findall(kin time ( )where is the number of entries returned howeverthis method is slightly more complicatedand the details are left as an exercise ( - admittedlythe height of can be as large as nbut we expect that it is usually much smaller indeedwe will show how to maintain an upper bound of (lognon the height of search tree in section before we describe such schemehoweverlet us describe implementations for dictionary update methods update operations binary search trees allow implementations of the insert and remove operations using algorithms that are fairly straightforwardbut not trivial insertion let us assume proper binary tree supports the following update operationinsertatexternal( , )insert the element at the external node vand expand to be internalhaving new (emptyexternal node children