COP 3530 Data Structures Sorting Dr Ron Eaglin
![COP 3530 - Data Structures Sorting Dr. Ron Eaglin COP 3530 - Data Structures Sorting Dr. Ron Eaglin](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-1.jpg)
![Objectives • Understand key elements of sorting algorithms • Select appropriate sorting algorithm for Objectives • Understand key elements of sorting algorithms • Select appropriate sorting algorithm for](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-2.jpg)
![Sorting • Systematically arrange items into groups or in a specific order. • A Sorting • Systematically arrange items into groups or in a specific order. • A](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-3.jpg)
![Evaluating Sorting • Computational Complexity (as expressed by Big O) • Computational Complexity of Evaluating Sorting • Computational Complexity (as expressed by Big O) • Computational Complexity of](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-4.jpg)
![Sorting Stability • IF two items to be sorted are equivalent, their relative order Sorting Stability • IF two items to be sorted are equivalent, their relative order](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-5.jpg)
![Algorithms used in sorting - Swap function swap(a, b) { var temp = a; Algorithms used in sorting - Swap function swap(a, b) { var temp = a;](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-6.jpg)
![Singly Linked List Sort A B B A NULL a. next = b. next; Singly Linked List Sort A B B A NULL a. next = b. next;](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-7.jpg)
![Single Linked List Swap A A B C Swap B and C C B Single Linked List Swap A A B C Swap B and C C B](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-8.jpg)
![Singly Linked List Swap A A B C Swap B and C C B Singly Linked List Swap A A B C Swap B and C C B](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-9.jpg)
![A A Swap B and C B C D C A. next = B A A Swap B and C B C D C A. next = B](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-10.jpg)
![A B C D A. next = B B. next = C C. next A B C D A. next = B B. next = C C. next](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-11.jpg)
![Swapping • Alternately the contents of the node can be swapped. • Implementation for Swapping • Alternately the contents of the node can be swapped. • Implementation for](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-12.jpg)
![Swapping Contents function swap( a, b) { var c = a. value; a. value Swapping Contents function swap( a, b) { var c = a. value; a. value](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-13.jpg)
![Bubble Sort • Simplest of sorting algorithms • O(n^2) • Uses swap set swapped Bubble Sort • Simplest of sorting algorithms • O(n^2) • Uses swap set swapped](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-14.jpg)
![Another look at Swap A B C D E F H Suppose we want Another look at Swap A B C D E F H Suppose we want](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-15.jpg)
![Quick. Sort Algorithm • Average Case Complexity O(n log n) and In-Place algorithm • Quick. Sort Algorithm • Average Case Complexity O(n log n) and In-Place algorithm •](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-16.jpg)
![Merge Sort • O( n log n) worst case complexity, NOT In-place algorithm • Merge Sort • O( n log n) worst case complexity, NOT In-place algorithm •](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-17.jpg)
![Merge Sort Example List: Sublists: 3– 4– 2– 1– 7– 5– 8– 9– 0– Merge Sort Example List: Sublists: 3– 4– 2– 1– 7– 5– 8– 9– 0–](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-18.jpg)
![Efficiency and Performance • Algorithm Worst Case and Average performance is important • Efficiency Efficiency and Performance • Algorithm Worst Case and Average performance is important • Efficiency](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-19.jpg)
![Sorting Algorithms • Full outline on Wikipedia • https: //en. wikipedia. org/wiki/Sorting_algorithm • Best, Sorting Algorithms • Full outline on Wikipedia • https: //en. wikipedia. org/wiki/Sorting_algorithm • Best,](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-20.jpg)
![Objectives • Understand key elements of sorting algorithms • Select appropriate sorting algorithm for Objectives • Understand key elements of sorting algorithms • Select appropriate sorting algorithm for](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-21.jpg)
- Slides: 21
![COP 3530 Data Structures Sorting Dr Ron Eaglin COP 3530 - Data Structures Sorting Dr. Ron Eaglin](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-1.jpg)
COP 3530 - Data Structures Sorting Dr. Ron Eaglin
![Objectives Understand key elements of sorting algorithms Select appropriate sorting algorithm for Objectives • Understand key elements of sorting algorithms • Select appropriate sorting algorithm for](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-2.jpg)
Objectives • Understand key elements of sorting algorithms • Select appropriate sorting algorithm for situation • Apply sorting algorithms to data structures
![Sorting Systematically arrange items into groups or in a specific order A Sorting • Systematically arrange items into groups or in a specific order. • A](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-3.jpg)
Sorting • Systematically arrange items into groups or in a specific order. • A sorting algorithm puts elements in a list in a specific order • Some algorithms are old, but newer algorithms have been introduced (Timsort, 2002) (Library Sort, 2006)
![Evaluating Sorting Computational Complexity as expressed by Big O Computational Complexity of Evaluating Sorting • Computational Complexity (as expressed by Big O) • Computational Complexity of](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-4.jpg)
Evaluating Sorting • Computational Complexity (as expressed by Big O) • Computational Complexity of swaps • Memory use • Stability • Comparison operators
![Sorting Stability IF two items to be sorted are equivalent their relative order Sorting Stability • IF two items to be sorted are equivalent, their relative order](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-5.jpg)
Sorting Stability • IF two items to be sorted are equivalent, their relative order will be preserved. • Not a problem if all items are unique • Sometimes a secondary comparison is used as a tie-breaker
