--ProjectEuler/lua/Problem8.lua
--Matthew Ellison
-- Created: 02-06-19
--Modified: 06-19-20
--Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?
--[[
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
]]
--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"


local timer = Stopwatch:create();
timer:start();

--Put the number into a variable. A string will do for now
NUMBER = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450";
local maxNum = "";	--Holds the largest number product we have found so far
local maxProduct = 0;	--Holds the product of what is currently stored in maxNum

--Loop through all elements in the number string
for location=13,string.len(NUMBER) do
	--Added 13 elements to it's own table
	local currentProduct = string.sub(NUMBER, location, location) * string.sub(NUMBER, location - 1, location - 1) * string.sub(NUMBER, location - 2, location - 2) * string.sub(NUMBER, location - 3, location - 3) * string.sub(NUMBER, location - 4, location - 4) * string.sub(NUMBER, location - 5, location - 5) * string.sub(NUMBER, location - 6, location - 6) * string.sub(NUMBER, location - 7, location - 7) * string.sub(NUMBER, location - 8, location - 8) * string.sub(NUMBER, location - 9, location - 9) * string.sub(NUMBER, location - 10, location - 10) * string.sub(NUMBER, location - 11, location - 11) * string.sub(NUMBER, location - 12, location - 12);
	--If the number is larger than the current max make it the max
	if(currentProduct > maxProduct) then
		maxProduct = currentProduct;
		maxNum = string.sub(NUMBER, location - 12, location);
	end
end

timer:stop();

--Print the results
print("The largest product of 13 adjacent digits in the number is " .. math.floor(maxProduct))
print("The numbers are " .. maxNum);
print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm");


--[[Results:
The largest product of 13 adjacent digits in the number is 23514624000
The numbers are 5576689664895
It took 2.662 milliseconds to run this algorithm
]]