Introduction to Algorithms

• Understanding the importance of algorithms in computer science
• Exploring algorithm analysis and complexity
• Comparing and contrasting different algorithm design techniques

Algorithm Analysis

• Analyzing the time and space complexity of algorithms
• Understanding asymptotic notation (big O, big Omega, big Theta)
• Evaluating the efficiency and performance of algorithms

Searching Algorithms

• Implementing linear search and binary search algorithms
• Analyzing their time complexity and performance characteristics
• Exploring variations of searching algorithms (interpolation search, exponential search)

Sorting Algorithms

• Implementing and analyzing various sorting algorithms (e.g., bubble sort, selection sort, insertion sort, merge sort, quicksort, heapsort)
• Understanding their time complexity and stability
• Exploring advanced sorting algorithms (e.g., radix sort, bucket sort)

Divide and Conquer

• Understanding the divide-and-conquer algorithm design paradigm
• Implementing algorithms using divide-and-conquer techniques
• Analyzing their time complexity and performance characteristics

Greedy Algorithms

• Understanding the greedy algorithm design paradigm
• Implementing greedy algorithms for various problems (e.g., coin change, interval scheduling, Dijkstra’s algorithm)
• Analyzing the optimality and efficiency of greedy algorithms

Dynamic Programming

• Understanding the dynamic programming algorithm design paradigm
• Implementing dynamic programming algorithms for solving optimization problems (e.g., knapsack problem, matrix chain multiplication)
• Analyzing their time complexity and efficiency

Graph Algorithms

• Exploring graph traversal algorithms (breadth-first search, depth-first search)
• Implementing graph algorithms for common problems (e.g., shortest path, minimum spanning tree, topological sorting)
• Analyzing the time complexity and efficiency of graph algorithms

Backtracking and Recursion

• Understanding backtracking and recursion as algorithmic techniques
• Implementing backtracking algorithms (e.g., N-queens problem, Sudoku solver)
• Analyzing the time complexity and efficiency of backtracking algorithms

String Algorithms

• Implementing string searching algorithms (e.g., brute force, Knuth-Morris-Pratt, Boyer-Moore)
• Exploring string matching algorithms (e.g., Rabin-Karp, Aho-Corasick)
• Analyzing the time complexity and efficiency of string algorithms

Advanced Topics

• Exploring advanced algorithmic topics like approximation algorithms, randomized algorithms, and network flow algorithms
• Understanding the applications and use cases for approximation algorithms, randomized algorithms and network flow algorithms
• Analyzing the time complexity and efficiency of advanced algorithms

Algorithm Design Techniques

• Understanding various algorithm design techniques (e.g., divide and conquer, dynamic programming, greedy, backtracking)
• Analyzing when to apply each technique based on problem characteristics
• Solving real-world problems using appropriate algorithm design techniques

Computational Geometry

• Understanding algorithms for solving geometric problems
• Implementing algorithms for geometric computations (e.g., convex hull, line intersections)
• Analyzing the time complexity and efficiency of computational geometry algorithms

Design and Analysis of Algorithms

• Applying principles of design and analysis in developing efficient algorithms
• Evaluating trade-offs in algorithm design decisions
• Solving real-world problems using appropriate algorithms