Data Structures and Algorithms

  1. Advanced Topics
    1. Amortized Analysis
      1. Definition and significance
        1. Explanation of amortized analysis
          1. Comparison with worst-case and average-case analysis
          2. Techniques
            1. Aggregate method
              1. Overview and examples
              2. Accounting method
                1. How it works with examples
                2. Potential method
                  1. Concept and applications
                3. Applications
                  1. Resizable arrays
                    1. Union-find data structures
                      1. Splay trees
                    2. Probabilistic Data Structures
                      1. Overview
                        1. Explanation of probabilistic data structures
                          1. Advantages and trade-offs compared to deterministic structures
                          2. Bloom Filters
                            1. Concept and use cases
                              1. False positive rate
                                1. Applications in web caching and database queries
                                  1. Variations
                                    1. Counting Bloom filters
                                      1. Scalable Bloom filters
                                    2. Skip Lists
                                      1. Structure and operations
                                        1. Comparison with balanced trees and linked lists
                                          1. Applications in databases and concurrent access
                                        2. Divide and Conquer
                                          1. Explanation and characteristics
                                            1. Master Theorem
                                              1. Definition and derivation
                                                1. Use cases for solving recurrence relations
                                                2. Notable algorithms
                                                  1. Merge sort
                                                    1. Quick sort
                                                    2. Applications
                                                      1. Multiplying large numbers (Karatsuba algorithm)
                                                        1. Fast Fourier Transform (FFT)
                                                      2. Backtracking
                                                        1. Fundamentals
                                                          1. Definition and how it works
                                                            1. Comparison with other problem-solving approaches
                                                            2. Common problems
                                                              1. N-queens problem
                                                                1. Sudoku solver
                                                                  1. Graph coloring
                                                                  2. Techniques
                                                                    1. Pruning branches
                                                                      1. Constraint satisfaction
                                                                    2. Computational Geometry
                                                                      1. Importance and applications
                                                                        1. Introduction to the field
                                                                          1. Applications in graphics, robotics, and GIS
                                                                          2. Convex Hull
                                                                            1. Definition and problem statement
                                                                              1. Algorithms
                                                                                1. Graham's scan
                                                                                  1. Jarvis's march (Gift wrapping)
                                                                                    1. Quickhull
                                                                                  2. Voronoi Diagrams
                                                                                    1. Definition and properties
                                                                                      1. Construction methods
                                                                                        1. Fortune's algorithm
                                                                                        2. Applications in biology, meteorology, and urban planning
                                                                                        3. Additional Topics
                                                                                          1. Delaunay triangulation
                                                                                            1. Closest pair of points
                                                                                              1. Line segment intersection detection
                                                                                          3. Algorithms
                                                                                          First Page
                                                                                          5. Practical Applications