--ProjectEuler/lua/Problem29.lua
-- Created: 10-10-19
--Modified: 06-19-20
--How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 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"
require "Algorithms"
local bigint = require("bigint")

--Setup the variables
local timer = Stopwatch:create();
local BOTTOM_A = 2;	--The lowest possible value for A
local TOP_A = 100;	--The highest possible value for A
local BOTTOM_B = 2;	--The lowest possible value for B
local TOP_B = 100;	--The highest possible value for B
local unique = {};	--A table to hold all of the unique answers for the equation
local currentNum = bigint.new();	--Holds the answer to the equation for a particular loop

--Start the timer
timer:start();

--Start with the lowest A and move towards the largest
for currentA = BOTTOM_A, TOP_A do
	--Start with the lowest B and move towards the largest
	for currentB = BOTTOM_B, TOP_B do
		--Get the new number
		currentNum = bigint.unserialize(bigint.exponentiate(bigint.new(currentA), bigint.new(currentB)), "s");
		--If the number isn't in the list add it
		if(not isFound(unique, currentNum)) then
			table.insert(unique, currentNum);
		end
	end
end

--Stop the timer
timer:stop();

--Print the results
io.write("The number of unique values generated by a^b for " .. BOTTOM_A .. " <= a <= " .. TOP_A .. " and " .. BOTTOM_B .. " <= b <= " .. TOP_B .. " is " .. #unique .. '\n');
io.write("It took " .. timer:getString() .. " to run this algorithm\n");

--[[ Results:
The number of unique values generated by a^b for 2 <= a <= 100 and 2 <= b <= 100 is 9183
It took 2.714 minutes to run this algorithm
]]