Data Structures - CSCI 102 Selection Sort Keep the list separated into sorted and unsorted sections Start by finding the minimum & put it at the front.

Data Structures - CSCI 102 Selection Sort Keep the list separated into sorted and unsorted sections Start by finding the minimum & put it at the front of the list Repeat by finding the minimum in the sublist On the i th iteration, find the i th smallest number in the list Keep going until you reach the end of the list 4 Copyright © William C. Cheng

20 Data Structures - CSCI 102 Copyright © William C. Cheng Selection Sort void selectionSort(vector & numbers) { for(int i=0; i < numbers.size()-1; i++) { //find the minimum int minValue = numbers[i] int minIndex = i; for(int j=i+1; j < numbers.size(); j++) { if(numbers[j] < minValue) { minValue = numbers[j]; minIndex = j; }}}} //move the minimum into the sorted section swap(numbers[i],numbers[minIndex]); }}}}

None, O(n ) O(n ) What’s the best case scenarios? What’s the Big O for this case? Selection Sort 22 Data Structures - CSCI 102 Copyright © William C. Cheng Selection Sort What’s the worst case scenario? What’s the Big O for this case? What’s the overall Big O? What are the problems with selection sort? 2 2 2 Still too many comparisons

Bubble Sort 23 Data Structures - CSCI 102 Copyright © William C. Cheng Bubble Sort Compare adjacent numbers If they’re out of order swap them Otherwise leave them be Loop through the list until there are no more swaps to make Smaller numbers slowly "bubble" up toward the top of the list

55 Copyright © William C. Cheng Data Structures - CSCI 102 Bubble Sort 4th pass through the list 57101619 57101619 During the 4th pass, nothing got swapped This means that the unsorted part is actually sorted No more pass needed

56 Data Structures - CSCI 102 Copyright © William C. Cheng Bubble Sort void naiveBubbleSort(vector & numbers) { for(int i=0; i < numbers.size()-1; i++) { for(int j=0; j < numbers.size()-1; j++) { if(numbers[j] > numbers[j+1]) { swap(numbers[j],numbers[j+1]); }}}}}}}} Naive Bubble Sort

BubbleSort(n) = O(n ) 2) Take advantage of the fact that on the i iteration, 58 Data Structures - CSCI 102 Copyright © William C. Cheng Bubble Sort Naive Bubble Sort What’s the Big O for this bubble sort? How could we improve this algorithm? 2 1) Make it terminate early if the sorting is already done th the last i elements are sorted

List in Reverse Order, O(n ) O(n ) 61 Data Structures - CSCI 102 Copyright © William C. Cheng Bubble Sort Better Bubble Sort What’s the overall Big O? What are the problems with bubble sort? What’s the best case scenarios? What’s the Big O for this case? What’s the worst case scenario? What’s the Big O for this case? Already Sorted, O(n) 2 2 Too much swapping! Too many comparisons!

On the i iteration, i items will be sorted Keep the list separated into sorted and unsorted sections Insertion Sort 62 Data Structures - CSCI 102 Copyright © William C. Cheng Insertion Sort Take each number in the unsorted portion of the list and shift it over into the sorted list th Keep going until you reach the end of the list "Bubble" to the left until finding the right place

82 Data Structures - CSCI 102 Insertion Sort 4th pass through the list 555555 777777 10 19 16 19 Too many swaps! Since the left part is sorted, just need to find a place to insert the value (16 in this case) Need to remember the value 16 Copyright © William C. Cheng

In Reverse Order, O(n ) O(n ) 115 Data Structures - CSCI 102 Copyright © William C. Cheng Insertion Sort What’s the best case scenarios? What’s the Big O for this case? Already Sorted, O(n) What’s the worst case scenario? What’s the Big O for this case? 2 What’s the overall Big O? What are the problems with insertion sort? 2 Still have to use nested loops

Divide 4 Data Structures - CSCI 102 Copyright © William C. Cheng Merge Sort Divide the N-element sequence to be sorted into two subsequences of N/2 elements each Conquer Sort the two subsequences recursively using merge sort Combine Merge the two sorted subsequences to produce the a single sorted result. Repeat.

