Add some exercises for scheme course

1 files changed, 36 insertions, 0 deletions

diff --git a/sem7/pp/lec1/exercises.sch b/sem7/pp/lec1/exercises.sch
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+(define (make-list-ft from to)
+  (if (> from to)
+      '()
+      (cons from (make-list-ft (1+ from) to))))
+
+;; Exercise 1.3 (proper lists)
+;;? Program own version of list?, thus proper-list?
+;; This is done by running to the end of list, always checking if pair.
+;; If last element is '() its a proper list, otherwize its not.
+(define (proper-list? list)
+  (if (pair? list)
+      (proper-list? (cdr list))
+      (null? list)))
+
+;;? Can you write your predicate without using if or cond?
+;; Hmm i cant see how this would be done, as we are using recursion which requires a stop condition.
+
+;;? Is your function efficient? What is the time complexity?
+;; This runs over all the elements in the list, so O(n).
+;; Hmm reading through the solution, i see that we can use other conditional functions like `or` and `and`.
+;; Lets try that
+(define (proper-list? list)
+  (or (null? list) (and (pair? list) (proper-list? (cdr list)))))
+
+;; Okay thats just his solution
+
+;; Exercise 1.5 (every second element)
+;; Hmm the text mentions that we could write it with (every-nth-element)
+(define (every-nth-element n list)
+  (let recur ((list list) (index 0))
+    (cond ((null? list) '())
+	  ((zero? (modulo index n)) (cons (car list) (recur (cdr list) (1+ index))))
+	  (else (recur (cdr list) (1+ index))))))
+
+(define (every-2th-element list)
+  (every-nth-element 2 list))