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64 lines
3.2 KiB
Lua
64 lines
3.2 KiB
Lua
--ProjectEuler/lua/Problem25.lua
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--Matthew Ellison
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-- Created: 03-26-19
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--Modified: 06-19-20
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--What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
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--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
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--I used the bigint library from https://github.com/empyreuma/bigint.lua
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--[[
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Copyright (C) 2020 Matthew Ellison
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>.
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]]
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require "Stopwatch";
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require "Algorithms";
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local bigint = require "bigint";
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local NUM_DIGITS = 1000; --The number of digits to calculate up to
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--Setup the variables
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local timer = Stopwatch:create();
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local number = bigint.new(0); --The current Fibonacci number
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local index = 2; --The index of the jest calculated Fibonacci number
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--Start the timer
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timer:start();
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--Move through all Fibonacci numbers until you reach the one with at least NUM_DIGITS digits
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while(#bigint.unserialize(number, 's') < NUM_DIGITS) do
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index = index + 1; --Increase the index number. Doing this at the beginning keeps the index correct at the end of the loop
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print("index: " .. index);
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--print("Size: " .. #bigint.unserialize(number, 's'));
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--print("number: " .. bigint.unserialize(number, 's'));
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number = getLargeFib(index); --Calculate the number
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end
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--Stop the timer
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timer:stop();
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--Print the results
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io.write("The first Fibonacci number with " .. NUM_DIGITS .. " digits is " .. bigint.unserialize(number, 's') .. '\n');
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io.write("The index is " .. index .. '\n');
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io.write("It took " .. timer:getMinutes() .. " minutes to run this algorithm\n");
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--[[ Results:
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The first Fibonacci number with 1000 digits is 1070066266382758936764980584457396885083683896632151665013235203375314520604694040621889147582489792657804694888177591957484336466672569959512996030461262748092482186144069433051234774442750273781753087579391666192149259186759553966422837148943113074699503439547001985432609723067290192870526447243726117715821825548491120525013201478612965931381792235559657452039506137551467837543229119602129934048260706175397706847068202895486902666185435124521900369480641357447470911707619766945691070098024393439617474103736912503231365532164773697023167755051595173518460579954919410967778373229665796581646513903488154256310184224190259846088000110186255550245493937113651657039447629584714548523425950428582425306083544435428212611008992863795048006894330309773217834864543113205765659868456288616808718693835297350643986297640660000723562917905207051164077614812491885830945940566688339109350944456576357666151619317753792891661581327159616877487983821820492520348473874384736771934512787029218636250627816
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The index is 4782
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It took 182.529 minutes to run this algorithm
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]]
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