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
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]
)
let square_of_sum n =
let sum = (1 + n) * n / 2 in
sum * sum
let rec sum_of_squares n =
match n with
| 0 -> 0
| _ -> n * n + sum_of_squares (n - 1)
let difference_of_squares n =
square_of_sum n - sum_of_squares n
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