Project Euler 19: Counting Sundays

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

• 1 January 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 January 1901 to 31 December 2000)?

The problem can be quickly solved with R base code and a tiny bit faster when using the lubridate package.

ProjectEuler

  ## Project Euler 19: Counting Sundays

  ## Base-R
  dates <- seq.Date(as.Date("1901-01-01"), as.Date("2000-12-31"), "days")
  days <- rep(1:7, length.out = length(dates))
  answer <- sum(days[substr(dates, 9, 10) == "01"] == 1)
  print(answer)

  ## Using Lubridate
  library(lubridate)
  dates <- seq.Date(as.Date("1901-01-01"), as.Date("2000-12-31"), "months")
  answer <- sum(wday(dates) == 1)
  print(answer)

To draw out this post a little bit further, I wrote some code to solve the problem without using any of the calendar functions in R.

  ## Calculate from scratch
  week.day <- 0
  answer <- 0
  for (y in 1901:2000) {
      for (m in 1:12) {
          max.day <- 31
          if (m %in% c(4, 6, 9, 11))
              max.day <- 30
          # Leap years
          if (m == 2) {
              if (y %% 4 == 0 & y %% 100 != 0 | y %% 400 == 0) 
                  max.day <- 29
              else 
                  max.day <- 28
          }
          for (d in 1:max.day) {
              week.day <- week.day + 1
              if (week.day == 8) week.day <- 1
              if (week.day == 1 & d == 1)
              answer <- answer + 1
          }
      }
  }
  print(answer)

The only aspect remotely interesting about this problem is the conversion from weekdays to numbers. In R, Monday is considered day one, which makes sense in the Christian context of Western culture. Saturday and Sunday are the weekends, the two last days of the week so they are day 6 and 7. According to international standard ISO 8601, Monday is the first day of the week. Although this is the international standard, several countries, including the United States and Canada, consider Sunday to be the first day of the week.

The international standard is biased towards Christianity. The Christian or Western world marks Sunday as their day of rest and worship. Muslims refer to Friday as their day of rest and prayer. The Jewish calendar counts Saturday—the Sabbath—as the day of rest and worship. This idea is also shared by Seventh-Day Adventists.

This Euler problem shows that data science is not only about data: it is always how people interpret the world.

  ## First day of the week
  library(tidyverse)
  firstday <- read_csv("data/first_day.csv")

  map_data(map = "world") %>%
    full_join(firstday) %>%
    ggplot(aes(long, lat, group = group, fill = firstday)) +
    geom_polygon() +
    theme_void() +
    coord_fixed() +
    labs(title = "First day of the week")

  ggsave("images/problem-019.png", width = 6, height = 4)

As seen on R Bloggers