ProjectEulerLua/Problem19.lua

--ProjectEuler/lua/Problem19.lua
--Matthew Ellison
-- Created: 03-13-19
--Modified: 06-19-20
--How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?
--[[
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.
]]
--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
--[[
	Copyright (C) 2020  Matthew Ellison

	This program is free software: you can redistribute it and/or modify
	it under the terms of the GNU Lesser General Public License as published by
	the Free Software Foundation, either version 3 of the License, or
	(at your option) any later version.

	This program is distributed in the hope that it will be useful,
	but WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
	GNU Lesser General Public License for more details.

	You should have received a copy of the GNU Lesser General Public License
	along with this program.  If not, see <https://www.gnu.org/licenses/>.
]]


require "Stopwatch"


DAYS = {
	SUNDAY = 0,
	MONDAY = 1,
	TUESDAY = 2,
	WEDNESDAY = 3,
	THURSDAY = 4,
	FRIDAY = 5,
	SATURDAY = 6,
	NUMBER_OF_DAYS = 7,
	ERROR = 8;
}

local START_YEAR = 1901;
local END_YEAR = 2000;

local function isLeapYear(year)
	local answer;
	if(year < 1) then
		answer = false;
	elseif((year % 100) == 0) then
		--This rule only applies at and after 1800
		if(year <= 1700) then
			answer = true;
		elseif((year % 400) == 0) then
			answer = true;
		else
			answer = false;
		end
	elseif((year % 4) == 0) then
		answer = true;
	else
		answer = false;
	end
	return answer;
end

--Return the day of the week that the date you pass into it is on
local function getDay(month, day, year)
	--Make sure the numbers are within propper bounds
	if((month < 1) or (month > 12) or (day < 1) or (day > 31) or (year < 1)) then
		return DAYS.ERROR;
	end

	local numDays = 0;
	local currentYear = 1;
	local currentMonth = 1;
	local currentDay = DAYS.SATURDAY;
	day = day - 1;

	--Add the correct number of days for every year
	while(currentYear < year) do
		if(isLeapYear(currentYear)) then
			numDays = numDays + 366;
		else
			numDays = numDays + 365;
		end
		currentYear = currentYear + 1;
	end
	--Add the correct number of days for every month
	while(currentMonth < month) do
		--February
		if(currentMonth == 2) then
			if(isLeapYear(currentYear)) then
				numDays = numDays + 29;
			else
				numDays = numDays + 28;
			end
		--31 day months
		elseif((currentMonth == 1) or (currentMonth == 3) or (currentMonth == 5) or (currentMonth == 7) or (currentMonth == 8) or (currentMonth == 10) or (currentMonth == 12)) then
			numDays = numDays + 31;
		--30 day months
		else
			numDays = numDays + 30;
		end
		currentMonth = currentMonth + 1;
	end
	--Account for the weird year of 1752
	if(year > 1752) then
		numDays = numDays - 11;
	elseif(year == 1752) then
		if(month > 9) then
			numDays = numDays - 11;
		elseif(month == 9) then
			if(day >= 14) then
				numDays = numDays - 11;
			--Days 3-13 were skipped that year
			elseif((day > 2) and (day < 14)) then
				return DAYS.ERROR;
			end
		end
	end
	--Add the correct number of days for every day
	numDays = numDays + day;

	currentDay = currentDay + numDays;
	currentDay = currentDay % DAYS.NUMBER_OF_DAYS;
	if(currentDay == DAYS.SUNDAY) then
		day =  DAYS.SUNDAY;
	elseif(currentDay == DAYS.MONDAY) then
		day = DAYS.MONDAY;
	elseif(currentDay == DAYS.TUESDAY) then
		day = DAYS.TUESDAY;
	elseif(currentDay == DAYS.WEDNESDAY) then
		day = DAYS.WEDNESDAY;
	elseif(currentDay == DAYS.THURSDAY) then
		day = DAYS.THURSDAY;
	elseif(currentDay == DAYS.FRIDAY) then
		day = DAYS.FRIDAY;
	elseif(currentDay == DAYS.SATURDAY) then
		day = DAYS.SATURDAY;
	else
		day = DAYS.ERROR;
	end
	--Return the day generated
	return day;
end

--Setup the variables
local timer = Stopwatch:create();
local totalSundays = 0;

--Start the timer
timer:start();

--Run for all years up to 2000
for year=START_YEAR,END_YEAR do
	--Run for all months in the year
	for month=1,12 do
		local day = getDay(month, 1, year);
		if(day == DAYS.ERROR) then
			io.output("There was an error with the day\n");
			os.exit();
		elseif(day == DAYS.SUNDAY) then
			totalSundays = totalSundays + 1;
		end
	end
end

--Stop the timer
timer:stop()

--Print the results
io.write("There are " .. totalSundays .. " Sundays that landed on the first of the months from " .. START_YEAR .. " to " .. END_YEAR .. '\n');
io.write("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm\n");

--[[ Results:
There are 171 Sundays that landed on the first of the months from 1901 to 2000
It took 390.0 milliseconds to run this algorithm
]]