mirror of
https://bitbucket.org/Mattrixwv/projecteulerlua.git
synced 2025-12-06 17:43:57 -05:00
87 lines
2.9 KiB
Lua
87 lines
2.9 KiB
Lua
--ProjectEuler/lua/Problem26.lua
|
|
--Matthew Ellison
|
|
-- Created: 08-02-19
|
|
--Modified: 06-19-20
|
|
--Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
|
|
--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 TOP_NUMBER = 999 --The largest denominator to tbe checked
|
|
|
|
|
|
--Setup the variables
|
|
local timer = Stopwatch:create();
|
|
local longestCycle = 0;
|
|
local longestNumber = 1;
|
|
|
|
--Start the timer
|
|
timer:start();
|
|
|
|
--Start with 1/2 and find out how long the longest cycle is by checking the remainders
|
|
--Loop through every number from 2-999 and use it for the denominator
|
|
for denominator = 2, TOP_NUMBER do
|
|
local remainderList = {}; --Holds the list of remainders
|
|
local endFound = false; --Holds whether we have found an end to the number (either a cycle or a 0 for remainder)
|
|
local cycleFound = false; --Holds whether a cycle was detected
|
|
local numerator = 1; --The numerator that will be divided
|
|
while(not endFound) do
|
|
--Get the remainder after the division
|
|
local remainder = numerator % denominator
|
|
--Check if the remainder is 0
|
|
--If it is, set the flag
|
|
if(remainder == 0) then
|
|
endFound = true;
|
|
--Check if the remainder is in the list
|
|
--If it is in the list, set the appropriate flags
|
|
elseif(remainderList[remainder]) then
|
|
endFound = true;
|
|
cycleFound = true;
|
|
--Else add it to the list
|
|
else
|
|
remainderList[remainder] = true;
|
|
end
|
|
--Multiply the remainder by 10 to continue finding the next remainder
|
|
numerator = remainder * 10;
|
|
end
|
|
--If a cycle was found check the size of the list against the largest cycle
|
|
if(cycleFound) then
|
|
--If it is larger than the largest, set it as the new largest
|
|
if(#remainderList > longestCycle) then
|
|
longestCycle = #remainderList;
|
|
longestNumber = denominator;
|
|
end
|
|
end
|
|
end
|
|
|
|
--End the timer
|
|
timer:stop();
|
|
|
|
--Print the results
|
|
io.write("The longest cycle is " .. longestCycle .. " digits long\n");
|
|
io.write("It is started with the number " .. longestNumber .. '\n');
|
|
io.write("It took " .. timer:getString() .. " to run this algorithm\n");
|
|
|
|
--[[ Results:
|
|
The longest cycle is 982 digits long
|
|
It is started with the number 983
|
|
It took 28.222 milliseconds to run this algorithm
|
|
]]
|