Key Concepts

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Big-Θ Notation

We compute the big-Θ of an algorithm by counting the number of iterations the algorithm always takes with an input of n. For instance, the loop in the pseudo code below will always iterate N times for a list size of N. The runtime can be described as Θ(N).

for each item in list: print item
Asymptotic Notation: Conceptual
Lesson 1 of 2
  1. 1
    Cheetahs. Ferraris. Life. All are fast, but how do you know which one is the fastest? You can measure a cheetah’s and a Ferrari’s speed with a speedometer. You can measure life with years and month…
  2. 2
    The first subtype of asymptotic notation we will explore is big Theta (denoted by Θ). We use big Theta when a program has only one case in term of runtime. But what exactly does that mean? Take a …
  3. 3
    Before we delve into the multiple runtime cases, let’s see the different common runtimes a program could have. Below is a list of common runtimes that run from fastest to slowest. - Θ(1). This…
  4. 4
    Sometimes, a program may have a different runtime for the best case and worst case. For instance, a program could have a best case runtime of Θ(1) and a worst case of Θ(N). We use a different notat…
  5. 5
    Sometimes, a program has so much going on that it’s hard to find the runtime of it. Take a look at the pseudocode program that first prints all the positive values up to N and then returns the numb…
  6. 6
    Let’s review what we learned: - We use asymptotic notation to describe the runtime of a program. The three types of asymptotic notation are big Theta, big Omega, and big O. - We use big Theta (Θ) t…

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