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Mattrixwv
2020-06-06 17:15:36 -04:00
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--ProjectEuler/lua/Problem29.lua
-- Created: 10-10-19
--Modified: 10-10-19
--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) 2019 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
]]