Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.
The square of the sum of the first ten natural numbers is (1 + 2 + ... + 10)² = 55² = 3025.
The sum of the squares of the first ten natural numbers is 1² + 2² + ... + 10² = 385.
Hence the difference between the square of the sum of the first ten natural numbers and the sum of the squares of the first ten natural numbers is 3025 - 385 = 2640.
Problem 6 at Project Euler http://projecteuler.net/problem=6
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
;; Load SRFI-64 lightweight testing specification (use-modules (srfi srfi-64)) ;; Suppress log file output. To write logs, comment out the following line: (module-define! (resolve-module '(srfi srfi-64)) 'test-log-to-file #f) ;; Require module (add-to-load-path (dirname (current-filename))) (use-modules (squares)) (test-begin "difference-of-squares") (test-eqv "square-of-sum-to-5" 225 (square-of-sum 5)) (test-eqv "sum-of-squares-to-5" 55 (sum-of-squares 5)) (test-eqv "difference-of-squares-to-5" 170 (difference 5)) (test-eqv "square-of-sum-to-10" 3025 (square-of-sum 10)) (test-eqv "sum-of-squares-to-10" 385 (sum-of-squares 10)) (test-eqv "difference-of-squares-to-10" 2640 (difference 10)) (test-eqv "square-of-sum-to-100" 25502500 (square-of-sum 100)) (test-eqv "sum-of-squares-to-100" 338350 (sum-of-squares 100)) (test-eqv "difference-of-squares-to-100" 25164150 (difference 100)) (test-end "difference-of-squares")
(define-module (squares) #:export (sum-of-squares square-of-sum difference) #:autoload (srfi srfi-1) (reduce iota)) (define (sum a b term next) (if (> a b) 0 (+ (term a) (sum (next a) b term next)))) (define (square x) (* x x)) (define (sum-of-squares limit) (sum 1 limit square 1+)) (define (square-of-sum limit) (square (sum 1 limit (lambda (x) x) 1+))) (define (difference limit) (- (square-of-sum limit) (sum-of-squares limit)))
A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.
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