CS 116 Tutorial 3 Accumulative RecursionRuntime Reminders Assignment

CS 116 – Tutorial 3 Accumulative Recursion/Runtime

Reminders: �Assignment Noon. 3 is due Wednesday at

Review �Accumulative �Run Time Recursion

How much runtime do you want me to cover for this tutorial? A) B) C) D) E) None A little bit Half the time It doesn’t matter to me What’s runtime?

Accumulative Recursion Usually use in place of lst when recursing Accumulators: can have as many as you (local need [(define (acc-fn whats-left acc 1 acc 2 … accn) (define (fn lst) (cond Put more [(base-case whats-left)…acck…] cases in … if you need [else (acc-fn update-parameters)]))] them (acc-fn initial-whats-left initial-acck … )) �Accumulators Use accs to help produce the correct result “keep track” of something so that you can quickly produce the expected result

Question 1 �Write an accumulatively recursive function sum-list which consumes a list of numbers and produces their sum. �Trace(sum-list �Compare (list 1 2 3)) this accumulative version with the structural recursive version from earlier.

Trace of list-to-num (list-to-num ‘(8 0 2)) ⇒ (list-to-num-acc ‘(8 0 2) 0) ⇒ (list-to-num-acc ‘(0 2) (+ (* 10 0) 8)) ⇒ (list-to-num-acc ‘(0 2) 8) ⇒ (list-to-num-acc ‘(2) (+ (* 10 8) 0)) ⇒ (list-to-num-acc ‘(2) 80) ⇒ (list-to-num-acc empty (+ (* 10 80) 2)) ⇒ (list-to-num-acc empty 802) ⇒ 802

Question 3 �Write an accumulatively recursive function find that consumes a list of symbols alos and a symbol sym, and returns the list of indices of positions in alos with symbol sym. Recall that the first position in a list has index 0. You may use reverse. �For example, (find (list ‘a ‘v ‘d ‘v) 'v) should return (list 1 3), while (find (list ‘a ‘v ‘d ‘v) 'q) should return empty.

Question 4 �Write an accumulatively recursive function count-max that consumes a nonempty list of numbers alon and returns the number of times the largest number in alon appears. �For example, ◦ (count-max (list 1 3 5 4 2 3 3 3 5)) => 2 ◦ since the largest element of the list, 5, appears twice. Your function should pass through the list only once.

Runtime Review �Look at the “worst case” scenario (i. e. longest time) �Only for code that gets executed when you run it �Assume function works (i. e. will not produce an error when you run it)

Runtime Review �O(1) – Constant ◦ does not depend on the size of the input (first x), (rest x), (symbol? x), (map sqr (list 1 2 3)) Ex: simple functions, or does not do something n times �O(n) – Linear ◦ depends on the size of the input (map sqr (list 1 2 … n)) Ex: abstract list functions, function call once (on a single cond case)

Runtime Review �O(n 2) – Quadratic ◦ time proportional to square of input (map sqr (build-list n add 1)) Ex: nested abstract list function, O(n) done multiple times �O(2 n) – Exponential ◦ As size of input increases, run time doubles Module 3, Slide 22: fib Ex: Multiple function calls (>1 calls in one cond case)

Question 5 �For each of the following determine what the worst-case runtime is.

Determine the worst-case run-time in terms of n, assuming n elements in lon (define (sum-list 1 lon) (cond [(empty? lon) 0] [else (+ (first lon) (sum-list 1 (rest lon)))]))

Determine worst-case run-time in terms of n, assuming n elements in loi (define (evens loi) (filter even? loi))

Determine the worst-case run-time in terms of n (define (create-number-lists n) (cond [(= n 0) empty] [else (cons (build-list n identity) (create-number-lists (sub 1 n)))]))

Determine the worst-case run-time in terms of n (define (create-a-list n) (cond [(even? n) empty] [else (build-list 3 (lambda (y) (+ n y)))]))