Algorithm Design and Analysis

  1. Greedy Algorithms
    1. The Greedy Strategy
      1. Making Locally Optimal Choices
        1. Greedy-Choice Property
          1. Optimal Substructure
            1. When Greedy Works
              1. When Greedy Fails
              2. Proving Correctness of Greedy Algorithms
                1. Greedy Stays Ahead Argument
                  1. Exchange Argument
                    1. Cut-and-Paste Argument
                    2. Classic Greedy Algorithms
                      1. Activity Selection Problem
                        1. Problem Statement
                          1. Greedy Solution
                            1. Correctness Proof
                              1. Implementation
                              2. Huffman Coding
                                1. Problem Statement
                                  1. Building the Huffman Tree
                                    1. Encoding Process
                                      1. Decoding Process
                                        1. Optimality Proof
                                        2. Fractional Knapsack Problem
                                          1. Problem Statement
                                            1. Greedy Solution
                                              1. Comparison with 0/1 Knapsack
                                                1. Analysis
                                                2. Coin Change Problem
                                                  1. Greedy Approach
                                                    1. When Greedy Works
                                                      1. Counterexamples
                                                      2. Job Scheduling
                                                        1. Minimizing Maximum Lateness
                                                          1. Weighted Job Scheduling
                                                          2. Dijkstra's Algorithm
                                                            1. Single-Source Shortest Path
                                                              1. Algorithm Description
                                                                1. Correctness Proof
                                                                  1. Implementation with Priority Queue
                                                                    1. Limitations with Negative Weights
                                                                    2. Minimum Spanning Tree Algorithms
                                                                      1. Problem Statement
                                                                        1. Kruskal's Algorithm
                                                                          1. Algorithm Description
                                                                            1. Union-Find Data Structure
                                                                              1. Analysis
                                                                              2. Prim's Algorithm
                                                                                1. Algorithm Description
                                                                                  1. Priority Queue Implementation
                                                                                    1. Analysis

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                                                                              4. Divide and Conquer

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                                                                              6. Dynamic Programming