notes write methods to implement queues in circular array with one unused entry in the array that iswe consider that the array is full when the rear is two positions before the frontwhen the rear is one position beforeit will always indicate an empty queue prove that "the binomial tree of order kbkcontains nodes extbfproof (by inductionlet nk be the number of nodes in bka binomial tree of order write menu driven demonstration program for manipulating deque of characterssimilar to the extended_queue demonstration program write the class definition and the method implementations needed to implement deque in linear array write the methods needed to implement deque in circular array consider the class deque as derived from the class queue write method to implement queueswhere the implementation does not keep count of the entries in the queue but instead uses the special conditions rear - and front to indicate an empty queue answersself assessment fores null path length zero enqueue findmin sleator and tarjan binomial tree right further readings books brian kernighan and dennis ritchiethe programming languageprentice hall burkhard moniendata structures and efficient algorithmsthomas ottmannspringer krusedata structure program designprentice hall of indianew delhi mark allen welesdata structure algorithm analysis in csecond ed addisonwesley publishing rg dromeyhow to solve it by computercambridge university press shi-kuo changdata structures and algorithmsworld scientific shi-kuo changdata structures and algorithmsworld scientific sorenson and tremblayan introduction to data structure with algorithms thomas cormencharles eleiserson ronald rivestintroduction to algorithmsprentice-hall of india pvt limitednew delhi timothy buddclassic data structures in ++addison wesley online links www en wikipedia org www web-source net www webopedia com lovely professional university