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Tài liệu Thuật toán Algorithms (Phần 17) pptx

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SELECTION AND MERGING 153 Exercises 1. For N = 1000, empirically determine: the value of k for which the Quick- sort-based partitioning procedure be :omes faster than using heaps to find the Ic th smallest element in a randc’m file. 2. Describe how you would rearrange an array of 4N elements so that the N smallest keys fall in the first N Isositions, the next N keys fall in the next N positions, the next N in the next N positions, and the N largest in the last N positions. 3. Show the recursive calls made when select is used to find the median of the keys EASYQUESTION. 4. Write a program to rearrange a file so that all the elements with keys equal to the median are in place, with smaller elements to the left and larger elements to the right. 5. What method would be best for an application that requires selection of the lath largest element (for various arbitrary Ic) a large number of times on the same file? 6. True or false: the running time of mergesort does not depend on the order of the keys in the input file. Explair. your answer. 7. What is the smallest number of steps mergesort could use (to within a constant factor)? 8. Implement a bottom-up non-recursive mergesort that uses two arrays instead of linked lists. 9. Show the contents of the linked lists l’assed as arguments to each call when the recursive mergesort is used to sort the keys EASY Q U E S T IO N. 10. Show the contents of the linked l&t at each iteration when the non- recursive mergesort is used to sort the keys EASY QUE S TIO N. . that we’ve been studying). There are two major factors which make external algorithms quite differ- ent from those we’ve seen until now. l’irst, the cost. the “s:istems” aspect of the problem is cer- tainly as important as the algorithms .ispect. Both areas must be carefully considered if an effective

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