Project Euler – Problem 19 Solution

Problem

You are given the following information, but you may prefer to do some research for yourself.

  • 1 Jan 1900 was a Monday.
  • Thirty days has September, April, June and November. All the rest have thirty-one, saving February alone, which has twenty-eight, rain or shine. And on leap years, twenty-nine.
  • A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.

How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?

Solution

open System

let ans =
    [1901..2000]
    |> List.collect (fun y -> [1..12] |> List.map (fun m -> new DateTime(y, m, 1)))
    |> List.filter (fun d -> d.DayOfWeek = DayOfWeek.Sunday)
    |> List.length

The solution here is simple, for the int list [1901..2000] generates the Cartesian product with the int list [1..12] to get a DateTime object representing the first day in each month from 1901 to 2000, e.g.

image

From this point, all that’s left is to filter the list of DateTime values to find the ones which represent a Sunday and count them.

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