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Diffstat (limited to 'asymptotic-notation.html.markdown')
| -rw-r--r-- | asymptotic-notation.html.markdown | 27 |
1 files changed, 14 insertions, 13 deletions
diff --git a/asymptotic-notation.html.markdown b/asymptotic-notation.html.markdown index e1f961f8..4167ba8d 100644 --- a/asymptotic-notation.html.markdown +++ b/asymptotic-notation.html.markdown @@ -72,45 +72,45 @@ for a given function. Say `f(n)` is your algorithm runtime, and `g(n)` is an arb 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). -*Example 1* +*Example 1* ``` -f(n) = 3log n + 100 +f(n) = 3log n + 100 g(n) = log n ``` -Is `f(n)` O(g(n))? -Is `3 log n + 100` O(log n)? +Is `f(n)` O(g(n))? +Is `3 log n + 100` O(log n)? Let's look to the definition of Big-O. ``` -3log n + 100 <= c * log n +3log n + 100 <= c * log n ``` -Is there some constant c that satisfies this for all n? +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-O has been met therefore `f(n)` is O(g(n)). -*Example 2* +*Example 2* ``` -f(n) = 3*n^2 +f(n) = 3*n^2 g(n) = n ``` -Is `f(n)` O(g(n))? -Is `3 * n^2` O(n)? +Is `f(n)` O(g(n))? +Is `3 * n^2` O(n)? Let's look at the definition of Big-O. ``` -3 * n^2 <= c * n +3 * n^2 <= c * n ``` -Is there some constant c that satisfies this for all n? +Is there some constant c that satisfies this for all n? No, there isn't. `f(n)` is NOT O(g(n)). ### Big-Omega @@ -137,3 +137,4 @@ code examples soon. * [MIT](http://web.mit.edu/16.070/www/lecture/big_o.pdf) * [KhanAcademy](https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/asymptotic-notation) +* [Big-O Cheatsheet](http://bigocheatsheet.com/) - common structures, operations, and algorithms, ranked by complexity. |