in algorithm analysiswe focus on the growth rate of the running time as function of the input size ntaking "big-pictureapproachrather than being bogged down with small details it is often enough just to know that the running time of an algorithm such as arraymaxgiven in section grows proportionally to nwith its true running time being times constant factor that depends on the specific computer we analyze data structures and algorithms using mathematical notation for functions that disregards constant factors namelywe characterize the running times of algorithms by using functions that map the size of the inputnto values that correspond to the main factor that determines the growth rate in terms of we do not formally define what meanshoweverand instead let refer to chosen measure of the input "size,which is allowed to be defined differently for each algorithm we are analyzing this approach allows us to focus attention on the primary "big-pictureaspects in running time function in additionthe same approach lets us characterize space usage for data structures and algorithmswhere we define space usage to be the total number of memory cells used the "big-ohnotation let (nand (nbe functions mapping nonnegative integers to real numbers we say that (nis ( ( )if there is real constant and an integer constant > such that (nn this definition is often referred to as the "big-ohnotationfor it is sometimes pronounced as " (nis big-oh of (nalternativelywe can also say " (nis order of ( (this definition is illustrated in figure figure illustrating the "big-ohnotation the function (nis ( ( ))since ( =