20 Data Structures - CSCI 102 Merge Sort What functions will we need to do merge sort? Need a function to split list in half Need a function to merge two sorted lists Most of the work in the merge sort algorithm is done in the "merge" method Precondition: Given two sorted arrays Postcondition: Need a single, merged sorted array How does it work? Please note that Merge Sort is not an in-place sorting algorithm It uses an output buffer whose size is on the order of the size of the input buffer, i.e., O(n) extra space Merge Sort may not be practical for some applications Copyright © William C. Cheng

Data Structures - CSCI 102 Merge Sort (Merge Algorithm) 5 7 10 19 3 8 14 16 3578101416 Left Sublist Right Sublist Copy all the remaining items from the left sublist to the output 42 Copyright © William C. Cheng

Data Structures - CSCI 102 Merge Sort (Merge Algorithm) 5 7 10 19 Left Sublist 3 8 14 16 Right Sublist 357810141619 Copy all the remaining items from the left sublist to the output Done 43 Copyright © William C. Cheng

What’s the best case scenarios? What’s the Big O for this case? Merge Sort 47 Data Structures - CSCI 102 Copyright © William C. Cheng Merge Sort What’s the worst case scenario? What’s the Big O for this case? What’s the overall Big O? What are the problems with merge sort? None, O(n log n) O(n log n)

Stable Sort (generally) Maintains original ordering of equal elements The Good 48 Data Structures - CSCI 102 Copyright © William C. Cheng Merge Sort Fairly easy to code Useful for lists that must be accessed sequentially e.g. Linked Lists Sorting in place is really difficult The Bad O(N) additional space complexity if not in place There are better in-place sorts Lots of copying data

51 Data Structures - CSCI 102 Copyright © William C. Cheng Quick Sort Pick an element in the array and call it Pivot Divide Split the rest of the array into two subarrays: One array containing all numbers <= Pivot One array containing all numbers > Pivot Sort the two new arrays recursively using quick sort Conquer The arrays are sorted in place. No recombination necessary. Combine We will simply use the last element

41852637 Data Structures - CSCI 102 Quick Sort The idea behind the Divide part 1) Choose the last element in the array as the pivot It doesn’t move (until the very end) So, we will pin it where it’s at for now 53 Copyright © William C. Cheng

Data Structures - CSCI 102 Quick Sort The idea behind the Divide part 41852637 Pivot 1) Choose the last element in the array as the pivot 2) Identify all the numbers smaller than the pivot (in blue) Identify all the numbers larger than the pivot (in orange) 54 Copyright © William C. Cheng

Data Structures - CSCI 102 Quick Sort The idea behind the Divide part 41852637 Pivot 1) Choose the last element in the array as the pivot 2) Identify all the numbers smaller than the pivot (in blue) Identify all the numbers larger than the pivot (in orange) 3) Move all the numbers smaller than the pivot to the left Move all the numbers larger than the pivot to the right 55 Copyright © William C. Cheng

Data Structures - CSCI 102 Quick Sort The idea behind the Divide part 41852637 Pivot 1) Choose the last element in the array as the pivot 2) Identify all the numbers smaller than the pivot (in blue) Identify all the numbers larger than the pivot (in orange) 3) Move all the numbers smaller than the pivot to the left Move all the numbers larger than the pivot to the right 4) Move the pivot between the blue and the orange numbers 56 Copyright © William C. Cheng

57 Data Structures - CSCI 102 Quick Sort The idea behind the Divide part 41852637 final sort order Copyright © William C. Cheng Pivot 1) Choose the last element in the array as the pivot 2) Identify all the numbers smaller than the pivot (in blue) Identify all the numbers larger than the pivot (in orange) 3) Move all the numbers smaller than the pivot to the left Move all the numbers larger than the pivot to the right 4) Move the pivot between the blue and the orange numbers The pivot is now at the correct position in the

58 Data Structures - CSCI 102 Quick Sort The idea behind the Divide part 41852637 final sort order Copyright © William C. Cheng Pivot QuickSort this 1) Choose the last element in the array as the pivot 2) Identify all the numbers smaller than the pivot (in blue) Identify all the numbers larger than the pivot (in orange) 3) Move all the numbers smaller than the pivot to the left Move all the numbers larger than the pivot to the right 4) Move the pivot between the blue and the orange numbers The pivot is now at the correct position in the

