Dynamic Programming

  1. Fundamental Principles of Dynamic Programming
    1. Optimal Substructure Property
      1. Definition and Mathematical Formulation
        1. Identifying Optimal Substructure in Problems
          1. Testing for Optimal Substructure
            1. Examples of Optimal Substructure
              1. Shortest Path Problems
                1. Longest Common Subsequence
                2. Counter-examples Where Optimal Substructure Fails
                3. Overlapping Subproblems Property
                  1. Definition and Characteristics
                    1. Identifying Overlapping Subproblems
                      1. Recursive Tree Analysis
                        1. Examples of Overlapping Subproblems
                          1. Fibonacci Sequence
                            1. Binomial Coefficients
                            2. Measuring Overlap Efficiency

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                          1. Introduction to Dynamic Programming

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                          3. Core Implementation Approaches