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Renamed Big-Oh to more prevalent notation, Big-O.

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Jake Prather 2015-03-04 17:48:10 -06:00
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@ -66,8 +66,8 @@ Polynomial - n^z, where z is some constant
Exponential - a^n, where a is some constant Exponential - a^n, where a is some constant
``` ```
### Big-Oh ### Big-O
Big-Oh, commonly written as O, is an Asymptotic Notation for the worst case, or ceiling of growth Big-O, commonly written as O, is an Asymptotic Notation for the worst case, or ceiling of growth
for a given function. Say `f(n)` is your algorithm runtime, and `g(n)` is an arbitrary time complexity for a given function. Say `f(n)` is your algorithm runtime, and `g(n)` is an arbitrary time complexity
you are trying to relate to your algorithm. `f(n)` is O(g(n)), if for any real constant c (c > 0), you are trying to relate to your algorithm. `f(n)` is O(g(n)), if for any real constant c (c > 0),
`f(n)` <= `c g(n)` for every input size n (n > 0). `f(n)` <= `c g(n)` for every input size n (n > 0).
@ -81,7 +81,7 @@ g(n) = log n
Is `f(n)` O(g(n))? Is `f(n)` O(g(n))?
Is `3 log n + 100` O(log n)? Is `3 log n + 100` O(log n)?
Let's look to the definition of Big-Oh. Let's look to the definition of Big-O.
``` ```
3log n + 100 <= c * log n 3log n + 100 <= c * log n
@ -93,7 +93,7 @@ Is there some constant c that satisfies this for all n?
3log n + 100 <= 150 * log n, n > 2 (undefined at n = 1) 3log n + 100 <= 150 * log n, n > 2 (undefined at n = 1)
``` ```
Yes! The definition of Big-Oh has been met therefore `f(n)` is O(g(n)). Yes! The definition of Big-O has been met therefore `f(n)` is O(g(n)).
*Example 2* *Example 2*
@ -104,7 +104,7 @@ g(n) = n
Is `f(n)` O(g(n))? Is `f(n)` O(g(n))?
Is `3 * n^2` O(n)? Is `3 * n^2` O(n)?
Let's look at the definition of Big-Oh. Let's look at the definition of Big-O.
``` ```
3 * n^2 <= c * n 3 * n^2 <= c * n
@ -119,7 +119,7 @@ for a given function.
`f(n)` is Ω(g(n)), if for any real constant c (c > 0), `f(n)` is >= `c g(n)` for every input size n (n > 0). `f(n)` is Ω(g(n)), if for any real constant c (c > 0), `f(n)` is >= `c g(n)` for every input size n (n > 0).
Feel free to head over to additional resources for examples on this. Big-Oh is the primary notation used Feel free to head over to additional resources for examples on this. Big-O is the primary notation used
for general algorithm time complexity. for general algorithm time complexity.
### Ending Notes ### Ending Notes