Algorithm Design and Analysis

  1. Divide and Conquer
    1. The Divide and Conquer Paradigm
      1. The Divide Step
        1. The Conquer Step
          1. The Combine Step
            1. When Divide and Conquer Works
              1. Recurrence Relations in Divide and Conquer
              2. Classic Divide and Conquer Algorithms
                1. Binary Search
                  1. Algorithm Description
                    1. Iterative Implementation
                      1. Recursive Implementation
                        1. Analysis
                        2. Merge Sort
                          1. Algorithm Description
                            1. Merging Process
                              1. Time Complexity Analysis
                                1. Space Complexity Analysis
                                  1. Stability
                                  2. Quick Sort
                                    1. Algorithm Description
                                      1. Partitioning Schemes
                                        1. Lomuto Partition
                                          1. Hoare Partition
                                          2. Pivot Selection Strategies
                                            1. Randomized Quick Sort
                                              1. Worst-Case Analysis
                                                1. Average-Case Analysis
                                                  1. Best-Case Analysis
                                                    1. In-Place Sorting
                                                    2. Heap Sort
                                                      1. Building a Heap
                                                        1. Heap Sort Algorithm
                                                          1. Analysis
                                                          2. Strassen's Algorithm
                                                            1. Matrix Multiplication Problem
                                                              1. Standard Algorithm
                                                                1. Strassen's Approach
                                                                  1. Matrix Partitioning
                                                                    1. Recursive Multiplication
                                                                      1. Complexity Comparison
                                                                      2. Closest-Pair of Points
                                                                        1. Problem Statement
                                                                          1. Brute-Force Approach
                                                                            1. Divide and Conquer Approach
                                                                              1. Efficient Merging
                                                                                1. Analysis
                                                                                2. Integer Multiplication
                                                                                  1. Karatsuba Algorithm
                                                                                    1. Analysis and Comparison

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                                                                                3. Brute-Force and Exhaustive Search

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                                                                                5. Greedy Algorithms