FuncProgHW1

Functional Programming, Assignment 1.

Implements Zeller's congruence to solve the Counting Sundays problem.

Equivalent ES7 implementation

function dayOfWeek(day, month, year) {
  const yearOfCentury = year % 100;
  const zeroBasedCentury = Math.floor(year / 100);
  const mappedMonth = [13, 14, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12][month];

  return (
    day + 
    Math.floor((13 * (mappedMonth + 1)) / 5) + 
    yearOfCentury + 
    Math.floor(yearOfCentury / 4) + 
    Math.floor(zeroBasedCentury / 4) + 
    (5 * zeroBasedCentury)
  ) % 7;
}

Installation and usage

1. Run cabal build engine: $ cabal install -j.
2. Run $ .cabal-sandbox/bin/ZellersCongruence to start the application.

Running HLint

1. Run $ cabal install hlint.
2. Run $ .cabal-sandbox/bin/hlint . to execute the HLint.

Answer for the math question

Quoting from Wikipedia.org:

... in the Gregorian calendar, each leap year has 366 days instead of the usual 365, by extending February to 29 days rather than the common 28. These extra days occur in years which are multiples of four (with the exception of years divisible by 100 but not by 400).

Each week contains 7 days. Without leap days, 400 years would contain (365 * 400) days, which would be equal to 146.000 days.

There should be 24 leap days in a century, if the destination year is not divisible by 400, which adds (24 * 3) days, which would be equal to 72.

One of the centuries found in 400 years interval has 25 leap days since it is divisible by 400.

That makes 146.097 days, number of days in 400 years is a multiple of 7.

Picking one day is bounded to the same probability, all days are equally possible since this is a uniform distribution.

License

MIT with additional statements. See license file for more information.