Algorithm Design and Analysis

  1. Backtracking and Branch-and-Bound
    1. Backtracking
      1. The General Method
        1. Recursive Search Framework
          1. Solution Space Exploration
            1. State-Space Trees
              1. Representation
                1. Traversal Strategies
                2. Pruning the Search Space
                  1. Feasibility Pruning
                    1. Optimality Pruning
                      1. Constraint Propagation
                      2. Classic Backtracking Problems
                        1. N-Queens Problem
                          1. Problem Statement
                            1. Board Representation
                              1. Constraint Checking
                                1. Pruning Strategies
                                  1. Implementation
                                  2. Sudoku Solver
                                    1. Problem Representation
                                      1. Constraint Propagation
                                        1. Search Strategy
                                        2. Subset Sum Problem
                                          1. Problem Statement
                                            1. Pruning Conditions
                                            2. Graph Coloring
                                              1. Problem Statement
                                                1. Backtracking Solution
                                                2. Hamiltonian Path
                                                  1. Problem Statement
                                                    1. Backtracking Approach
                                                3. Branch-and-Bound
                                                  1. The General Method
                                                    1. Bounding and Pruning
                                                      1. Search Tree Representation
                                                        1. Best-First Search Strategy
                                                          1. Bounding Functions
                                                            1. Upper Bounds
                                                              1. Lower Bounds
                                                                1. Relaxation Techniques
                                                                2. Comparison with Backtracking
                                                                  1. Classic Branch-and-Bound Problems
                                                                    1. Traveling Salesperson Problem
                                                                      1. Problem Statement
                                                                        1. Lower Bound Computation
                                                                          1. Branching Strategy
                                                                            1. Pruning Conditions
                                                                            2. 0/1 Knapsack Problem
                                                                              1. Fractional Bound
                                                                                1. Branching Strategy
                                                                                  1. Implementation
                                                                                  2. Job Assignment Problem
                                                                                    1. Problem Statement
                                                                                      1. Bounding Function
                                                                                        1. Search Strategy

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                                                                                  6. Dynamic Programming

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                                                                                  8. Graph Algorithms