Mind Map: Analysis of Algorithms Overview

Analysis_of_Algorithms_Mind_Map.md

Analysis of Algorithms Mind Map

Overview

This mind map provides a structured overview of Analysis of Algorithms, covering key concepts such as Complexity Analysis, Performance Measures, Growth Rates, Case Analysis, and Applications in Data Structures.

Mermaid Diagram

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mindmap
  root((Analysis of Algorithms))
    Definition
      The study of the efficiency and resource consumption of algorithms

    Complexity Analysis
      Big-O Notation
        Best Case
        Worst Case
        Average Case
      Omega Notation
        Best Case
        Worst Case
      Theta Notation
        Balanced Case

    Performance Measures
      Time Complexity
        Constant Time - O(1)
        Linear - O(N)
        Quadratic - O(N^2)
        Exponential - O(2^N)
      Space Complexity
        Fixed memory requirement
        Growth with input size

    Growth Rates and Limits
      Asymptotic Analysis
      Function Growth
        Linear Growth
        Quadratic Growth
        Exponential Growth

    Case Analysis
      Best Case
        Minimal input size effect
      Average Case
        Typical input size effect
      Worst Case
        Largest input size effect

    Applications in Data Structures
      Sorting Algorithms
        Bubble Sort - O(N^2)
        Merge Sort - O(N log N)
      Searching Algorithms
        Binary Search - O(log N)
        Linear Search - O(N)
      Graph Algorithms
        Dijkstra's - O(V^2)
        DFS - O(V + E)

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Mind Map Contents

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• Central Topic: Analysis of Algorithms

  • Definition: The study of the efficiency and resource consumption of algorithms.

• Complexity Analysis

  • Big-O Notation
    • Best Case, Worst Case, Average Case
  • Omega Notation
    • Best Case, Worst Case
  • Theta Notation
    • Balanced Case

• Performance Measures

  • Time Complexity
    • Constant Time - O(1)
    • Linear - O(N)
    • Quadratic - O(N^2)
    • Exponential - O(2^N)
  • Space Complexity
    • Fixed memory requirement
    • Growth with input size

• Growth Rates and Limits

  • Asymptotic Analysis
  • Function Growth (Linear, Quadratic, Exponential)

• Case Analysis

  • Best Case (Minimal input size effect)
  • Average Case (Typical input size effect)
  • Worst Case (Largest input size effect)

• Applications in Data Structures

  • Sorting Algorithms (Bubble Sort - O(N^2), Merge Sort - O(N log N))
  • Searching Algorithms (Binary Search - O(log N), Linear Search - O(N))
  • Graph Algorithms (Dijkstra's - O(V^2), DFS - O(V + E))

About This Resource

This mind map is part of a learning series on algorithms and data structures, intended for both students and professionals looking to deepen their understanding of algorithm analysis. If you find this useful, feel free to share it with others or fork the Gist!