Project Euler – Problem 4 Solution

Problem

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

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

Solution

open System.Linq

let isPalindromic n =
    let charArray = n.ToString().ToCharArray()
    let revCharArray = Array.rev charArray
    charArray.SequenceEqual(revCharArray)

let numbers = [100..999]
let products = numbers |> List.collect (fun x -> numbers |> List.map (fun y -> x * y))
let maxPalindromic = products |> Seq.filter isPalindromic |> Seq.max

In my solution above, I first built a function to check whether a given number is palindromic by comparing the original and reversed char array representing the number and see if they’re the same, i.e. 9009 is represented by the char array [‘9′;’0′;’0′;’9’], and the reversed array is still [‘9′;’0′;’0′;’9’].

Notice how I used the Array.rev function in the isPalindromic function, it returns a new array with all the elements in reverse order. Another thing you might have noticed in this function is that I used the Enumerable.SequenceEqual Linq extension method to compare the two arrays, as I’ve mentioned before, with F# being a first class citizens of the .Net family you’re free to use whatever CLR library of your choice.

The rest of the solution might be relatively straight forward, however, you might be wondering what the List.collect function does. Like the List.map function, it applies a function to each element in the list, except that each element produces a list and all these lists are concatenated into a final list.

Now let’s see how the two differs, say we have a list of numbers from 1 to 10, and I want to find out the Cartesian product of the list multiplied by itself, i.e. 1 * 1, 1 * 2, … 1 * 10, 2 * 1, 2 * 2… 10 * 10:

let numbers = [1..10]

// List.map returns an array of array containing results of 1 *  [1..10], 2 * [1..10], etc.
numbers |> List.map (fun x -> numbers |> List.map(fun y -> x * y));;
val it : int list list =
[[1; 2; 3; 4; 5; 6; 7; 8; 9; 10];
 [2; 4; 6; 8; 10; 12; 14; 16; 18; 20];
 [3; 6; 9; 12; 15; 18; 21; 24; 27; 30];
 [4; 8; 12; 16; 20; 24; 28; 32; 36; 40];
 [5; 10; 15; 20; 25; 30; 35; 40; 45; 50];
 [6; 12; 18; 24; 30; 36; 42; 48; 54; 60];
 [7; 14; 21; 28; 35; 42; 49; 56; 63; 70];
 [8; 16; 24; 32; 40; 48; 56; 64; 72; 80];
 [9; 18; 27; 36; 45; 54; 63; 72; 81; 90];
 [10; 20; 30; 40; 50; 60; 70; 80; 90; 100]]

// List.collect returns a 1-dimensional array instead
numbers |> List.collect (fun x -> numbers |> List.map (fun y -> x * y));;
val it : int list =
[1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 2; 4; 6; 8; 10; 12; 14; 16; 18; 20; 3; 6; 9;
 12; 15; 18; 21; 24; 27; 30; 4; 8; 12; 16; 20; 24; 28; 32; 36; 40; 5; 10; 15;
 20; 25; 30; 35; 40; 45; 50; 6; 12; 18; 24; 30; 36; 42; 48; 54; 60; 7; 14;
 21; 28; 35; 42; 49; 56; 63; 70; 8; 16; 24; 32; 40; 48; 56; 64; 72; 80; 9;
 18; 27; 36; 45; 54; 63; 72; 81; 90; 10; 20; 30; 40; 50; 60; 70; 80; 90; 100]

Enjoy what you’re reading? Subscribe to my newsletter and get more content on AWS and serverless technologies delivered straight to your inbox.


Yan Cui

I’m an AWS Serverless Hero and the author of Production-Ready Serverless. I have run production workload at scale in AWS for nearly 10 years and I have been an architect or principal engineer with a variety of industries ranging from banking, e-commerce, sports streaming to mobile gaming. I currently work as an independent consultant focused on AWS and serverless.

You can contact me via Email, Twitter and LinkedIn.

Hire me.


Check out my new course, Complete Guide to AWS Step Functions.

In this course, we’ll cover everything you need to know to use AWS Step Functions service effectively. Including basic concepts, HTTP and event triggers, activities, design patterns and best practices.

Get Your Copy