function [] = Problem30()
%ProjectEuler/Octave/Problem30.m
%Matthew Ellison
% Created: 10-28-19
%Modified: 10-28-19
%Find the sum of all the numbers that can be written as the sum of the fifth powers of their digits.
%{
	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/>.
%}


%Setup the variables
TOP_NUM = 1000000;	%This is the largest number that will be check
BOTTOM_NUM = 2;	%Starts with 2 because 0 and 1 don't count
POWER_RAISED = 5;	%This is the power that the digits are raised to
sumOfFifthNumbers = [];	%This is an array of the numbers that are the sum of the fifth power of their digits

%Start the timer
startTime = clock();

%Start with the lowest number and increment until you reach the largest number
for currentNum = BOTTOM_NUM : TOP_NUM
	printf("%d\n", currentNum)
	%Get the digits of the number
	digits = getDigits(currentNum);
	%Get the sum of the powers
	sumOfPowers = 0;
	for cnt = 1 : size(digits)(2)
		sumOfPowers += digits(cnt)^POWER_RAISED;
	end
	%Check if the sum of the powers is the same as the number
	%If it is add it to the list, otherwise continue to the next number
	if(sumOfPowers == currentNum)
		sumOfFifthNumbers(end + 1) = currentNum;
	end
end

%Stop the timer
endTime = clock();

%Print the results
printf("The sum of all the numbers that can be written as the sum of the fifth powers of their digits is %d\n", sum(sumOfFifthNumbers))
printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime))

end


%Returns an array with the individual digits of the number passed to it
function [listOfDigits] = getDigits(num)
	listOfDigits = [];	%This array holds the individual digits of num
	%The easiest way to get the individual digits of a number is by converting it to a string
	digits = num2str(num);
	%Start with the first digit, convert it to an integer, store it in the table, and move to the next digit
	for cnt = 1 : size(digits)(2)
		listOfDigits(end + 1) = str2num(substr(digits, cnt, 1));
	end
end

%{
Results:
The sum of all the numbers that can be written as the sum of the fifth powers of their digits is 443839
It took 1849.877525 seconds to run this algorithm
%}