Comments on: Project Euler in F# – Problem 6 http://www.fsharp.it/2008/01/23/project-euler-in-f-problem-6/ Functional programming on .Net Wed, 23 Mar 2011 17:29:06 +0100 http://wordpress.org/?v=2.8.5 hourly 1 By: Project Euler - Problem 19 - Noticias externas http://www.fsharp.it/2008/01/23/project-euler-in-f-problem-6/comment-page-1/#comment-107 Project Euler - Problem 19 - Noticias externas Fri, 07 Mar 2008 05:38:00 +0000 http://www.fsharp.it/2008/01/23/project-euler-in-f-problem-6/#comment-107 [...] haven't been to Project Euler in a while, but since I'm seeing other F# folks are getting into it, I figured I'd help work to improve the average F# 'genus rating' [...] [...] haven't been to Project Euler in a while, but since I'm seeing other F# folks are getting into it, I figured I'd help work to improve the average F# 'genus rating' [...]

]]> By: Michiel Borkent http://www.fsharp.it/2008/01/23/project-euler-in-f-problem-6/comment-page-1/#comment-94 Michiel Borkent Mon, 03 Mar 2008 14:21:48 +0000 http://www.fsharp.it/2008/01/23/project-euler-in-f-problem-6/#comment-94 Of course I meant the expression (x_1 + .. + x_2)^2 - (x_1^2 + .. + x_100^2) , not (x_1^2 .. x_100^2) - (x_1 + .. + x_2)^2 Of course I meant the expression (x_1 + .. + x_2)^2 – (x_1^2 + .. + x_100^2) , not (x_1^2 .. x_100^2) – (x_1 + .. + x_2)^2

]]> By: Michiel Borkent http://www.fsharp.it/2008/01/23/project-euler-in-f-problem-6/comment-page-1/#comment-93 Michiel Borkent Mon, 03 Mar 2008 14:19:38 +0000 http://www.fsharp.it/2008/01/23/project-euler-in-f-problem-6/#comment-93 With some cleverness the expression (x_1^2 .. x_100^2) - (x_1 .. x_2)^2 can be simplified to the sum of x_i*x_j, where i ranges from [1 .. 100] and j > i. Example: (a + b)^2 - (a^2 + b^2) = 2ab. Exameple: (a + b + c)^2 - (a^2 + b^2 + c^2) = 2(ab+ac+bc) The following uses this simplification: #light let rec diff2 l = match l with | [] -> 0 | _ -> 2 * List.sumByInt (fun x -> List.hd l * x) (List.tl l) + diff2 (List.tl l) diff2 [1 .. 100] With some cleverness the expression (x_1^2 .. x_100^2) – (x_1 .. x_2)^2 can be simplified to the sum of x_i*x_j, where i ranges from [1 .. 100] and j > i.

Example: (a + b)^2 – (a^2 + b^2) = 2ab.
Exameple: (a + b + c)^2 – (a^2 + b^2 + c^2) = 2(ab+ac+bc)

The following uses this simplification:

#light
let rec diff2 l =
match l with
| [] -> 0
| _ -> 2 * List.sumByInt (fun x -> List.hd l * x) (List.tl l) + diff2 (List.tl l)
diff2 [1 .. 100]

]]> By: Continuing Adventures in F# - Matthew Podwysocki's Blog http://www.fsharp.it/2008/01/23/project-euler-in-f-problem-6/comment-page-1/#comment-11 Continuing Adventures in F# - Matthew Podwysocki's Blog Tue, 29 Jan 2008 16:42:59 +0000 http://www.fsharp.it/2008/01/23/project-euler-in-f-problem-6/#comment-11 [...] Euler problems in F# Problem #1 in F# Problem #1 (alternate) Problem #6 Problem [...] [...] Euler problems in F# Problem #1 in F# Problem #1 (alternate) Problem #6 Problem [...]

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