Big Oh(O) vs Big Omega(Ω) vs Big Theta(θ) notations | Asymptotic Analysis of Algorithms with Example

Support Simple Snippets by Donations - Google Pay UPI ID - tanmaysakpal11@okicici PayPal - paypal.me/tanmaysakpal11 --------------------------------------------------------------------------------------------- In this tutorial we will understand the 3 different Asymptotic Time Complexity analysis of Algorithms namely - Big Oh(O) Big Omega(Ω) Big Theta(θ) We will understand each Complexity by taking its mathematical definition as well as example with graph. Lastly we will understand its practical usage & understand why we really need 3 different time complexity measures. Big O notation - Big O notation specifically describes worst case scenario. It represents the upper bound running time complexity of an algorithm. Mathematically - Let f and g be functions of n - where n is natural no denoting size or steps of the algorithm then - f(n) = O(g(n)) IFF f(n) less than or = c.g(n) where n greater than = n0, c greater than 0, n0 greater than = 1 Big Omega notation - Big Omega notation specifically describes best case scenario. It represents the lower bound running time complexity of an algorithm. Basically it tells you what is the fastest time/behavior in which the algorithm can run. f(n) = Ω(g(n)) IFF f(n) greater than or = c.g(n) where n greater than = n0, c greater than 0, n0 greater than = 1 Big Theta (θ) notation - Big Omega notation specifically describes average case scenario. It represents the most realistic time complexity of an algorithm. f(n) = θ(g(n)) IFF c1.g(n) less than or = f(n) less than or = c2.g(n) where n greater than = n0, c1,c2 greater than 0, n greater than = n0, n0 greater = 1 Big Ω - Best Case Big O - Worst Case Big θ - Average Case Simple Snippets Official Website - http://simplesnippets.tech/ Simple Snippets on Facebook - https://www.facebook.com/simplesnippets/ Simple Snippets on Instagram - https://www.instagram.com/simplesnippets/ Simple Snippets on Twitter - https://twitter.com/simplesnippet Simple Snippets Google Plus Page - https://plus.google.com/+SimpleSnippets Simple Snippets email ID - simplesnippetsinfo@gmail.com For More Technology News, Latest Updates and Blog articles visit our Official Website - http://simplesnippets.tech/