Data Structures

  1. Advanced Data Structures
    1. Tries
      1. Structure and Properties
        1. Node Structure
          1. Character-based Branching
          2. Core Operations
            1. Insertion Operation
              1. Search Operation
                1. Deletion Operation
                2. Complexity Analysis
                  1. Space Complexity
                    1. Time Complexity
                    2. Applications
                      1. Autocomplete Systems
                        1. Spell Checkers
                          1. IP Routing Tables
                        2. Disjoint Set Union
                          1. Core Operations
                            1. Find Operation
                              1. Union Operation
                              2. Optimization Techniques
                                1. Union by Rank
                                  1. Union by Size
                                    1. Path Compression
                                    2. Applications
                                      1. Connected Components in Graphs
                                        1. Kruskal's Algorithm Support
                                      2. Segment Trees
                                        1. Purpose and Use Cases
                                          1. Range Sum Queries
                                            1. Range Minimum Queries
                                              1. Range Maximum Queries
                                              2. Structure and Construction
                                                1. Tree Representation
                                                  1. Building Process
                                                  2. Operations
                                                    1. Range Query Operation
                                                      1. Point Update Operation
                                                        1. Range Update Operation
                                                          1. Lazy Propagation
                                                          2. Complexity Analysis
                                                            1. Time Complexity
                                                              1. Space Complexity
                                                              2. Applications
                                                                1. Interval Problems
                                                                  1. Dynamic Array Queries
                                                                2. Fenwick Trees
                                                                  1. Purpose
                                                                    1. Prefix Sum Queries
                                                                    2. Structure and Operations
                                                                      1. Tree Representation
                                                                        1. Point Update Operation
                                                                          1. Prefix Query Operation
                                                                          2. Complexity Analysis
                                                                            1. Time Complexity
                                                                              1. Space Complexity
                                                                              2. Segment Trees vs Fenwick Trees Comparison
                                                                                1. Applications
                                                                                  1. Cumulative Frequency Tables

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                                                                              5. Graph Data Structures

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                                                                              7. Practical Application and Selection