exercises for help with exercisesplease visit the sitewww wiley com/college/goodrich reinforcement - how long would it take to remove the log nsmallest elements from heap that contains entriesusing the remove min operationr- suppose you label each position of binary tree with key equal to its preorder rank under what circumstances is heapr- what does each remove min call return within the following sequence of priority queue adt methodsadd( , )add( , )add( , )add( , )remove min)add( , )add( , )remove min)remove min)add( , )remove min)add( , )remove min)remove min) - an airport is developing computer simulation of air-traffic control that handles events such as landings and takeoffs each event has time stamp that denotes the time when the event will occur the simulation program needs to efficiently perform the following two fundamental operationsinsert an event with given time stamp (that isadd future eventextract the event with smallest time stamp (that isdetermine the next event to processwhich data structure should be used for the above operationswhyr- the min method for the unsortedpriorityqueue class executes in (ntimeas analyzed in table give simple modification to the class so that min runs in ( time explain any necessary modifications to other methods of the class - can you adapt your solution to the previous problem to make remove min run in ( time for the unsortedpriorityqueue classexplain your answer - illustrate the execution of the selection-sort algorithm on the following input sequence( - illustrate the execution of the insertion-sort algorithm on the input sequence of the previous problem - give an example of worst-case sequence with elements for insertionsortand show that insertion-sort runs in ( time on such sequence - at which positions of heap might the third smallest key be storedr- at which positions of heap might the largest key be stored