8.12

Lecture 23: Quick sortðŸ”—

This assignment is due on Sunday, March 31 at 11:59pm. Submit it using Handin as assignment lecture23.

Exercise 1. How does quick sort decompose this sorting problem into smaller sorting problems?
 5 6 2 1 8 2 3 7
1. Use this app to draw the decomposition. Make a rectangle for every problem.

2. Click the “Copy to clipboard” button in the lower-left corner of the app.

3. Paste the code as a comment, like this:
 ; Quick sort: ;

 ; A PivotTree is one of: ; - (make-no-pivot) ; - (make-pivot PivotTree Number PivotTree) (define-struct no-pivot []) (define-struct pivot [left val right]) (define pt0 (make-no-pivot)) (define pt1 (make-pivot pt0 1 (make-no-pivot))) (define pt2 (make-pivot pt1 2 (make-pivot (make-no-pivot) 3 (make-no-pivot))))

Exercise 2. Define pt3 to be the PivotTree that decomposes this sorting problem:
 5 6 2 1 8 2 3 7

Exercise 3. Write the template for a function that processes a PivotTree. Make it look like a function called process-pivottree, and do not put it in a comment.

Exercise 4. Design the function larger, which takes a Number and a [ListOf Number] and produces a new list of all the numbers in the list greater than the given number. You can use filter.

Exercise 5. What would happen if smaller used < instead of <=? Write a correct test for the quick-sort function that would detect the problem. In other words, the test should fail if smaller used < instead of <=.