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109 lines
3.4 KiB
Matlab
109 lines
3.4 KiB
Matlab
function [] = Problem25()
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%ProjectEuler/Octave/Problem25.m
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%Matthew Ellison
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% Created: 03-26-19
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%Modified: 03-28-19
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%What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
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%This project uses the symbolic library. Make sure that you install the symbolic library as well as sympy before running this script
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%The way to do this is run this command in octave: pkg install -forge symbolic
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%This library requires sympy as well. This is easily installed with pip: pip install sympy
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%{
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Copyright (C) 2019 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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pkg load symbolic;
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digits(500) %Keep track of enough digits to do this calculation correctly
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NUM_DIGITS = 1000; %The number of digits to calculate up to
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%Setup the variables
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syms number; %The current Fibonacci number
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syms x; %A helper that will allow us to do easy math with the symbolics
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number = x;
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number = subs(number, x, 0); %Set the number to 0
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indexNum = 2; %The index of the just calculated Fibonacci number
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%Start the timer
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startTime = clock();
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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(size(char(number))(2) < NUM_DIGITS)
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indexNum += 1; %Increase the index number. Doing this at the beginning keeps the index correct at the end of the loop
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number = getFib(indexNum);
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printf("Index: %d\n", indexNum)
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end
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%Stop the timer
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endTime = clock();
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%Print the results
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printf("The first Fibonacci number with %d digits is %s\n", NUM_DIGITS, char(number))
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printf("The index is %d\n", indexNum);
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printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime));
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end %Problem25
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function [num] = getFib(goalSubscript)
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%Setup the variables
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fibNums = {};
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syms tempNum;
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syms x;
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tempNum = x;
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tempNum = subs(tempNum, x, 1);
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fibNums(end + 1) = tempNum;
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fibNums(end + 1) = tempNum;
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tempNum = x;
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tempNum = subs(tempNum, x, 0);
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fibNums(end + 1) = tempNum;
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%If the number is <= 0 return 0
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if(goalSubscript <= 0)
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num = 0;
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return;
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end
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%Loop through the list, generating Fibonacci numbers until it finds the correct subscript
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fibLoc = 2;
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while(fibLoc <= goalSubscript)
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tempNum = x;
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tempNum = subs(tempNum, x, fibNums(mod((fibLoc - 1), 3) + 1));
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fibNums(mod(fibLoc, 3) + 1) = tempNum;
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tempNum = x;
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tempNum = subs(tempNum, x, fibNums(mod((fibLoc - 2), 3) + 1));
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fibNums(mod(fibLoc, 3) + 1) += tempNum;
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fibLoc += 1;
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end
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%Make sure the correct number is chosen for return
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answerLocation = mod((fibLoc - 1), 3);
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if(answerLocation == 0)
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answerLocation = 3;
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end
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num = fibNums(answerLocation);
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end %getFib
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%{
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Results:
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I partially tested this and it seems to be working propperly.
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Because I am using the symbolic package to simulate a bigint library it is very slow.
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It looks as though it would take several days before it finished.
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%}
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