Project Euler 06. Sum square difference with F#

Problem Definition

The sum of the squares of the first ten natural numbers is,

1² + 2² + ... + 10² = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + ... + 10)² = 55² = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025-385 = 2640.Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Implementation

	open System

	let squareOfSum n =
	let i = n*(n+1)/2
	i*i

	let sumOfSquare n =
	[1..n]
	\|> List.fold (fun acc x -> acc + x*x) 0

	let solveEuler6 N =
	(squareOfSum N)- (sumOfSquare N)

view raw euler06.fs hosted with ❤ by GitHub

Project Euler 04. Largest Palindrome Product with F#

Problem Definition

Available at Largest Palindrome Product

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 * 99.

Find the largest palindrome made from the product of two 3-digit numbers.

Implementation

We have to find out a palindrome p such that —

where both a and b are three digit number. To do so, we first define a function that checks whether a number (e.g., p) is a palindrome.

	let ispalindrom (x:int):bool =
	let s = x.ToString()
	s = (s \|> (fun x -> new string(x.ToCharArray() \|> Array.rev)))

view raw ispalindrom.fs hosted with ❤ by GitHub

Then, we iterate over all the tuples (a,b) of three digit numbers e.g., [100..999] that satisfy the following equation.

Finally, we check if a*b is a palindrome and get the largest palindrome, as outlined below.

	seq{
	for x in 100..999 do
	for y in x..999 do
	if ispalindrom (xy) then yield (xy)}
	\|> Seq.max

view raw euler04.fs hosted with ❤ by GitHub

Would/did you solve it differently? Please let me know your opinion in the comment section below.

Happy problem solving …

problem solving

Euler Problem 002 with F#

Problem Statement

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

Solutions

Recursive Solution:

	// Recursive solution
	let eulerProblem2Answer'' =
	let maxF = 4000000
	let rec computeSum f1 f2 sum =
	match f1 + f2 with
	\| n -> computeSum f2 n sum
	\| n when n%2 = 0 -> if (n<maxF) then (computeSum f2 n (sum+n)) else sum
	computeSum 0 1 0

view raw euler02.fsx hosted with ❤ by GitHub

Using infinite Fibonacci sequence:

	let eulerProblem2Answer =
	(0,1)
	\|> Seq.unfold (fun (f1,f2) -> Some(f2, (f2, f1+f2))) // Fibonacci Sequence
	\|> Seq.takeWhile(fun x -> x < 4000000) // Taking upto Max Fibbonacci
	\|> Seq.filter (fun x -> x%2=0) // Filtering only even numbers
	\|> Seq.sum // computing sum

view raw euler02.fsx hosted with ❤ by GitHub

A bit shorter version can be derived using Seq.SumBy:

	let eulerProblem2Answer' =
	(0,1)
	\|> Seq.unfold (fun (f1,f2) -> Some(f2, (f2, f1+f2)))
	\|> Seq.takeWhile(fun x -> x < 4000000)
	\|> Seq.sumBy (fun x -> if (x%2)=0 then x else 0) // using SumBy with a projection

view raw euler02.fsx hosted with ❤ by GitHub

Result

> 
val eulerProblem2Answer : int = 4613732
val eulerProblem2Answer' : int = 4613732
val eulerProblem2Answer'' : int = 4613732