(require (lib "trace.ss")) (define (insertl f lst start) (if (null? lst) start (f (car lst) (insertl f (cdr lst) start)))) ;;; Evaluates to the list parameter with exactly one instance of el removed. (define (delete lst el) (if (null? lst) (error "Element not found!") (if (eq? (car lst) el) (cdr lst) (cons (car lst) (delete (cdr lst) el))))) (define (find-most cf lst) (insertl (lambda (c1 c2) (if (cf c1 c2) c1 c2)) lst (car lst))) (define (bubblesort cf lst) (if (null? lst) lst (let ((most (find-most cf lst))) (cons most (bubblesort cf (delete lst most)))))) (define (revintsto n) (if (= n 0) null (cons n (revintsto (- n 1))))) (define (intsto n) (reverse (revintsto n))) (define (rand-int-list n) (if (= n 0) null (cons (random 10000) (rand-int-list (- n 1))))) (define (insertel cf el lst) (if (null? lst) (list el) (if (cf el (car lst)) (cons el lst) (cons (car lst) (insertel cf el (cdr lst)))))) (define (insertsort cf lst) (if (null? lst) null (insertel cf (car lst) (insertsort cf (cdr lst))))) (define (filter f lst) (insertl (lambda (el rest) (if (f el) (cons el rest) rest)) lst null)) (define (quicksort cf lst) (if (null? lst) lst (append (quicksort cf (filter (lambda (el) (cf el (car lst))) (cdr lst))) (list (car lst)) (quicksort cf (filter (lambda (el) (not (cf el (car lst)))) (cdr lst)))))) (define (sublist lst start end) (if (= start 0) (if (= end 0) null (cons (car lst) (sublist (cdr lst) start (- end 1)))) (sublist (cdr lst) (- start 1) (- end 1)))) (define (first-half lst) (sublist lst 0 (floor (/ (+ 1 (length lst)) 2)))) (define (second-half lst) (sublist lst (floor (/ (+ 1 (length lst)) 2)) (length lst))) (define (insertelh cf el lst) (if (null? lst) (list el) (if (= (length lst) 1) (if (cf el (car lst)) (cons el lst) (list (car lst) el)) (let ((fh (first-half lst)) (sh (second-half lst))) (if (cf el (car sh)) (append (insertelh cf el fh) sh) (append fh (insertelh cf el sh))))))) (define (insertsorth cf lst) (if (null? lst) null (insertelh cf (car lst) (insertsorth cf (cdr lst))))) (define (make-tree left el right) (list left el right)) (define (get-left tree) (first tree)) (define (get-element tree) (second tree)) (define (get-right tree) (third tree)) (define (insertel-tree cf el tree) (if (null? tree) (make-tree null el null) (if (cf el (get-element tree)) (make-tree (insertel-tree cf el (get-left tree)) (get-element tree) (get-right tree)) (make-tree (get-left tree) (get-element tree) (insertel-tree cf el (get-right tree)))))) (define (extract-elements tree) (if (null? tree) null (append (extract-elements (get-left tree)) (cons (get-element tree) (extract-elements (get-right tree)))))) (define (insertsort-tree cf lst) (define (insertsort-worker cf lst) (if (null? lst) null (insertel-tree cf (car lst) (insertsort-worker cf (cdr lst))))) (extract-elements (insertsort-worker cf lst))) ;;; Don't worry about this code - its for me to count the number of applications of < ;;; We will learn about set! for PS5. (define counter 0) (define (counter-lt v1 v2) (set! counter (+ counter 1)) (< v1 v2)) (define testlist (rand-int-list 20)) (define (timesort sortproc len) (let ((vals (rand-int-list len))) (let-values ([(val utime ptime gctime) (time-apply sortproc (list < vals))]) utime))) (define (timeappend len1 len2) (let ((vals1 (rand-int-list len1)) (vals2 (rand-int-list len2))) (let-values ([(val utime ptime gctime) (time-apply append (list vals1 vals2))]) utime))) (define (find-ratios lst) (if (< (length lst) 2) null (let ((thisone (car lst)) (nextone (cadr lst))) (if (= (cdr thisone) 0) (find-ratios (cdr lst)) (cons (exact->inexact (/ (cdr nextone) ;; ratio of times (cdr thisone))) (find-ratios (cdr lst))))))) (define (testgrowth sortproc) (let ((sizes (list 250 500 1000 2000 4000 8000 16000 32000 64000 128000))) (find-ratios (map (lambda (len) (let ((time (timesort sortproc len))) (printf "n = ~a, time = ~a~n" len time) (cons len time))) sizes)))) (define (testgrowthappend) (let ((nsizes (list 10000 20000 40000 80000 160000 320000 640000 1280000 2560000)) (msizes (list 10000 20000 40000 80000 160000 320000 640000 1280000 2560000))) (find-ratios (map (lambda (nlen mlen) (let ((time (timeappend nlen mlen))) (printf "n = ~a, m = ~a, time = ~a~n" nlen mlen time) (cons nlen time))) nsizes msizes))))