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Exercise 4 (Sorting Methods) Trace the execution of the selection sort, insertion sort, and mergesort algorithms when executed on the following array of integers: {1, 29, 14, 15, 94} For selection and insertion sort, show how the array will look like after each iteration of the outer loop. For mergesort, show how elements will be split into smaller arrays and then merged into bigger, sorted arrays. Explanation of Sorting Sorting is the task of arranging a group of items into a defined order based on particular criteria. It is assumed, just like with Binary Search, that pairs of elements can be compared to find if one should precede another. This defines the order in which the sorting should be done. Sorting methods that only rely on this assumption are called comparison-based sorting methods. Among those, there are two main groups of sorting algorithms, and they differ by whether they sort by exchanging adjacent elements. If they do, they are called sequential sorting methods. Those algorithms have time complexity that is at least quadratic. These include selection sort and insertion sort. To sort faster, we must use a non-sequential sorting method. The best example is the mergesort algorithm, which has a time complexity of O(N log N). Selection Sort Pseudocode FOR i=0.. (next to last index): LET X = smallest element with index >= i SWAP X with element at index i Note: to find the "smallest element with index >=i", we must use another (inner) loop to iterate through all indexes from i to the last index. Insertion Sort Pseudocode FOR i=1..(last index): LET X = i'th element FOR j=i..0: IF j-1'th element > x: COPY j-1'th element value to j'th index ELSE: COPY x into j'th element BREAK from inner loop Mergesort Pseudocode IF array has only one element, RETURN array ELSE: MERGESORT left half MERGESORT right half MERGE both halves into one sorted array Note: you can do the merging by successively going through all array indexes for both arrays (left and right halves) and picking the smallest element from either array to be the next element in the merged array. Each time an element is picked, the current index from its array is incremented. This allows for completing the merging in linear time.

Exercise 4 (Sorting Methods) Trace the execution of the selection sort, insertion sort, and mergesort algorithms when executed on the following array of integers: {1, 29, 14, 15, 94} For selection and insertion sort, show how the array will look like after each iteration of the outer loop. For mergesort, show how elements will be split into smaller arrays and then merged into bigger, sorted arrays. Explanation of Sorting Sorting is the task of arranging a group of items into a defined order based on particular criteria. It is assumed, just like with Binary Search, that pairs of elements can be compared to find if one should precede another. This defines the order in which the sorting should be done. Sorting methods that only rely on this assumption are called comparison-based sorting methods. Among those, there are two main groups of sorting algorithms, and they differ by whether they sort by exchanging adjacent elements. If they do, they are called sequential sorting methods. Those algorithms have time complexity that is at least quadratic. These include selection sort and insertion sort. To sort faster, we must use a non-sequential sorting method. The best example is the mergesort algorithm, which has a time complexity of O(N log N). Selection Sort Pseudocode FOR i=0.. (next to last index): LET X = smallest element with index >= i SWAP X with element at index i Note: to find the "smallest element with index >=i", we must use another (inner) loop to iterate through all indexes from i to the last index. Insertion Sort Pseudocode FOR i=1..(last index): LET X = i'th element FOR j=i..0: IF j-1'th element > x: COPY j-1'th element value to j'th index ELSE: COPY x into j'th element BREAK from inner loop Mergesort Pseudocode IF array has only one element, RETURN array ELSE: MERGESORT left half MERGESORT right half MERGE both halves into one sorted array Note: you can do the merging by successively going through all array indexes for both arrays (left and right halves) and picking the smallest element from either array to be the next element in the merged array. Each time an element is picked, the current index from its array is incremented. This allows for completing the merging in linear time.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Exercise 4 (Sorting Methods) Trace the execution of the selection sort, insertion sort, and mergesort algorithms when executed on the following array of integers: {1, 29, 14, 15, 94} For selection and insertion sort, show how the array will look like after each iteration of the outer loop. For mergesort, show how elements will be split into smaller arrays and then merged into bigger, sorted arrays. Explanation of Sorting Sorting is the task of arranging a group of items into a defined order based on particular criteria. It is assumed, just like with Binary Search, that pairs of elements can be compared to find if one should precede another. This defines the order in which the sorting should be done. Sorting methods that only rely on this assumption are called comparison-based sorting methods. Among those, there are two main groups of sorting algorithms, and they differ by whether they sort by exchanging adjacent elements. If they do, they are called sequential sorting methods. Those algorithms have time complexity that is at least quadratic. These include selection sort and insertion sort. To sort faster, we must use a non-sequential sorting method. The best example is the mergesort algorithm, which has a time complexity of O(N log N). Selection Sort Pseudocode FOR i=0..(next to last index): LET X = smallest element with index >= i SWAP X with element at index i Note: to find the "smallest element with index >= i", we must use another (inner) loop to iterate through all indexes from i to the last index. Insertion Sort Pseudocode FOR i=1..(1last index): LET X = i'th element FOR j=i..0: IF j-1'th element > x: CÓPY j-1'th element value to j’th index ELSE: COPY x into j'th element BREAK from inner loop Mergesort Pseudocode IF array has only one element, RETURN array ELSE: MERGESORT left half MERGESORT right half MERGE both halves into one sorted array Note: you can do the merging by successively going through all array indexes for both arrays (left and right halves) and picking the smallest element from either array to be the next element in the merged array. Each time an element is picked, the current index from its array is incremented. This allows for completing the merging in linear time.
Transcribed Image Text:Exercise 4 (Sorting Methods) Trace the execution of the selection sort, insertion sort, and mergesort algorithms when executed on the following array of integers: {1, 29, 14, 15, 94} For selection and insertion sort, show how the array will look like after each iteration of the outer loop. For mergesort, show how elements will be split into smaller arrays and then merged into bigger, sorted arrays. Explanation of Sorting Sorting is the task of arranging a group of items into a defined order based on particular criteria. It is assumed, just like with Binary Search, that pairs of elements can be compared to find if one should precede another. This defines the order in which the sorting should be done. Sorting methods that only rely on this assumption are called comparison-based sorting methods. Among those, there are two main groups of sorting algorithms, and they differ by whether they sort by exchanging adjacent elements. If they do, they are called sequential sorting methods. Those algorithms have time complexity that is at least quadratic. These include selection sort and insertion sort. To sort faster, we must use a non-sequential sorting method. The best example is the mergesort algorithm, which has a time complexity of O(N log N). Selection Sort Pseudocode FOR i=0..(next to last index): LET X = smallest element with index >= i SWAP X with element at index i Note: to find the "smallest element with index >= i", we must use another (inner) loop to iterate through all indexes from i to the last index. Insertion Sort Pseudocode FOR i=1..(1last index): LET X = i'th element FOR j=i..0: IF j-1'th element > x: CÓPY j-1'th element value to j’th index ELSE: COPY x into j'th element BREAK from inner loop Mergesort Pseudocode IF array has only one element, RETURN array ELSE: MERGESORT left half MERGESORT right half MERGE both halves into one sorted array Note: you can do the merging by successively going through all array indexes for both arrays (left and right halves) and picking the smallest element from either array to be the next element in the merged array. Each time an element is picked, the current index from its array is incremented. This allows for completing the merging in linear time.
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