section so that the union and find operations each use at most (logn/logbdisk transfers - suppose we are given sequence of elements with integer keys such that some elements in are colored "blueand some elements in are colored "red in additionsay that red element pairs with blue element if they have the same key value describe an efficient externalmemory algorithm for finding all the red-blue pairs in how many disk transfers does your algorithm performc- consider the page caching problem where the memory cache can hold pagesand we are given sequence of requests taken from pool of possible pages describe the optimal strategy for the offline algorithm and show that it causes at most / page misses in totalstarting from an empty cache - consider the page caching strategy based on the least frequently used (lfurulewhere the page in the cache that has been accessed the least often is the one that is evicted when new page is requested if there are tieslfu evicts the least frequently used page that has been in the cache the longest show that there is sequence of requests that causes lfu to miss (ntimes for cache of pageswhereas the optimal algorithm will miss only (mtimes - suppose that instead of having the node+search function ( in an order- -tree twe have (dlogd what does the asymptotic running time of performing search in now becomec- describe an external-memory algorithm that determines (using ( /btransferswhether list of integers contains value occurring more than / times projects - write java class that implements all the methods of the ordered dictionary adt by means of an (abtreewhere and are integer constants passed as parameters to constructor