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.
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Problem 6 at Project Euler http://projecteuler.net/problem=6
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
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)
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.