# \footnotesize f(n)  URL:: https://brilliant.org/courses/computer-science-algorithms/the-speed-of-algorithms-2/comparing-algos/4/ Author:: brilliant.org ## Highlights > Computer scientists have a shorthand to describe the fact that, when you use some measure of cost (like the number of comparisons) to think about the speed of an algorithm, only the largest exponent matters for large inputs. > This shorthand is called **Big** OOO **notation**. ([View Highlight](https://read.readwise.io/read/01ga4t3ec5cgbj3k0nvsk51dxa)) > The upshot is that if you are trying to determine how a function scales when nnn gets large, the **largest exponent** in the polynomial is really the only one that matters. ([View Highlight](https://read.readwise.io/read/01ga4t2dkte0mm3fmqmsbnna2v)) > When trying to determine how algorithms behave with large inputs, only the highest exponent matters. If the costs of two algorithms have different maximum exponents, the algorithm with the smallest exponent is the one that will eventually win if the input gets large enough. ([View Highlight](https://read.readwise.io/read/01ga4t2rrzkec51wyyg64hpbx1)) --- Title: \footnotesize f(n) Author: brilliant.org Tags: readwise, articles date: 2024-01-30 --- # \footnotesize f(n)  URL:: https://brilliant.org/courses/computer-science-algorithms/the-speed-of-algorithms-2/comparing-algos/4/ Author:: brilliant.org ## AI-Generated Summary Larger powers of n grow much faster than smaller powers. So much faster that when a function has more than one term, for example x3−x2. ## Highlights > Computer scientists have a shorthand to describe the fact that, when you use some measure of cost (like the number of comparisons) to think about the speed of an algorithm, only the largest exponent matters for large inputs. > This shorthand is called **Big** OOO **notation**. ([View Highlight](https://read.readwise.io/read/01ga4t3ec5cgbj3k0nvsk51dxa)) > The upshot is that if you are trying to determine how a function scales when nnn gets large, the **largest exponent** in the polynomial is really the only one that matters. ([View Highlight](https://read.readwise.io/read/01ga4t2dkte0mm3fmqmsbnna2v)) > When trying to determine how algorithms behave with large inputs, only the highest exponent matters. If the costs of two algorithms have different maximum exponents, the algorithm with the smallest exponent is the one that will eventually win if the input gets large enough. ([View Highlight](https://read.readwise.io/read/01ga4t2rrzkec51wyyg64hpbx1))