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# homework10 - 15-121 FALL 2009[CORTINA/REID-MILLER]HOMEWORK...

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Unformatted text preview: 15-121 FALL 2009 [CORTINA/REID-MILLER]HOMEWORK 10Program due Monday, November 30 by 11:59PMWritten problems due Wednesday, December 2 by 11:59PMELECTRONIC HANDIN AVAILABLE BY MONDAYPROBLEMS (10 pts)a.(1.5 pt) A Dateobject consists of a month (an int) and a day (an int). A hash table stores Dateobjects in an array of length 10 using the following hashing function: (month + day) % 10b.The following dates are added to an initially empty hash table in the order shown: c.1/1 (January 1) d.1/18 (January 18) e.2/10 (February 10) f. 3/31 (March 31) g.4/18 (April 18) h.6/13 (June 13) i. 9/24 (September 24) Show the resulting hash table with chaining (buckets) to resolve collisions. j. If the hash table represents a Set and duplicates are not allowed, should the chain of dates objects be maintained in unsorted or sorted order? Explain. k.(1 pt) Consider a hash function H(k) that returns an index into a hash table given a key k. You have a 50-cell hash table indexed from 0 to 49. The keys are positive integers. l. Alice proposes the following hash function: H(k) = (int)(Math.random()*50). Explain why this hash function is a poor choice. m.Bob proposes the following hash function: H(k) = the sum of the digits in key k. Explain why this hash function is a poor choice. n.(1.5 pts) Consider the min-heap below: 18/ \34 26/ \ / \60 46 52 44/ \ 88 75o.Using the min-heap above, add the value 23 and restore the heap using the algorithm discussed in lecture. For your answer, show how the resulting heap would be stored in an array. p.Using the originalmin-heap above, remove the minimum value and restore the heap using the algorithm discussed in lecture. For your answer, show how the resulting heap would be stored in an array. q.Why are binary search trees not usually stored using arrays? Explain. r.(2 pts) s.You are given the following array of integers in the order shown: 45 24 30 58 82 64 92 12 36 (corrected)Trace the algorithm for building a max-heap out of an array of elements, showing the contents of the array after each value is "inserted" into the max-heap. Use a vertical line to separate the elements in the array that are part of max-heap with those that are not. The first four steps are shown below for you along with the corresponding max-heaps. You do not have to draw the max-heaps in your answer. 45 | 24 30 58 82 64 92 12 36 4545 24 | 30 58 82 64 92 12 36 45/2445 24 30 | 58 82 64 92 12 36 45/ \24 3058 45 30 24 | 82 64 92 12 36 58/ \45 30/24t. Using your heap from part (a), trace the Heap Sort algorithm to transform the array to a sorted array in increasing order. Show the contents of the array each time the element in index 1 (the root of the heap) is moved to its...
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homework10 - 15-121 FALL 2009[CORTINA/REID-MILLER]HOMEWORK...

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