performed with nand the size of the collection returned by operation findall with the expected space requirement is (noperation time sizeisempty ( entries (nfindinsertremove (logn(expectedfindall (logn (expected extensions and applications of dictionaries in this sectionwe explore several extensions and applications of dictionaries supporting location-aware dictionary entries as we did for priority queues (section )we can also use location-aware entries to speed up the running time for some operations in dictionary in particulara location-aware entry can greatly speed up entry removal in dictionary for in removing location-aware entry ewe can simply go directly to the place in our data structure where we are storing and remove it we could implement location-aware entryfor exampleby augmenting our entry class with private location variable and protected methodslocation(and setlocation( )which return and set this variable respectively we then require that the location variable for an entry ealways refer to ' position or index in the data structure implementing our dictionary we wouldof coursehave to update this variable any time we moved an entryso it would probably make the most sense for this entry class to be closely related to the class implementing the dictionary (the location-aware entry class could even be nested inside the dictionary