problem size running time new maximum problem size + using the big-oh notation having made the case of using the big-oh notation for analyzing algorithmslet us briefly discuss few issues concerning its use it is considered poor tastein generalto say " ( < ( ( )),since the big-oh already denotes the "less-than-orequal-toconcept likewisealthough commonit is not fully correct to say " (no( ( ))(with the usual understanding of the "=relation)since there is no way to make sense of the statement " ( ( ) (nin additionit is completely wrong to say " ( > ( ( ))or " (no( ( )),since the (nin the big-oh expresses an upper bound on (nit is best to say" (nis ( ( )for the more mathematically inclinedit is also correct to say" (no( ( )),for the big-oh notation istechnically speakingdenoting whole collection of functions in this bookwe will stick to presenting big-oh statements as " (nis ( ( )even with this interpretationthere is considerable freedom in how we can use arithmetic operations with the big-oh notationand with this freedom comes certain amount of responsibility some words of caution few words of caution about asymptotic notation are in order at this point firstnote that the use of the big-oh and related notations can be somewhat misleading