Merge-Sort and Quick-Sort Algorithms Analysis, Slides of Design and Analysis of Algorithms

Download Merge-Sort and Quick-Sort Algorithms Analysis and more Slides Design and Analysis of Algorithms in PDF only on Docsity! 26 3 7 5 1 8 4 6 2 Merge-Sort(A, 1, 1) , base case A: Merge-Sort(A, 0, 7) Docsity.com 27 3 7 5 1 8 4 6 2 Merge-Sort(A, 1, 1), return A: Merge-Sort(A, 0, 7) Docsity.com 30 3 7 5 1 8 4 2 6 Merge-Sort(A, 2, 3) , divide A: Merge-Sort(A, 0, 7) Docsity.com 31 3 7 5 1 4 2 6 8 Merge-Sort(A, 2, 2), base case A: Merge-Sort(A, 0, 7) Docsity.com 32 3 7 5 1 4 2 6 8 Merge-Sort(A, 2, 2), return A: Merge-Sort(A, 0, 7) Docsity.com 35 3 7 5 1 2 6 4 8 Merge(A, 2, 2, 3) A: Merge-Sort(A, 0, 7) Docsity.com 36 3 7 5 1 2 6 4 8 Merge-Sort(A, 2, 3), return A: Merge-Sort(A, 0, 7) Docsity.com 37 3 7 5 1 2 4 6 8 Merge(A, 0, 1, 3) A: Merge-Sort(A, 0, 7) Docsity.com 40 1 3 5 7 2 4 6 8 A: Merge (A, 4, 5, 7) Merge-Sort(A, 0, 7) Docsity.com 41 1 3 5 7 2 4 6 8 Merge-Sort(A, 4, 7), return A: Merge-Sort(A, 0, 7) Docsity.com 42 1 2 3 4 5 6 7 8 Merge(A, 0, 3, 7) A: Merge-Sort(A, 0, 7) Merge-Sort(A, 0, 7), done! Docsity.com 45 Overview  Divide and Conquer  Merge Sort  Quick Sort Docsity.com 46 Quick Sort  Divide:  Pick any element p as the pivot, e.g, the first element  Partition the remaining elements into FirstPart, which contains all elements < p SecondPart, which contains all elements ≥ p  Recursively sort the FirstPart and SecondPart  Combine: no work is necessary since sorting is done in place Docsity.com 47 Quick Sort x < p p p ≤ x Partition FirstPart SecondPart p pivot A: Recursive call x < p p p ≤ x Sorted FirstPart Sorted SecondPart Sorted Docsity.com