element in an array ofn integersruns in (ntime justificationthe number of primitive operations executed by algorithm arraymax in each iteration is constant hencesince each primitive operation runs in constant timewe can say that the running time of algorithm arraymax on an input of size is at most constant times nthat iswe may conclude that the running time of algorithm arraymax is (nsome properties of the big-oh notation the big-oh notation allows us to ignore constant factors and lower order terms and focus on the main components of function that affect its growth example is ( justificationnote that <( ) cn for when > in factwe can characterize the growth rate of any polynomial function proposition if (nis polynomial of degree dthat isf(na na ndand then (nis (ndjustificationnote thatfor > we have < < <<ndhencea nd <( )nd thereforewe can show (nis (ndby defining and thusthe highest-degree term in polynomial is the term that determines the asymptotic growth rate of that polynomial we consider some additional properties of the big-oh notation in the exercises let us consider some further examples herehoweverfocusing on combinations of the seven fundamental functions used in algorithm design example nlog is (