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shmibs's solution

to Difference Of Squares in the OCaml Track

Published at Dec 15 2018 · 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.

Getting Started

For installation and learning resources, refer to the exercism help page.

Installation

To work on the exercises, you will need Opam and Base. Consult opam website for instructions on how to install opam for your OS. Once opam is installed open a terminal window and run the following command to install base:

opam install base

To run the tests you will need OUnit. Install it using opam:

opam install ounit

Running Tests

A Makefile is provided with a default target to compile your solution and run the tests. At the command line, type:

make

Interactive Shell

utop is a command line program which allows you to run Ocaml code interactively. The easiest way to install it is via opam:

opam install utop

Consult utop for more detail.

Feedback, Issues, Pull Requests

The exercism/ocaml repository on GitHub is the home for all of the Ocaml exercises.

If you have feedback about an exercise, or want to help implementing a new one, head over there and create an issue. We'll do our best to 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.

test.ml

open OUnit2
open Difference_of_squares

let ae exp got _test_ctxt = assert_equal exp got

let square_of_sum_tests = [
   "square of sum 1" >::
     ae 1 (square_of_sum 1);
   "square of sum 5" >::
     ae 225 (square_of_sum 5);
   "square of sum 100" >::
     ae 25502500 (square_of_sum 100);
]


let sum_of_squares_tests = [
   "sum of squares 1" >::
     ae 1 (sum_of_squares 1);
   "sum of squares 5" >::
     ae 55 (sum_of_squares 5);
   "sum of squares 100" >::
     ae 338350 (sum_of_squares 100);
]


let difference_of_squares_tests = [
   "difference of squares 1" >::
     ae 0 (difference_of_squares 1);
   "difference of squares 5" >::
     ae 170 (difference_of_squares 5);
   "difference of squares 100" >::
     ae 25164150 (difference_of_squares 100);
]

let () =
  run_test_tt_main (
    "difference of squares tests" >:::
      List.concat [square_of_sum_tests; sum_of_squares_tests; difference_of_squares_tests]
  )
open Base

let errstr = "n must be non-negative"

let square n = n * n

let rec do_sum n a fstep =
  match n with
  | 0 -> a
  | n -> do_sum (n - 1) (a + (fstep n)) fstep

let square_of_sum (n : int) =
  if n < 0 then raise (Invalid_argument errstr)
  else do_sum n 0 (fun n -> n) |> square

let sum_of_squares (n : int) =
  if n < 0 then raise (Invalid_argument errstr)
  else do_sum n 0 square

let difference_of_squares (n : int) =
  if n < 0 then raise (Invalid_argument errstr)
  else (square_of_sum n) - (sum_of_squares n)

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