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firgun's solution

to Difference Of Squares in the Scheme Track

Published at Sep 24 2019 · 0 comments
Instructions
Test suite
Solution

Note:

This exercise has changed since this solution was written.

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.

Source

Problem 6 at Project Euler http://projecteuler.net/problem=6

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

difference-of-squares-test.scm

;; 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))

(define (sum-of-squares n)
  (/ (* n (+ n 1) (+ (* 2 n) 1)) 6))

(define (square-of-sum n)
  (let ((x (/ (* n (+ n 1)) 2)))
    (* x x)))

(define (difference n)
  (- (square-of-sum n) (sum-of-squares n)))

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