Dynamic Programming

  1. Core Implementation Approaches
    1. Top-Down Approach (Memoization)
      1. Recursive Problem Decomposition
        1. Memoization Mechanics
          1. Cache Data Structures
            1. Cache Lookup Strategy
              1. Cache Storage Strategy
              2. Implementation Patterns
                1. Function Signature Design
                  1. Base Case Handling
                    1. Recursive Case Implementation
                    2. Advantages of Memoization
                      1. Natural Problem Decomposition
                        1. Lazy Evaluation
                          1. Easier Debugging
                          2. Disadvantages of Memoization
                            1. Stack Overflow Risk
                              1. Function Call Overhead
                                1. Memory Fragmentation
                              2. Bottom-Up Approach (Tabulation)
                                1. Iterative Problem Building
                                  1. Table Construction
                                    1. Determining Table Dimensions
                                      1. Initialization Strategies
                                        1. Fill Order Determination
                                        2. Implementation Patterns
                                          1. Base Case Initialization
                                            1. Iterative Fill Process
                                              1. Result Extraction
                                              2. Advantages of Tabulation
                                                1. No Recursion Overhead
                                                  1. Predictable Memory Usage
                                                    1. Space Optimization Opportunities
                                                    2. Disadvantages of Tabulation
                                                      1. Less Intuitive Implementation
                                                        1. May Compute Unnecessary States
                                                          1. Complex State Dependencies
                                                        2. Choosing Between Approaches
                                                          1. Problem Characteristics Analysis
                                                            1. Performance Considerations
                                                              1. Implementation Complexity
                                                                1. Memory Constraints

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                                                              2. Fundamental Principles of Dynamic Programming

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                                                              4. Problem-Solving Framework