Lecture 20-Sorting Algorithms

Lecture 20-Sorting Algorithms - Comments on A5 CS1110 9...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Comments on A5 CS1110 9 November 2010 insertion sort, selection sort, quick sort Do exercises on pp. 311-312 to get familiar with concepts and develop skill. Practice in DrJava! Test your methods! A5 times min 2 median 6 mean 6.5 max 19 hours 2-3 4 5 6 7 10 11 15 18-19 number 14 26 19 34 16 12 02 01 02 Liked not having to write test cases! Needed too much help, took too long Add more methods; it did not take long Allow us to do recursive methods with loops rather than recursively. Good time drinking beer while watching the demo after I was done. 2 Recursion: Make requirements/descriptions less ambiguous, clearer; give more direction. Need optional problem with more complicated recursive solution would have been an interesting challenge, more recursive functions. They make us think! Make task 5 easier. I could not finish it. 1 I had intended here to erupt in largely incoherent rage over that wretched concept of recursion, which I came to hate like an enemy: like a sentient being who, knowing the difference between right and wrong, had purposely chosen to do me harm. However, I then figured out how it works, and it is actually quite elegant, so now I suppose I have learned something against my will. Sorting: 0 pre: b insertion sort 0 inv: b “sorted” means in ascending order n 0 post: b ? sorted i sorted ? 0 n n pre: b insertion sort 0 invariant: b ? n post: b i sorted 0 sorted n n ? for (int i= 0; i < n; i= i+1) { Push b[i] down into its sorted position in b[0..i]; } 0 i 2 4 4 6 6 7 5 0 i 2 4 4 5 6 6 7 b[0..i-1]: i elements in worst case: Iteration 0: 0 swaps Iteration 1: 1 swap Iteration 2: 2 swaps 3 … Add property to invariant: first segment contains smaller values. selection sort invariant: b 0 ≤ b[i..], sorted i ≥ b[0..i-1], ? n for (int i= 0; i < n; i= i+1) { Iteration i makes up to i swaps. In worst case, number of swaps needed is 0 + 1 + 2 + 3 + … (n-1) = (n-1)*n / 2. Called an “n-squared”, or n2, algorithm. int j= index of min of b[i..n-1]; Swap b[j] and b[i]; } i n 2 4 4 6 6 8 9 9 7 8 9 i n 2 4 4 6 6 7 9 9 8 8 9 Also an “n-squared”, or n2, algorithm. 4 Partition algorithm: Given an array b[h..k] with some value x in b[h]: h k P: b x ? /** Sort b[h..k] */ public static void qsort(int b, int h, int k) { Quicksort Swap elements of b[h..k] and store in j to truthify P: h Q: b <= x j x >= x k change: into or h k b 3 5 4 1 6 2 3 8 1 h j k b 1 2 1 3 5 4 6 3 8 h j k b 1 2 3 1 3 4 5 6 8 if (b[h..k] has fewer than 2 elements) return; To sort array of size n. e.g. 215 int j= partition(b, h, k); Worst case: n2 e.g. 230 // b[h..j–1] <= b[j] <= b[j+1..k] Average case: // Sort b[h..j–1] and b[j+1..k] n log n. e.g. 15 * 215 qsort(b, h, j–1); qsort(b, j+1, k); h pre: b x ? 215 = 32768 k x is called the pivot value. x is not a program variable; x just denotes the value initially in b[h]. 5 } j= partition(b, h, k); h post: b <= x j x k >= x 6 1 Tony Hoare, in 1968 The NATO Software Engineering Conferences homepages.cs.ncl.ac.uk/brian.randell/NATO/ 7-11 Oct 1968, Garmisch, Germany 27-31 Oct 1969, Rome, Italy Download Proceedings, which have transcripts of discussions. See photographs. Software crisis: Academic and industrial people. Admitted for first time that they did not know how to develop software efficiently and effectively. Quicksort author Tony Hoare in 2007 in Germany Thought of Quicksort in ~1958. Tried to explain it to a colleague, but couldn’t. Few months later: he saw a draft of the definition of the language Algol 58 –later turned into Algol 60. It had recursion. He went and explained Quicksort to his colleague, using recursion, who now understood it. 7 Software Engineering, 1968 Next 10-15 years: intense period of research on software engineering, language design, proving programs correct, etc. 9 Software Engineering, 1968 10 During 1970s, 1980s, intense research on How to prove programs correct, How to make it practical,  Methodology for developing algorithms The way we understand recursive methods is based on that methodology. Our understanding of and development of loops is based on that methodology. Throughout, we try to give you thought habits to help you solve programming problems for effectively The way we understand recursive methods is based on that methodology. Our understanding of and development of loops is based on that methodology. Simplicity is key: Learn not only to simplify, learn not to complify. Separate concerns, and focus on one at a time. Develop and test incrementally. Throughout, we try to give you thought habits to help you solve programming problems for effectively Don’t solve a problem until you know what the problem is (give precise and thorough specs). Learn to read a program at different levels of abstraction. 12 Mark Twain: Nothing needs changing so much as the habits of others. 11 2 ...
View Full Document

Ask a homework question - tutors are online