linked lists (as noted in the introductionqualified instructors may obtain completed solutions to the programming projects on the publisher' web site implement priority queue based on sorted linked list the remove operation on the priority queue should remove the item with the smallest key implement deque based on doubly linked list (see programming project in the preceding the user should be able to carry out the normal operations on the deque circular list is linked list in which the last link points back to the first link there are many ways to design circular list sometimes there is pointer to the "startof the list howeverthis makes the list less like real circle and more like an ordinary list that has its end attached to its beginning make class for singly linked circular list that has no end and no beginning the only access to the list is single referencecurrentthat can point to any link on the list this reference can move around the list as needed (see programming project for situation in which such circular list is ideally suited your list should handle insertionsearchingand deletion you may find it convenient if these operations take place one link downstream of the link pointed to by current (because the upstream link is singly linkedyou can' get at it without going all the way around the circle you should also be able to display the list (although you'll need to break the circle at some arbitrary point to print it on the screena step(method that moves current along to the next link might come in handy too implement stack class based on the circular list of programming project this exercise is not too difficult (howeverimplementing queue can be harderunless you make the circular list doubly linked the josephus problem is famous mathematical puzzle that goes back to ancient times there are many stories to go with the puzzle one is that josephus was one of group of jews who were about to be captured by the romans rather than be enslavedthey chose to commit suicide they arranged themselves in circle andstarting at certain personstarted counting off around the circle every nth person had to leave the circle and commit suicide josephus decided he didn' want to dieso he arranged the rules so he would be the last person left if there were (say peopleand he was the seventh person from the start of the circlewhat number should he tell them to use for counting offthe problem is made much more complicated because the circle shrinks as the counting continues create an application that uses circular linked list (like that in programming project to model this problem inputs are the number of people in the circlethe number used for counting offand the number of the person where