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Homework (Heap Problems) [1/1] |

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+ Read Algorithms through the end of 2.5 (you can skip 2.2,2.3). + Do the following eight problems on paper. Be sure to do the starred ones. + 2.4.2 Criticize the following idea: To implement find the maximum in constant time, why not use a stack or a queue, but keep track of the maximum value inserted so far, then return that value for find the maximum? (Don't confuse find-the-max and remove-the-max) + 2.4.4 Is an array that is sorted in decreasing order a max-oriented heap? + 2.4.5 Give the heap that results when the keys E A S Y Q U E S T I O N are inserted in that order into an initially empty max-oriented heap. + 2.4.9* Draw all of the different heaps that can be made from the five keys A B C D E, then draw all of the different heaps that can be made from the five keys A A A B B. (Draw min heaps.) + 2.4.11 Suppose that your application will have a huge number of insert operations, but only a few remove the maximum operations. Which priority-queue implementation do you think would be most effective: heap, unordered array, or ordered array? (Also say why. Don't confuse find-the-max and remove-the-max) + 2.4.12 Suppose that your application will have a huge number of find the maximum operations, but a relatively small number of insert and remove the maximum operations. Which priority-queue implementation do you think would be most effective: heap, unordered array, or ordered array? (Also say why. Don't confuse find-the-max and remove-the-max) + 2.4.15* Design a linear-time certification algorithm to check whether an array pq[] is a min-oriented heap. (The method MinPQ.isMinHeap does this recursively. What would an iterative solution be? You should make sure you understand this and can do it without looking at MinPQ.isMinHeap.) + 2.4.27* Find the minimum. Add a min() method to MaxPQ. Your implementation should use constant time and constant extra space. (Argue that your solution is constant time/space.)

Revised: 2008/03/17 13:01