--ProjectEuler/lua/Problem20.lua
--Matthew Ellison
-- Created: 03-14-19
--Modified: 06-19-20
--What is the sum of the digits of 100!
--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
--I used the bigint library from https://github.com/empyreuma/bigint.lua
--[[
	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"
local bigint = require("bigint")

TOP_NUM = 100;


--Start the timer
local timer = Stopwatch:create();
timer:start();

local num = bigint.new(1);	--The number to be generated
local sum = 0;	--The sum of the digits in num

for cnt = 1, TOP_NUM do
	num = bigint.multiply(num, bigint.new(cnt));
end

--Get a string of the number because it is easier to pull appart the individual characters to get the sum
local numString = bigint.unserialize(num, 's');
--Run through every character in the string, convert it back to an integer and add it to the running sum
for cnt = 1, string.len(numString) do
	sum = sum + tonumber(string.sub(numString, cnt, cnt));
end

--Stop the timer
timer:stop()

--Print the results
io.write("100! = " .. numString .. '\n');
io.write("The sum of the digits is: " .. sum .. '\n');
io.write("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm\n");

--[[ Results:
100! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
The sum of the digits is: 648
It took 81.113 milliseconds to run this algorithm
]]