An steady sorting algorithm is one in which the relative order of all identical elements (or keys) is the same in the output as it was in the input. For example, a steady sorting of array [1, 3, 6, 1', 4, 6', 4'] gives [1, 1', 3, 4, 4', 6, 6']. a) Indicate whether heap sort is stable or not. You need to justify your answer via a counter-example or a proof. b) In Radix sort, we iteratively and digit by digit (often starting from the least significant digit, moving towards most significant digit). In the i'th iteration, a steady sorting method A is used to sort items based on their i'th digit; given that the A is steady, at the end of the i'th iteration, the numbers will be sorted with respect to their rightmost i digit. Here is an example: 123 435 396 45 257 394 246 581 763 sort by the rightmost digit 581 123 763 394 435 045 396 246 257 →sort by the second digit 123 435 045 246 257 763 581 394 396 →sort by the third digit 045 123 246 257 394 396 435 581 763 Note that if a linear-time stable sorting algorithm is used as A, the running time of Radix Sort will be (n x b). Apply Radix Sort to sort the following input. Show your work. [624, 238, 180, 384, 1006, 446, 164, 1, 184]

An steady sorting algorithm is one in which the relative order of all identical elements (or keys) is the same in the output as it was in the input. For example, a steady sorting of array [1, 3, 6, 1', 4, 6', 4'] gives [1, 1', 3, 4, 4', 6, 6']. a) Indicate whether heap sort is stable or not. You need to justify your answer via a counter-example or a proof. b) In Radix sort, we iteratively and digit by digit (often starting from the least significant digit, moving towards most significant digit). In the i'th iteration, a steady sorting method A is used to sort items based on their i'th digit; given that the A is steady, at the end of the i'th iteration, the numbers will be sorted with respect to their rightmost i digit. Here is an example: 123 435 396 45 257 394 246 581 763 sort by the rightmost digit 581 123 763 394 435 045 396 246 257 →sort by the second digit 123 435 045 246 257 763 581 394 396 →sort by the third digit 045 123 246 257 394 396 435 581 763 Note that if a linear-time stable sorting algorithm is used as A, the running time of Radix Sort will be (n x b). Apply Radix Sort to sort the following input. Show your work. [624, 238, 180, 384, 1006, 446, 164, 1, 184]

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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Question

An steady sorting algorithm is one in which the relative order of all identical elements (or
keys) is the same in the output as it was in the input. For example, a steady sorting of array
[1, 3, 6, 1', 4, 6', 4′] gives [1, 1', 3, 4, 4', 6, 6'].
a) Indicate whether heap sort is stable or not. You need to justify your answer via a
counter-example or a proof.
b) In Radix sort, we iteratively and digit by digit (often starting from the least significant
digit, moving towards most significant digit). In the i'th iteration, a steady sorting
method A is used to sort items based on their i'th digit; given that the A is steady, at
the end of the i'th iteration, the numbers will be sorted with respect to their rightmost
i digit. Here is an example:
123
435
396
45
257
394
246
581
763
sort by the
rightmost digit
581
123
763
394
435
045
396
246
257
→ sort by the
second digit
123
435
045
246
257
763
581
394
396
→ sort by the
third digit
045
123
246
257
394
396
435
581
763
Note that if a linear-time stable sorting algorithm is used as A, the running time of
Radix Sort will be (n x b).
Apply Radix Sort to sort the following input. Show your work.
[624, 238, 180, 384, 1006, 446, 164, 1, 184]

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