# Difference between asymptotic running time and asymptotic space required for a dynamic program

I'm not exactly sure what the difference between these two are. Basically I have a problem that I describe how to complete recursively and then I have so give the asymptotic running time and asymptotic space required for it. I know these have to with giving the Big-O notation but I'm not certain and don't really understand the difference between the two.

Asymptotic running time is a time your program need to compute result for an input of lenght $n$.

Asymptotic space required is how many space will your program use in order to compute result for an input of lenght $n Both of them should be written in O-e.t.c. notations. For example if for input of lenght$n$you need to do at least$5 n$computational steps your time will be O(n). If you need to create 3 matrices$n\times n$in size each in order to compute the result for an input of length$n$you require O(n^2) space. • so i'm assuming running time would be answered in Big-O notation but how would you answer how much space required? like how much space a in memory? Can you explain that more? – PeteGuru Oct 29 '15 at 17:15 • If you have a fixed number of n x n matrices, that will take$O(n^2)\$ space, no matter how long the program takes to run. – marty cohen Oct 29 '15 at 17:29