![Algorithms used in sorting Swap function swapa b var temp a Algorithms used in sorting - Swap function swap(a, b) { var temp = a;](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-6.jpg)
Algorithms used in sorting - Swap function swap(a, b) { var temp = a; a = b; b = temp; } Swaps actual variables
![Singly Linked List Sort A B B A NULL a next b next Singly Linked List Sort A B B A NULL a. next = b. next;](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-7.jpg)
Singly Linked List Sort A B B A NULL a. next = b. next; b. next = a;
![Single Linked List Swap A A B C Swap B and C C B Single Linked List Swap A A B C Swap B and C C B](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-8.jpg)
Single Linked List Swap A A B C Swap B and C C B NULL var temp = a. next; // Node B a. next = b. next; // Node C b. next = c. next; // NULL c. next = temp; // Node B
![Singly Linked List Swap A A B C Swap B and C C B Singly Linked List Swap A A B C Swap B and C C B](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-9.jpg)
Singly Linked List Swap A A B C Swap B and C C B NULL function swap(a) { var b = a. next; var c = a. next; var temp = a. next; // Node B a. next = b. next; // Node C b. next = c. next; // NULL c. next = temp; // Node B } Don’t forget to check to see if next is not null
![A A Swap B and C B C D C A next B A A Swap B and C B C D C A. next = B](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-10.jpg)
A A Swap B and C B C D C A. next = B B. next = C C. next = D B D A. next = C B. next = D C. next = B
![A B C D A next B B next C C next A B C D A. next = B B. next = C C. next](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-11.jpg)
A B C D A. next = B B. next = C C. next = D A. next = C B. next = D C. next = B function swap(A) { var B= A. next; var C = B. next; var D = C. next; A. next = C; B. next = D; C. next = B; } Can be done many ways – simplest conceptual implementation A C B D
![Swapping Alternately the contents of the node can be swapped Implementation for Swapping • Alternately the contents of the node can be swapped. • Implementation for](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-12.jpg)
Swapping • Alternately the contents of the node can be swapped. • Implementation for singly linked list, also doubly linked lists or other architectures. • Swap is key to some algorithms.
![Swapping Contents function swap a b var c a value a value Swapping Contents function swap( a, b) { var c = a. value; a. value](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-13.jpg)
Swapping Contents function swap( a, b) { var c = a. value; a. value = b. value; b. value = c; } Much simpler conceptually than switching pointers – but… if other properties are attached to node – will be left behind.
![Bubble Sort Simplest of sorting algorithms On2 Uses swap set swapped Bubble Sort • Simplest of sorting algorithms • O(n^2) • Uses swap set swapped](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-14.jpg)
Bubble Sort • Simplest of sorting algorithms • O(n^2) • Uses swap set swapped Boolean to false iterate through list if node. value > node. next. value swap nodes set swapped Boolean to true Repeat until no swaps made
![Another look at Swap A B C D E F H Suppose we want Another look at Swap A B C D E F H Suppose we want](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-15.jpg)
Another look at Swap A B C D E F H Suppose we want to swap B and F A B C D E F H We would need to change pointers a. next and f. next We need a. next, b, e. next, and f to make the swap efficiently
![Quick Sort Algorithm Average Case Complexity On log n and InPlace algorithm Quick. Sort Algorithm • Average Case Complexity O(n log n) and In-Place algorithm •](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-16.jpg)
Quick. Sort Algorithm • Average Case Complexity O(n log n) and In-Place algorithm • Steps • 1. Pick a Pivot from the array • 2. Rearrange array so all elements < pivot are before, all elements > are after • 3. Re-apply steps 1 and 2 recursively on the sub-arrays. • Plenty of tutorials online – follow step-by-step
![Merge Sort O n log n worst case complexity NOT Inplace algorithm Merge Sort • O( n log n) worst case complexity, NOT In-place algorithm •](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-17.jpg)
Merge Sort • O( n log n) worst case complexity, NOT In-place algorithm • Steps • 1. Divide the unsorted list into n sublists • 2. Merge sorted sublists into new sorted sublists • Relies on efficient Merge algorithm
![Merge Sort Example List Sublists 3 4 2 1 7 5 8 9 0 Merge Sort Example List: Sublists: 3– 4– 2– 1– 7– 5– 8– 9– 0–](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-18.jpg)
Merge Sort Example List: Sublists: 3– 4– 2– 1– 7– 5– 8– 9– 0– 6 3– 4 2 1– 7 5– 8– 9 0– 6 Merge: 2– 3– 4 Merge: 1– 2– 3– 4– 5– 7– 8– 9 Merge: 0– 1– 2– 3– 4– 5– 6– 7– 8– 9 1– 5– 7– 8– 9 0– 6
![Efficiency and Performance Algorithm Worst Case and Average performance is important Efficiency Efficiency and Performance • Algorithm Worst Case and Average performance is important • Efficiency](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-19.jpg)
Efficiency and Performance • Algorithm Worst Case and Average performance is important • Efficiency of sub-algorithms are important (swap, merge) • Differences for different structures
![Sorting Algorithms Full outline on Wikipedia https en wikipedia orgwikiSortingalgorithm Best Sorting Algorithms • Full outline on Wikipedia • https: //en. wikipedia. org/wiki/Sorting_algorithm • Best,](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-20.jpg)
Sorting Algorithms • Full outline on Wikipedia • https: //en. wikipedia. org/wiki/Sorting_algorithm • Best, average, and worst case complexity • Memory requirements • Stable • Limitations for various structures
![Objectives Understand key elements of sorting algorithms Select appropriate sorting algorithm for Objectives • Understand key elements of sorting algorithms • Select appropriate sorting algorithm for](https://slidetodoc.com/presentation_image_h/80babf41d56a4bdba34bbab280205f3b/image-21.jpg)
Objectives • Understand key elements of sorting algorithms • Select appropriate sorting algorithm for situation • Apply sorting algorithms to data structures
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