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Time & Space Complexity Analysis

Understanding how to analyze and compare algorithm efficiency is fundamental to writing good code and solving problems optimally.

Big O, Big Theta, Big Omega notation​

  • Big O (O): Upper bound - worst case scenario
  • Big Theta (Θ): Tight bound - average case scenario
  • Big Omega (Ω): Lower bound - best case scenario

Best, Average, Worst case analysis​

  • Best Case: Minimum time/space required
  • Average Case: Expected time/space for typical inputs
  • Worst Case: Maximum time/space required

Common complexity classes​

  • O(1): Constant time - direct access, hash table lookup
  • O(log n): Logarithmic - binary search, balanced tree operations
  • O(n): Linear - single pass through data
  • O(n log n): Linearithmic - efficient sorting algorithms
  • O(n²): Quadratic - nested loops, bubble sort
  • O(2ⁿ): Exponential - recursive algorithms without optimization

Amortized analysis​

Understanding the average cost per operation over a sequence of operations, even if individual operations may be expensive.

Space-time tradeoffs​

Balancing memory usage against computation time - sometimes using more space can significantly reduce time complexity.