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Double Insertion Sort is a variation on Insertion Sort that works from the middle of the array out. After each iteration, some middle portion of the array is sorted. On the next iteration, take the two adjacent elements to the sorted portion of the array. If they are out of order with respect to each other, then swap them. Now, push the left element toward the right in the array so long as it is greater than the element to its right, and push the right element toward the left in the array so long as it is less than the element to its left. The algorithm begins by processing the middle two elements of the array if the array length is even. If it is odd, then skip processing the middle item and begin with processing the elements to its immediate left and right. a) Find the worst-case cost (in terms of number of comparisons) of Double Insertion Sort and compare it to the worst-case cost of the standard Insertion Sort. b) ( Implement Double Insertion Sort. Make sure you handle properly both cases when the array length is odd and when it is even. ) Compare its running time in practice against standard Insertion Sort. For this purpose, measure the running time in milliseconds of the 2 implementations for N= 10000, 20000, 40000, 80000 and 160000. For each data size N, generate a random list of N random integers ranging from 1 to 107 and use the same list to measure the running time of the 2 implementations. Take the average of 3 measurements and present the results in the following table: Pivot N-10000 N-20000 N-40000 N-80000 N=160000 Insertion sort Double insertion sort d) (- Plot the obtained running time results of the two algorithms in the same chart.

Double Insertion Sort is a variation on Insertion Sort that works from the middle of the array out. After each iteration, some middle portion of the array is sorted. On the next iteration, take the two adjacent elements to the sorted portion of the array. If they are out of order with respect to each other, then swap them. Now, push the left element toward the right in the array so long as it is greater than the element to its right, and push the right element toward the left in the array so long as it is less than the element to its left. The algorithm begins by processing the middle two elements of the array if the array length is even. If it is odd, then skip processing the middle item and begin with processing the elements to its immediate left and right. a) Find the worst-case cost (in terms of number of comparisons) of Double Insertion Sort and compare it to the worst-case cost of the standard Insertion Sort. b) ( Implement Double Insertion Sort. Make sure you handle properly both cases when the array length is odd and when it is even. ) Compare its running time in practice against standard Insertion Sort. For this purpose, measure the running time in milliseconds of the 2 implementations for N= 10000, 20000, 40000, 80000 and 160000. For each data size N, generate a random list of N random integers ranging from 1 to 107 and use the same list to measure the running time of the 2 implementations. Take the average of 3 measurements and present the results in the following table: Pivot N-10000 N-20000 N-40000 N-80000 N=160000 Insertion sort Double insertion sort d) (- Plot the obtained running time results of the two algorithms in the same chart.

Database System Concepts
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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Subject: Data structure 

Double Insertion Sort is a variation on Insertion Sort that works from the middle of the array out. After each iteration, some middle portion of the array is sorted. On the next iteration, take the two adjacent elements to the sorted portion of the array. If they are out of order with respect to each other, then swap them. Now, push the left element toward the right in the array so long as it is greater than the element to its right, and push the right element toward the left in the array so long as it is less than the element to its left. The algorithm begins by processing the middle two elements of the array if the array length is even. If it is odd, then skip processing the middle item and begin with processing the elements to its immediate left and right. a) Find the worst-case cost (in terms of number of comparisons) of Double Insertion Sort and compare it to the worst-case cost of the standard Insertion Sort. b) ( Implement Double Insertion Sort. Make sure you handle properly both cases when the array length is odd and when it is even. ») Compare its running time in practice against standard Insertion Sort. For this purpose, measure the running time in milliseconds of the 2 implementations for N=10000, 20000, 40000, 80000 and 160000. For each data size N, generate a random list of N random integers ranging from 1 to 10' and use the same list to measure the running time of the 2 implementations. Take the average of 3 measurements and present the results in the following table: Pivot N-10000 N-20000 | N-40000 N-80000 N=160000 Insertion sort Double insertion sort d) (- Plot the obtained running time results of the two algorithms in the same chart.
Transcribed Image Text:Double Insertion Sort is a variation on Insertion Sort that works from the middle of the array out. After each iteration, some middle portion of the array is sorted. On the next iteration, take the two adjacent elements to the sorted portion of the array. If they are out of order with respect to each other, then swap them. Now, push the left element toward the right in the array so long as it is greater than the element to its right, and push the right element toward the left in the array so long as it is less than the element to its left. The algorithm begins by processing the middle two elements of the array if the array length is even. If it is odd, then skip processing the middle item and begin with processing the elements to its immediate left and right. a) Find the worst-case cost (in terms of number of comparisons) of Double Insertion Sort and compare it to the worst-case cost of the standard Insertion Sort. b) ( Implement Double Insertion Sort. Make sure you handle properly both cases when the array length is odd and when it is even. ») Compare its running time in practice against standard Insertion Sort. For this purpose, measure the running time in milliseconds of the 2 implementations for N=10000, 20000, 40000, 80000 and 160000. For each data size N, generate a random list of N random integers ranging from 1 to 10' and use the same list to measure the running time of the 2 implementations. Take the average of 3 measurements and present the results in the following table: Pivot N-10000 N-20000 | N-40000 N-80000 N=160000 Insertion sort Double insertion sort d) (- Plot the obtained running time results of the two algorithms in the same chart.
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