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montxero's solution

to Difference Of Squares in the Scheme Track

Published at Oct 28 2019 · 0 comments
Test suite


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.

You are not expected to discover an efficient solution to this yourself from first principles; research is allowed, indeed, encouraged. Finding the best algorithm for the problem is a key skill in software engineering.

Running and testing your solutions


Suppose you're solving halting-problem:

  • Start a REPL, either in your favorite editor or from the command line.
  • Type (load "halting-problem.scm") at the prompt.
  • Test your code by calling (test) from the REPL. At first this should result in failed tests.
  • Develop your solution in "halting-problem.scm" and reload the file to run the tests again.

Testing options

You can see more information about failing test cases by passing arguments to the procedure test. To see the failing input call (test 'input) and to see the input and output together call (test 'input 'output).


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.


(define test-fields '(input output who))

(define (test-run-solution solution input)
  (if (procedure? solution) (apply solution input) solution))

(define (test-success description success-predicate
         procedure input output)
    (lambda (k)
        (lambda (e)
          (k `(fail
                (description . ,description)
                (input . ,input)
                (output . ,output)
                (who . ,procedure))))
        (lambda ()
          (let ([result (test-run-solution procedure input)])
            (unless (success-predicate result output)
              (error 'exercism-test
                "test fails"
          `(pass . ,description))))))

(define (test-error description procedure input)
    (lambda (k)
        (lambda (e) (k `(pass . ,description)))
        (lambda ()
          (test-run-solution procedure input)
             (description . ,description)
             (input . ,input)
             (output . error)
             (who . ,procedure)))))))

(define (run-test-suite tests . query)
    (lambda (field)
      (unless (and (symbol? field) (memq field test-fields))
        (error 'run-test-suite
          (format "~a not in ~a" field test-fields))))
  (let-values ([(passes failures)
                  (lambda (result) (eq? 'pass (car result)))
                  (map (lambda (test) (test)) tests))])
      [(null? failures) (format #t "~%Well done!~%~%") 'success]
         "~%Passed ~a/~a tests.~%~%The following test cases failed:~%~%"
         (length passes)
         (length tests))
         (lambda (failure)
             "* ~a~%"
               [(assoc 'description (cdr failure)) => cdr]
               [else (cdr failure)]))
             (lambda (field)
               (let ([info (assoc field (cdr failure))])
                 (format #t "  - ~a: ~a~%" (car info) (cdr info))))

(define (test . args)
      (lambda ()
        (test-success "square of sum 1" = square-of-sum '(1) 1))
      (lambda ()
        (test-success "square of sum 5" = square-of-sum '(5) 225))
      (lambda ()
        (test-success "square of sum 100" = square-of-sum '(100)
      (lambda ()
        (test-success "sum of squares 1" = sum-of-squares '(1) 1))
      (lambda ()
        (test-success "sum of squares 5" = sum-of-squares '(5) 55))
      (lambda ()
        (test-success "sum of squares 100" = sum-of-squares '(100)
      (lambda ()
        (test-success "difference of squares 1" =
          difference-of-squares '(1) 0))
      (lambda ()
        (test-success "difference of squares 5" =
          difference-of-squares '(5) 170))
      (lambda ()
        (test-success "difference of squares 100" =
          difference-of-squares '(100) 25164150)))
;;;; difference-of-squares.scm
;;;; an exercism exercise

(import (rnrs (6)))

(load "test.scm")

(define (square-of-sum n)
  "return (1 + ... + n)^2"
  (expt (/ (* n (+ n 1)) 2) 2))

(define (sum-of-squares n)
  "return (1^2 + ... + n^2)"
  (* (/ n 3) (+ n 1) (+ n 1/2)))

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

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