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Mattrixwv
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function [] = Problem25()
%ProjectEuler/Octave/Problem25.m
%Matthew Ellison
% Created: 03-26-19
%Modified: 03-28-19
%What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
%This project uses the symbolic library. Make sure that you install the symbolic library as well as sympy before running this script
%The way to do this is run this command in octave: pkg install -forge symbolic
%This library requires sympy as well. This is easily installed with pip: pip install sympy
%{
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/>.
%}
pkg load symbolic;
digits(500) %Keep track of enough digits to do this calculation correctly
NUM_DIGITS = 1000; %The number of digits to calculate up to
%Setup the variables
syms number; %The current Fibonacci number
syms x; %A helper that will allow us to do easy math with the symbolics
number = x;
number = subs(number, x, 0); %Set the number to 0
indexNum = 2; %The index of the just calculated Fibonacci number
%Start the timer
startTime = clock();
%Move through all Fibonacci numbers until you reach the one with at least NUM_DIGITS digits
while(size(char(number))(2) < NUM_DIGITS)
indexNum += 1; %Increase the index number. Doing this at the beginning keeps the index correct at the end of the loop
number = getFib(indexNum);
printf("Index: %d\n", indexNum)
end
%Stop the timer
endTime = clock();
%Print the results
printf("The first Fibonacci number with %d digits is %s\n", NUM_DIGITS, char(number))
printf("The index is %d\n", indexNum);
printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime));
end %Problem25
function [num] = getFib(goalSubscript)
%Setup the variables
fibNums = {};
syms tempNum;
syms x;
tempNum = x;
tempNum = subs(tempNum, x, 1);
fibNums(end + 1) = tempNum;
fibNums(end + 1) = tempNum;
tempNum = x;
tempNum = subs(tempNum, x, 0);
fibNums(end + 1) = tempNum;
%If the number is <= 0 return 0
if(goalSubscript <= 0)
num = 0;
return;
end
%Loop through the list, generating Fibonacci numbers until it finds the correct subscript
fibLoc = 2;
while(fibLoc <= goalSubscript)
tempNum = x;
tempNum = subs(tempNum, x, fibNums(mod((fibLoc - 1), 3) + 1));
fibNums(mod(fibLoc, 3) + 1) = tempNum;
tempNum = x;
tempNum = subs(tempNum, x, fibNums(mod((fibLoc - 2), 3) + 1));
fibNums(mod(fibLoc, 3) + 1) += tempNum;
fibLoc += 1;
end
%Make sure the correct number is chosen for return
answerLocation = mod((fibLoc - 1), 3);
if(answerLocation == 0)
answerLocation = 3;
end
num = fibNums(answerLocation);
end %getFib
%{
Results:
I partially tested this and it seems to be working propperly.
Because I am using the symbolic package to simulate a bigint library it is very slow.
It looks as though it would take several days before it finished.
%}