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## to Difference Of Squares in the Scheme Track

Published at Jun 11 2020 · 0 comments
Instructions
Test suite
Solution

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

### From the command line

Simply type `make chez` if you're using ChezScheme or `make guile` if you're using GNU Guile. Sometimes the name for the scheme binary on your system will differ from the defaults. When this is the case, you'll need to tell make by running `make chez chez=your-chez-binary` or `make guile guile=your-guile-binary`.

### From a REPL

• Enter `(load "test.scm")` at the repl prompt.
• Develop your solution in `difference-of-squares.scm` reloading as you go.
• Run `(test)` to check your solution.

### Failed Test Cases

If some of the test cases fail, you should see the failing input and the expected output. The failing input is presented as a list because the tests call your solution by `(apply difference-of-squares input-list)`. To learn more about `apply` see The Scheme Programming Language -- Chapter 5

## 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.

### test.scm

``````(import (except (rnrs) current-output-port))

(define test-fields '(input output))

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

(define (test-success description success-predicate
procedure input output)
(call/cc
(lambda (k)
(let ([out (open-output-string)])
(with-exception-handler
(lambda (e)
(let ([result `(fail
(description . ,description)
(input . ,input)
(output . ,output)
(stdout . ,(get-output-string out)))])
(close-output-port out)
(k result)))
(lambda ()
(let ([result (parameterize ([current-output-port out])
(test-run-solution procedure input))])
(unless (success-predicate result output)
(error 'exercism-test
"test fails"
description
input
result
output)))
(let ([result `(pass
(description . ,description)
(stdout . ,(get-output-string out)))])
(close-output-port out)
result)))))))

(define (test-error description procedure input)
(call/cc
(lambda (k)
(let ([out (open-output-string)])
(with-exception-handler
(lambda (e)
(let ([result `(pass
(description . ,description)
(stdout . ,(get-output-string out)))])
(close-output-port out)
(k result)))
(lambda ()
(parameterize ([current-output-port out])
(test-run-solution procedure input))
(let ([result `(fail
(description . ,description)
(input . ,input)
(output . error)
(stdout . ,(get-output-string out)))])
(close-output-port out)
result)))))))

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

(define (run-docker test-cases)
(write (map (lambda (test) (test)) test-cases)))

(define sum-of-squares)

(define difference-of-squares)

(define square-of-sum)

(define test-cases
(list
(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)
25502500))
(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)
338350))
(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))))

(define (test . query)
(apply run-test-suite test-cases query))

(let ([args (command-line)])
(cond
[(null? (cdr args))
(load "difference-of-squares.scm")
(test 'input 'output)]
[(string=? (cadr args) "--docker")
(load "difference-of-squares.scm")
(run-docker test-cases)]
[else (load (cadr args)) (test 'input 'output)]))``````
``````(import (rnrs))

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

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

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

### What can you learn from this solution?

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.

Here are some questions to help you reflect on this solution and learn the most from it.

• What compromises have been made?
• Are there new concepts here that you could read more about to improve your understanding?