🎉 Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io 🎉
Avatar of jpleboeuf

jpleboeuf's solution

to Difference Of Squares in the Nim Track

Published at Sep 21 2020 · 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.

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 the tests

To compile and run the tests, just run the following in your exercise directory:

$ nim c -r difference_of_squares_test.nim

Submitting Exercises

Note that, when trying to submit an exercise, make sure the solution is in the $EXERCISM_WORKSPACE/nim/difference-of-squares directory.

You can find your Exercism workspace by running exercism debug and looking for the line that starts with Exercises Directory.

Need help?

These guides should help you,

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.nim

import unittest
import difference_of_squares

# version 1.2.0

suite "Difference of Squares":
  test "square of sum 1":
    check squareOfSum(1) == 1

  test "square of sum 5":
    check squareOfSum(5) == 225

  test "square of sum 100":
    check squareOfSum(100) == 25_502_500

  test "sum of squares 1":
    check sumOfSquares(1) == 1

  test "sum of squares 5":
    check sumOfSquares(5) == 55

  test "sum of squares 100":
    check sumOfSquares(100) == 338_350

  test "difference of squares 1":
    check difference(1) == 0

  test "difference of squares 5":
    check difference(5) == 170

  test "difference of squares 100":
    check difference(100) == 25_164_150
from math import `^`, sum
from sequtils import toSeq, mapIt

template raiseValueError(): untyped =
  raise newException(ValueError, "n has to be a natural number")

func squareOfSum*(n: uint): uint =
  if n < 1: raiseValueError
  (sum toSeq(uint(1)..n)) ^ uint(2)

func sumOfSquares*(n: uint): uint =
  if n < 1: raiseValueError
  sum toSeq(uint(1)..n).mapIt(it ^ uint(2))

func difference*(n: uint): uint =
  if n < 1: raiseValueError
  squareOfSum(n) - sumOfSquares(n)

Community comments

Find this solution interesting? Ask the author a question to learn more.

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?