Data Structures - CSCI 102 Quick Sort How to do steps (2) and (3) together? 41852637 PivotUnsorted Keep array split into 3 sections: Numbers less than or equal to the pivot (<= 4, in blue) Numbers greater than the pivot (> 4, in orange) Numbers yet to be sorted 65 Copyright © William C. Cheng

Data Structures - CSCI 102 Quick Sort How to do steps (2) and (3) together? 41852637 PivotUnsorted Keep array split into 3 sections: Numbers less than or equal to the pivot (<= 4, in blue) Numbers greater than the pivot (> 4, in orange) Numbers yet to be sorted 66 Copyright © William C. Cheng

Data Structures - CSCI 102 Quick Sort How to do steps (2) and (3) together? 41852637 PivotUnsortedLess Than Pivot Keep array split into 3 sections: Numbers less than or equal to the pivot (<= 4, in blue) Numbers greater than the pivot (> 4, in orange) Numbers yet to be sorted 67 Copyright © William C. Cheng

Data Structures - CSCI 102 Quick Sort How to do steps (2) and (3) together? 41852637 PivotUnsorted Keep array split into 3 sections: Numbers less than or equal to the pivot (<= 4, in blue) Numbers greater than the pivot (> 4, in orange) Numbers yet to be sorted 68 Copyright © William C. Cheng Less Than Pivot More Than Pivot

Data Structures - CSCI 102 Quick Sort How to do steps (2) and (3) together? 41852637 PivotUnsorted Keep array split into 3 sections: Numbers less than or equal to the pivot (<= 4, in blue) Numbers greater than the pivot (> 4, in orange) Numbers yet to be sorted 69 Copyright © William C. Cheng Less Than Pivot More Than Pivot

Data Structures - CSCI 102 Quick Sort How to do steps (2) and (3) together? 48152673 PivotLess Than Pivot More Than Pivot Note: we only swap when the number is < pivot When the number is > pivot, we just move along and did nothing 76 Copyright © William C. Cheng

Data Structures - CSCI 102 Quick Sort Step (4) 84152673 PivotLess Than Pivot More Than Pivot What if some other cell has the same value as the pivot? Does that cell belong to the blue or the orange section? 79 Copyright © William C. Cheng

Data Structures - CSCI 102 Quick Sort Step (4) 84152673 PivotLess Than Pivot More Than Pivot What if some other cell has the same value as the pivot? Does that cell belong to the blue or the orange section? The answer is: it does not matter if it is done consistently Arbitrarily, we use: blue is for numbers  pivot 80 Copyright © William C. Cheng

Sorted or reverse sorted, O(n ) O(n ), but O(n log n) on the average 1) certain inputs can be O(n ) Quick Sort 92 Data Structures - CSCI 102 Copyright © William C. Cheng Quick Sort What’s the best case scenarios? What’s the Big O for this case? What’s the worst case scenario? What’s the Big O for this case? What’s the overall Big O? What are the problems with quick sort? Every partition splits list in half, O(n log n) 2 2 2 2) slow on small lists

116 Data Structures - CSCI 102 Copyright © William C. Cheng Extra Material What do sorting algorithms sound like? http://flowingdata.com/2010/09/01/what-different- sorting-algorithms-sound-like/ http://www.math.ucla.edu/~rcompton/musical_sorting_ algorithms/musical_sorting_algorithms.html http://www.youtube.com/usccs102 CSCI 102 YouTube channel Sorting Algorithm Animations http://www.sorting-algorithms.com/

Data Structures - CSCI 102 Selection Sort Keep the list separated into sorted and unsorted sections Start by finding the minimum & put it at the front.

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Data Structures - CSCI 102 Selection Sort Keep the list separated into sorted and unsorted sections Start by finding the minimum & put it at the front.

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Presentation on theme: "Data Structures - CSCI 102 Selection Sort Keep the list separated into sorted and unsorted sections Start by finding the minimum & put it at the front."— Presentation transcript:

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