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Difference between Big o vs Omega vs Theta notation

NotationMeaningRepresentsExample
Big O (O)Upper boundWorst-case growth rateO(n2) – Quadratic time
Omega (Ω)Lower boundBest-case growth rateΩ(n) – Linear time
Theta (Θ)Tight boundAsymptotically tight growth rateΘ(n2) – Quadratic time

Key points to note:

  • Big O notation represents the maximum or worst-case growth rate of an algorithm.
  • Omega notation represents the minimum or best-case growth rate of an algorithm.
  • Theta notation represents the tight or asymptotically tight growth rate of an algorithm.
  • Big O provides an upper bound, Omega provides a lower bound, and Theta provides both upper and lower bounds.
  • Big O notation is commonly used to analyze and compare algorithms.
  • Omega notation is less commonly used but can be helpful in understanding best-case scenarios.
  • Theta notation is used when the upper and lower bounds of an algorithm match, providing a precise estimate of its complexity.