CS 135 Midterm 2

Outline of The Session

• Structures• Lists– Association Lists

• Recursions• Types of Recursions

Structures

Structures

• Allow you to store several values in one entity• e.g. posn – predefined structure in Scheme• (define-struct posn (x y))• The following are created:– Constructor: (make-posn x y)– Selectors: (posn-x) (posn-y)– Predicate: posn?

• (make-posn 3 2) is in its most simplified form

Structures

• Example:• (define-struct chair (color material))• (define mychair (make-chair ‘blue ‘wood))• (chair-color mychair) => ‘blue• (chair-material mychair) => ‘wood• Predicate: chair?

Structures: Design Recipe

• Define the structure• Write the data definition– What are the types of each field?

• Create a template for a function that consumes the structure

Structures: Design Recipe

(define-struct student (first last id));; a Student = (make-student String String Number);; my-student-fn: Student -> Any(define (my-student-fn data) … (student-first data) … … (student-last data) … … (student-id data) …)

Structures: Examples

Question 1:(define-struct student (first last id));; a Student = (make-student String String Number)

• Write a function “swap” that takes a Student as input, and outputs another Student with the first name and last name swapped.

Structures: Examples

Question 2• Define a struct called “fivenum” that has five

fields, all of which are numbers.• Write a function “fivenum-avg” that takes a

fivenum as input, and output a number that is the average of the five fields that are in fivenum.

Structures: ExamplesHTDP, Section 7, Question 2: Develop data and structure definition for a collection of 3D shapes. The collection includes:• Cubes, with relevant properties being the length of an edge• Prisms, which are rectangular solids and with relevant properties being

length, width, and height• Spheres, with relevant property being the radiusDevelop the function “volume”. The function consumes a 3D shape and produces the volume of the object. • The volume of a cube is the cube of the length of one its edges. • The volume of a prism is the product of its length, width, and height. • The Volume of a sphere is 4/3 * PI * r^3

ListsQuestions so far?

Lists

• Lists vs. Structs– Unbounded vs. fixed amount of data

• An ordered set of data elements, each containing a list to its successor

Lists• List selector functions:– First– Cons– Rest

• Built-in predicates:– Empty?– Cons?– Member?

• Other list functions:– Length– Reverse

Lists

;; A List is one of:;; * empty;; * (cons Any List)

• empty is also a list

When stepping through code, a list, like structures, cannot be simplified any further.

Lists

• (define lst (cons 2 (cons 3 (cons 4 empty))))• Selectors:– (first lst) => 2– (rest lst) => (cons 3 (cons 4 empty))– (first (rest lst)) => 3

Lists: Box-and-Pointer Diagrams

• Write out the code for these Box-and-Pointer diagrams

Lists: Box-and-Pointer Diagrams

• Solutions• (cons (cons empty empty) (cons 3 empty))• (cons (cons 1 empty) (cons (cons 4 (cons 7

(cons 8 empty))) (cons (cons empty empty) empty)))

Lists: Box-and-Pointer Diagrams

• Draw Box-and-Pointer diagrams:• (cons 1 (cons 2 (cons 3 empty)))• (cons (cons 1 (cons 2 empty)) (cons (cons 3

(cons 4 empty)) empty))• (cons (cons (cons 3 empty) (cons 4 (cons 6

empty))) (cons 7 (cons (cons 8 empty) empty)))

Coding with Lists

;; my-list-fn: (listof Any) -> Any(define (my-lst-fn lst) (cond [(empty? lst) …] [else … (first lst) … (my-lst-fn (rest lst)) … ]))

This is for a general list function

Coding with Lists

Question 1:Write a function “addone” that takes a (listof Num) as input, and output a (listof Num) with each element of list incremented by 1.

Lists: Tracing (define (addone lon) (cond [(empty? lon) empty] [else (cons (add1 (first lon) ) (addone (rest lon)))]))

• (addone (cons 3 (cons 1 (cons 9 (cons 4 empty)))))• (cons 4 (addone (cons 1 (cons 9 (cons 4 empty)))))• (cons 4 (cons 2 (addone (cons 9 (cons 4 empty)))))• (cons 4 (cons 2 (cons 10 (addone (cons 4 empty)))))• (cons 2 (cons 4 (cons 6 (cons 5 (addone empty)))))• (cons 2 (cons 4 (cons 6 (cons 5 empty))))

Coding with Lists

Question 2:Develop the function “string-append-n”, which consumes a list of strings and produces a single string resulting from appending all the strings together. Use the built-in function “string-append”: String String -> String, which appends two strings. If the list is empty, produce an empty string “”.

List Abbreviations

• (cons 1 (cons 2 (cons 3 empty)))• (list 1 2 3)

• (cons ‘Apple (cons ‘Orange (cons ‘Fruit empty)))• ‘(Apple Orange Fruit)

Association Lists

• List of pairs– Pair is a two-element list– First element is the key– Second element is the value

• E.g. Storing definitions

Association Lists

(define (my-al-fn alst)(cond

[(empty? alst) ...][else … (first (first alst) ;; first key … (second (first alst)) ;; first value

… (my-al-fn (rest alst))]))

Association Lists: Example

Question 1:Create the function “remove-entry” for an association list. The function “remove-entry” consumes an association list and a key, and produces the association list without the key/value pair for the given key. If the key is not in the association list, return the original association list.

Recursion

Recursion

• You have just used recursion on lists• A function that calls itself in order to compute

data of unknown size• Must have a base case

Recursion

• Natural number recursion– Used to work with any natural number N– Base case is usually N = 0

Question:Write a function “fac” that takes a natural number as input, and outputs the factorial of that number.(fac 4) -> 4*3*2*1 -> 24

Recursion

Question 1:Develop list-pick0 that takes a (listof Any) and a natural number as input, and produces the n-th element of the list (index starts at 0). (You can assume n < length of list)

(list-pick0 (list ‘hello ‘world) 0) -> ‘hello

Types of Recursion

Structural Recursion

• Each recursive call leaves all parameters unchanged or moves the recursion one step closer to a base case

• e.g. traversing a list until empty

Accumulative Recursion

• Parameter(s) contain partial answers

(define (my-reverse lst0) ;; wrapper function (my-rev-helper lst0 empty))

(define (my-rev-helper lst acc) ;; helper function(cond [(empty? lst) acc] [else (my-rev-helper (rest lst) (cons (first lst) acc))]))

Generative Recursion

• Parameters are freely calculated at each step

(define (euclid-gcd n m)(cond [(zero? m) n] [else (euclid-gcd m (remainder n m))])

Practice Problems

Determine whether the following recursive functions uses structural recursion, accumulative recursion, or generative recursion.

Type of Recr: Practice Problems

n is a natural number(define (fac n)

(cond [(zero? n) 1] [else (* n (fac (sub1 n)))]))

Type of Recr: Practice Problems

(define (fac n)(fac-helper n 1))

(define (fac-helper n acc)(cond [(zero? n) acc]

[else (fac-helper (sub1 n) (* n acc))]))

Type of Recr: Practice Problems

n is a natural number(define (collatz n)

(cond [(= n 1) empty][(even? n) (cons (/ n 2) (collatz (/ n 2)) [(odd? n) (cons (add1 (* n 3))

(collatz (add1 (* n 3))))]))

Type of Recr: Practice Problems

Lon is a list of numbers(define (sum lon)

(cond [(empty? lon) 0] [else (+ (first lon) (sum (rest lon)))]))

Any Final Questions?

Good luck on your midterm!khzhu@uwaterloo.ca