implementation of dictionary with entries only if the height of is small in the best caset has height log( which yields logarithmic-time performance for all the dictionary operations in the worst casehowevert has height nin which case it would look and feel like an ordered list implementation of dictionary such worst-case configuration arisesfor exampleif we insert series of entries with keys in increasing or decreasing order (see figure figure example of binary search tree with linear heightobtained by inserting entries with keys in increasing order the performance of dictionary implemented with binary search tree is summarized in the following proposition and in table proposition binary search tree with height for key-value entries uses (nspace and executes the dictionary adt operations with the following running times operationssize andisempty each take ( time operationsfindinsertandremove each take (htime the operationfindall takes ( stimewhere is the size of the collection returned table running times of the main methods of dictionary realized by binary search tree we denote the current height of the tree with and the size of the collection returned by findall with the space usage is ( )where is the number of entries stored in the dictionary