Dynamic Programming

  1. Problem-Solving Framework
    1. Problem Recognition
      1. Identifying Optimization Problems
        1. Identifying Counting Problems
          1. Recognizing Decision Problems
            1. Checking for DP Applicability
            2. State Definition
              1. Parameter Identification
                1. State Space Design
                  1. One-Dimensional States
                    1. Multi-Dimensional States
                      1. Complex State Representations
                      2. State Meaning and Interpretation
                      3. Recurrence Relation Formulation
                        1. State Transition Analysis
                          1. Decision Point Identification
                            1. Constraint Integration
                              1. Boundary Condition Handling
                              2. Base Case Identification
                                1. Minimal Subproblem Recognition
                                  1. Base Case Value Assignment
                                    1. Edge Case Consideration
                                    2. Implementation Strategy
                                      1. Approach Selection Criteria
                                        1. Code Structure Design
                                          1. Testing and Validation
                                            1. Performance Optimization

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                                          3. Core Implementation Approaches

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                                          5. Linear Dynamic Programming