notes task consider the following binary search treea splay this tree at each of the following keys in turndbgfadbd applications databasesa database is collection of data organized in fashion that facilitates updatingretrievingand managing the data the data can consist of anythingincludingbut not limited to namesaddressespicturesand numbers databases are commonplace and are used everyday for examplean airline reservation system might maintain database of available flightscustomersand tickets issued teacher might maintain database of student names and grades because computers excel at quickly and accurately manipulatingstoringand retrieving datadatabases are often maintained electronically using database management system database management systems are essential components of many everyday business operations database serve as foundation for accounting systemsinventory systemsmedical recordkeeping sytemsairline reservation systemsand countless other important aspects of modern businesses it is not uncommon for database to contain millions of records requiring many gigabytes of storage in order for database to be useful and usableit must support the desired operationssuch as retrieval and storagequickly because databases cannot typically be maintained entirely in memoryb-trees are often used to index the data and to provide fast access for examplesearching an unindexed and unsorted database containing key values will have worst case running time of ( )if the same data is indexed with -treethe same search operation will run in (log nto perform search for single key on set of one million keys ( , , ) linear search will require at most , , comparisons if the same data is indexed with -tree of minimum degree comparisons will be required in the worst case clearlyindexing large amounts of data can significantly improve search performance although other balanced tree structures can be useda -tree also optimizes costly disk accesses that are of concern when dealing with large data sets lovely professional university