algorithm Analysis II

✏️ Advanced algorithm analysis problems

✏️ Algorithm optimization techniques

✏️ Comparative efficiency analysis

✏️ Deeper mathematical and logical reasoning

10. Graph Algorithms Curriculum

✏️ Graph representation

✏️ Directed and undirected graphs

✏️ Graph traversal techniques

✏️ Breadth-First Search (BFS)

✏️ Depth-First Search (DFS)

✏️ Cycle detection

11. Sorting Algorithms I

✏️ Bubble Sort

✏️ Selection Sort

✏️ Insertion Sort

✏️ Step-by-step sorting execution

✏️ Time complexity comparison

12. Sorting Algorithms II

✏️ Counting Sort

✏️ Radix Sort

✏️ Merge Sort

✏️ Comparison vs non-comparison sorting

✏️ Divide and conquer sorting

13. Searching Algorithms

✏️ Linear Search

✏️ Binary Search

✏️ Jump Search

✏️ Interpolation Search

✏️ Performance comparison of searching techniques

14. Pattern Searching Algorithms

✏️ Naive pattern searching

✏️ Pattern matching operations

✏️ Text and pattern representation

✏️ Pattern sliding techniques

✏️ Algorithmic pattern detection

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