Pascal's triangle

Here is another exercise from David Evans book Introduction to Computing, Explorations in Language, Logic, and Machines.

This is a possible solution for the Pascal's triangle exploration at the end of chapter 5:

	#lang racket
	(require rackunit)
	(define (pascal-triangle-number row col)
	(if (or (= col 0)
	(= col row))
	1
	(+ (pascal-triangle-number (- row 1) col)
	(pascal-triangle-number (- row 1) (- col 1)))))
	(check-equal?
	(pascal-triangle-number 0 0) 1)
	(check-equal?
	(pascal-triangle-number 1 0) 1)
	(check-equal?
	(pascal-triangle-number 1 1) 1)
	(check-equal?
	(pascal-triangle-number 2 0) 1)
	(check-equal?
	(pascal-triangle-number 2 1) 2)
	(check-equal?
	(pascal-triangle-number 2 2) 1)
	(check-equal?
	(pascal-triangle-number 3 1) 3)
	(check-equal?
	(pascal-triangle-number 3 2) 3)
	(check-equal?
	(pascal-triangle-number 4 1) 4)
	(check-equal?
	(pascal-triangle-number 4 2) 6)
	(check-equal?
	(pascal-triangle-number 4 3) 4)
	(define (pascal-triangle-row n)
	(define (helper n i)
	(if (< i 0)
	null
	(cons (pascal-triangle-number n i)
	(helper n (- i 1)))))
	(helper n n))
	(check-equal? (pascal-triangle-row 0) (list 1))
	(check-equal? (pascal-triangle-row 1) (list 1 1))
	(check-equal? (pascal-triangle-row 2) (list 1 2 1))
	(define (range from to)
	(if (> from to)
	null
	(cons from
	(range (+ from 1) to))))
	(define (pascal-triangle n)
	(map
	pascal-triangle-row
	(range 0 n)))
	(check-equal?
	(pascal-triangle 0)
	(list (list 1)))
	(check-equal?
	(pascal-triangle 1)
	(list (list 1) (list 1 1)))
	(check-equal?
	(pascal-triangle 2)
	(list (list 1) (list 1 1) (list 1 2 1)))
	(check-equal?
	(pascal-triangle 4)
	(list (list 1) (list 1 1) (list 1 2 1) (list 1 3 3 1) (list 1 4 6 4 1)))

view raw pascal-triangle.rkt hosted with ❤ by GitHub

It's a nice exercise to practise recursion.