8/12/2019 Fundamentals of Algorithms - CS502 Handouts

1/4

but have never dened it. Lets remedy this

, we dene

8/12/2019 Fundamentals of Algorithms - CS502 Handouts

2/4

8/12/2019 Fundamentals of Algorithms - CS502 Handouts

3/4

both the upper and lower bounds. The lower bound is satised b

Since this is true for all sufciently large innity. If we divide both sides by

The denition of

8/12/2019 Fundamentals of Algorithms - CS502 Handouts

4/4

These denitions suggest an alternative way of showing the a

dene the asymptotic behavior. Limit rule for

(strictly positive but not innity) then

(nonnegative but not innite) then

(either a strictly positive constant or innity) then

: Inserting into a balanced binary tree; time to nd an item in