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Insertion Sort, Selection Sort, Quick Sort - Lecture Slides | CS 1110, Exams of Computer Science

Cornell UniversityComputer Science
Prof. D. Gries

Material Type: Exam; Professor: Gries; Class: Introduction to Computing Using Java; Subject: Computer Science; University: Cornell University; Term: Spring 2009;

Typology: Exams

Pre 2010

Uploaded on 08/31/2009

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1!
1!
CS1110 2 April 2009!
Sorting: 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!!
Course website
contains more
prelims and answers, "
for Prelim 1, 2, and 3!
Time spent on A5:!
min ! !2 (11 students)!
average !5.7!
median !5!
max ! !15!
15 students took 9-14 hours!
26 students took 7-8 hours!
2!
Comments on A5!
Recursion:!
Make requirements/descriptions less
ambiguous, clearer; give more direction.!
Should be a part where you can create
your own recursive functions!
Need optional problem with more
complicated recursive solution would
have been an interesting challenge, more
recursive functions.!
Do more of recursive graphics-type
problems. They really make us think!!
Make task 5 easier. I could not finish it.!
Include a clue that more than one
recursive call can be included in a
recursive method. I wasted hours
because I didn't know this.!
Clarify clear(), setPanel-
Size(). Improve graphic
rendering. Explain diff
between JFrame and JPanel!
Liked not having to
write test cases!!
Needed too much
help, took too long!
Add more methods;
it did not take long!
Give us the option to do the
recursive methods with loops
rather than recursively. !
3!
Sorting: !
?!
0 n!
pre: b! sorted !
0 n!
post: b!
sorted ? !
0 i n!insertion sort !
inv: b!
for (int i= 0; i < n; i= i+1) {!
}!
“sorted” means in ascending order!
2 4 4 6 6 7 5!
0 i!
2 4 4 5 6 6 7!
0 i!
Push b[i] down into its sorted!
position in b[0..i];!
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.!
b[0..i-1]: i elements!
in worst case:!
Iteration 0: 0 swaps!
Iteration 1: 1 swap!
Iteration 2: 2 swaps!
…!
4!
?!
0 n!
pre: b! sorted !
0 n!
post: b!
Add property to invariant: first segment contains smaller values."
≤ b[i..], sorted ≥ b[0..i-1], ? !
0 i n!
invariant: b!
selection sort!
sorted ? !
0 i n!
invariant: b!
insertion sort!
for (int i= 0; i < n; i= i+1) {!
}!
2 4 4 6 6 8 9 9 7 8 9!
i n!
2 4 4 6 6 7 9 9 8 8 9!
i n!
7"
int j= index of min of b[i..n-1];!
Swap b[j] and b[i];!
Also an “n-squared”, or n2, algorithm.!
5!
Quicksort"
/** Sort b[h..k] */!
public static void qsort(int[] b, int h, int k) {"
}!
if (b[h..k] has fewer than 2 elements)"
return;"
j= partition(b, h, k);!
<= x x >= x !
h j k!
post: b!
x ?!
h k!
pre: b!
int j= partition(b, h, k);!
// b[h..j–1] <= b[j] < b[j+1..k]"
// Sort b[h..j–1] and b[j+1..k]!
qsort(b, h, j–1);!
qsort(b, j+1, k);!
To sort array of size n. e.g. 215!
Worst case: n2 e.g. 230!
Average case:"
n log n. e.g. 15 * 215!
! ! 215 = 32768!
6!
Tony Hoare,!
in 1968 !
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.!
pf2

Partial preview of the text

Download Insertion Sort, Selection Sort, Quick Sort - Lecture Slides | CS 1110 and more Exams Computer Science in PDF only on Docsity!

1 CS1110 2 April 2009 Sorting: 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! Course website contains more prelims and answers, for Prelim 1, 2, and 3 Time spent on A5: min 2 (11 students) average 5. median 5 max 15 15 students took 9-14 hours 26 students took 7-8 hours 2 Comments on A5 Recursion : Make requirements/descriptions less ambiguous, clearer; give more direction. Should be a part where you can create your own recursive functions Need optional problem with more complicated recursive solution would have been an interesting challenge, more recursive functions. Do more of recursive graphics-type problems. They really make us think! Make task 5 easier. I could not finish it. Include a clue that more than one recursive call can be included in a recursive method. I wasted hours because I didn't know this. Clarify clear(), setPanel- Size(). Improve graphic rendering. Explain diff between JFrame and JPanel Liked not having to write test cases! Needed too much help, took too long Add more methods; it did not take long Give us the option to do the recursive methods with loops rather than recursively. 3 Sorting: ? 0 n pre: b sorted 0 n post: b sorted? insertion sort 0 i n inv: b for ( int i= 0; i < n; i= i+1) { } “sorted” means in ascending order 2 4 4 6 6 7 5 0 i 2 4 4 5 6 6 7 0 i Push b[i] down into its sorted position in b[0..i]; 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 n^2 , algorithm. b[0..i-1]: i elements in worst case: Iteration 0: 0 swaps Iteration 1: 1 swap Iteration 2: 2 swaps … 4 ? 0 n pre: b sorted 0 n post: b Add property to invariant: first segment contains smaller values. ≤ b[i..], sorted ≥ b[0..i-1],? 0 i n invariant: b selection sort sorted? 0 i n invariant: b insertion sort for ( int i= 0; i < n; i= i+1) { } 2 4 4 6 6 8 9 9 7 8 9 i n 2 4 4 6 6 7 9 9 8 8 9 i n

int j= index of min of b[i..n-1]; Swap b[j] and b[i]; Also an “n-squared”, or n^2 , algorithm. 5 /** Sort b[h..k] */^ Quicksort public static void qsort (int [] b, int h, int k ) { } if (b[h..k] has fewer than 2 elements) return; j= partition(b, h, k); <= x x >= x h j k post: b x? h k pre: b int j= partition(b, h, k); // b[h..j–1] <= b[j] < b[j+1..k] // Sort b[h..j–1] and b[j+1..k] qsort(b, h, j–1); qsort(b, j+1, k); To sort array of size n. e.g. 2^15 Worst case: n^2 e.g. 2^30 Average case: n log n. e.g. 15 * 2^15 215 = 32768 6 Tony Hoare, in 1968 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.

Viewpoint On teaching programming Reply 7 I don't like how we are forced to visualize things in Dr. Gries' way. … Entire point of programming is to be able to look at things in different ways and come up with different solutions for one problem. Forcing us to think of things in his way and testing us on it has been detrimental to my learn- ing because in my opinion it wastes time and confuses me. This course should focus more on solving problems rather than drawing folders to represent objects.

  1. A model of execution of Java programs is needed in order to bring understanding.
  2. Problem solving is the focus. The programs you wrote for A5, the algorithms we are now studying, and the way we develop them, could not have been possible without the basics that we have given you.
  3. We are giving you tools for coming up with good solutions, not just different ones. 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. 9 Software Engineering, 1968 Next 10-15 years: intense period of research of software engineering, language design, proving programs correct, etc. Software Engineering, 1968 10 During 1970s, 1980s, intense research on How to prove programs correct, How to make it practical,  Methodology for developing algorithms 11 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 Mark Twain: Nothing needs changing so much as the habits of others. 12 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 Simplicity is key: Learn not only to simplify, learn not to complify. Separate concerns, and focus on one at a time. Don’t solve a problem until you know what the problem is (give precise and thorough specs). Develop and test incrementally. Learn to read a program at different levels of abstraction.