Big-O Complexity Analyzer

About the Big-O Complexity Analyzer

The Big-O Complexity Analyzer helps users understand the time and space complexity of algorithms, expressed in Big-O notation (\( O(n) \), \( O(\log n) \), etc.). This tool is designed for computer science students, developers, and educators analyzing algorithm efficiency.

Big-O Notation: Describes the upper bound of an algorithm's running time or space requirements as a function of input size (\( n \)).

This analyzer is ideal for studying algorithm performance in data structures, competitive programming, or software optimization.

• Features:
  • Analyzes time and space complexity for predefined algorithms (e.g., Linear Search, Merge Sort).
  • Supports custom algorithm analysis via simplified pseudocode.
  • Validates input size (\( n \)) and supports units (units, thousands, millions).
  • Keypad includes digits and pseudocode symbols (e.g., \{, \}, n).
  • Clear and backspace functionality, with a "Copy" button for results.
• Practical Applications: Useful in algorithm design, performance optimization, competitive programming, and computer science education.
• How to Use:
  • Select an algorithm from the dropdown or choose "Custom Algorithm."
  • For custom algorithms, enter simplified pseudocode (e.g., nested loops).
  • Enter the input size (\( n \)) and select the unit (units, thousands, millions).
  • Use the keypad to insert digits for \( n \) or pseudocode symbols for custom algorithms.
  • Click "Analyze" to compute the complexity, then use "Copy" to copy the result.
  • Use "Clear" to reset, or "⌫" to delete the last character.
  • Share or embed the analyzer using the action buttons.
• Helpful Tips:
  • Input size (\( n \)) must be positive.
  • For custom algorithms, use clear pseudocode with loops or recursive calls.
  • Use the unit dropdown for large input sizes (e.g., millions).
  • Results include best, average, and worst-case complexities where applicable.
  • This analyzer assumes asymptotic analysis for large \( n \).
• Examples:
  • Example 1: Linear Search:
    • Input: Algorithm = Linear Search, \( n = 1000 \) units
    • Steps:
      • Linear Search checks each element in an array of size \( n \).
      • Time Complexity: Worst case is \( O(n) \), as it may check all \( n \) elements.
      • Space Complexity: \( O(1) \), as it uses a constant amount of extra space.
    • Result: Time Complexity = \( O(n) \), Space Complexity = \( O(1) \)
  • Example 2: Merge Sort:
    • Input: Algorithm = Merge Sort, \( n = 1 \) million
    • Steps:
      • Merge Sort divides the array into halves recursively and merges them.
      • Time Complexity: \( O(n \log n) \), due to \( \log n \) levels of recursion, each processing \( n \) elements.
      • Space Complexity: \( O(n) \), for the temporary arrays used in merging.
    • Result: Time Complexity = \( O(n \log n) \), Space Complexity = \( O(n) \)
  • Example 3: Custom Algorithm:
    • Input: Pseudocode = "for i from 1 to n { for j from 1 to n { print(i,j) } }", \( n = 100 \) units
    • Steps:
      • Outer loop runs \( n \) times.
      • Inner loop runs \( n \) times for each iteration of the outer loop.
      • Time Complexity: \( O(n^2) \), as total iterations are \( n \times n \).
      • Space Complexity: \( O(1) \), as only loop variables are used.
    • Result: Time Complexity = \( O(n^2) \), Space Complexity = \( O(1) \)

Analyze algorithm complexity with detailed steps using this tool. Share or embed it on your site!