asymptotic analysis in algorithm analysiswe focus on the growth rate of the running time as function of the input size ntaking "big-pictureapproach for exampleit is often enough just to know that the running time of an algorithm grows proportionally to we analyze 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 this approach reflects that each basic step in pseudo-code description or high-level language implementation may correspond to small number of primitive operations thuswe can perform an analysis of an algorithm by estimating the number of primitive operations executed up to constant factorrather than getting bogged down in language-specific or hardware-specific analysis of the exact number of operations that execute on the computer as tangible examplewe revisit the goal of finding the largest element of python listwe first used this example when introducing for loops on page of section code fragment presents function named find max for this task def find max(data) """return the maximum element from nonempty python list "" biggest data[ the initial value to beat for val in datafor each value if val biggest if it is greater than the best so far biggest val we have found new best (so far return biggest when loop endsbiggest is the max code fragment function that returns the maximum value of python list this is classic example of an algorithm with running time that grows proportional to nas the loop executes once for each data elementwith some fixed number of primitive operations executing for each pass in the remainder of this sectionwe provide framework to formalize this claim the "big-ohnotation let (nand (nbe functions mapping positive integers to positive 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 (nfigure illustrates the general definition