University of Virginia, Department of Computer Science CS200: Computer Science, Spring 2002

Notes: Monday 18 February 2002

• Friday, 22 February: Problem Set 4
• Monday, 25 February: Exam 1 Out (will be take-home, shouldn't take more than a few hours, but there will be no time limit; covers Lecture 1-13, Problem Sets 1-4, assigned readings through today)
• Wednesday, 27 February: Exam 1 Due
• Before 18 March: GEB all of Part I

Permute Sort
```(define (flat-one lst)
(if (null? lst) lst (append (car lst) (flat-one (cdr lst)))))

(define (all-permutations lst)
(flat-one
(map
(lambda (n)
(if (= (length lst) 1)
(list lst) ;; Only one permutation of 1-length list
(map
(lambda (oneperm) (cons (nth lst n) oneperm))
(all-permutations (exceptnth lst n)))))
(intsto (length lst)))))

(define (is-sorted? cf lst)
(or (null? lst) (= 1 (length lst))
(and (cf (car lst) (cadr lst))
(is-sorted? cf (cdr lst)))))

(define (permute-sort cf lst)
(car
(filter (lambda (lst) (is-sorted? cf lst))
(all-permutations lst))))
```
How much work is permute-sort?

What is a problem?

What does it mean to say a problem is O (n2)?

What does it mean to say a problem is Ω (n2)?

What does it mean to say a problem is in P?

What does it mean to say a problem is in NP?

Are all problems in P also in NP?

Are all problems in NP also in P?

 Note: this is the Millennium Prize Problem: The P versus NP Problem. Clay Mathematics Institute will give you \$1M if you answer it, so you may need more space.