;; The first three lines of this file were inserted by DrScheme. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-intermediate-lambda-reader.ss" "lang")((modname more_lambda) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp") (lib "hangman.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "draw.ss" "teachpack" "htdp") (lib "hangman.ss" "teachpack" "htdp")))))
(build-list 10 (lambda (x) (* x x)))

;; if I want it starting at 1? 

;; modifying the lambda function 
(check-expect (build-list 10 (lambda (x) (* (+ x 1) (+ x 1)))) 
              (list 1 4 9 16 25 36 49 64 81 100))

;; using a trick: generate 11 elements starting at 0, 
;; and take the last 10
(check-expect (rest (build-list 11 (lambda (x) (* x x)))) 
              (list 1 4 9 16 25 36 49 64 81 100))

;; if I want to define a function that, given n, returns the 
;; first n squares, starting at 0?

(define (squares n)
  (local ((define (sq x) (* x x)))
    (build-list n sq))
)

(squares 5)

;; using lambda:

(define (squares1 n)
    (build-list n (lambda (x) (* x x)))
)

(squares1 5)

;; write a function build-range that takes two integers, 
;; n and m, n <=m, and returns a list (n n+1 ... m)

(define (build-range n m) 
  (build-list (+ (- m n) 1) (lambda (x) ( + x n))))

;; Test cases:

(check-expect (build-range 2 2) (list 2))

(check-expect (build-range 2 5) (list 2 3 4 5))

;; use lambda to define the following functions:

;; a function that takes two numbers and returns the sum of their squares
(define sum-squares (lambda (x y) (+ (* x x) (* y y))))

(check-expect (sum-squares 2 3) 13)

;; a function that takes two integers and returns true if the first number
;; is divisible by the second one. 
;; hint: use modulo function

(define divisible? (lambda (n m) (= (modulo n m) 0)))

(check-expect (divisible? 4 2) true)

(check-expect (divisible? 5 2) false)