function [] = Problem34()
%ProjectEuler/ProjectEulerOctave/Problem34.lua
%Matthew Ellison
% Created: 06-01-21
%Modified: 06-01-21
%Find the sum of all numbers which are equal to the sum of the factorial of their digits
%{
	Copyright (C) 2021  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
MAX_NUM = 1499999;	%The largest num that can be the sum of its own digits
numberFactorials = [];	%Holds the pre-computed factorials of the numbers 0-9
totalSum = 0;	%Holds the sum of all numbers equal to the sum of their digit's factorials

%Start the timer
startTime = clock();

%Pre-compute the possible factorials from 0! to 9!
for cnt = 1 : 9
	numberFactorials(cnt) = factorial(cnt);
end
%Run through all possible numbers from 3-MAX_NUM and see if they equal the sum of their digit's factorials
for cnt = 3 : MAX_NUM
	%Split the number into its digits and add each one to the sum
	numString = num2str(cnt);
	currentSum = 0;
	for numCnt = 1 : size(numString)(2)
		num = str2num(numString(numCnt));
		if(num != 0)
			currentSum += numberFactorials(num);
		else
			currentSum += 1;
		end
	end
	%If the number is equal to the sum add the sum to the running sum
	if(currentSum == cnt)
		totalSum += currentSum;
	end
end

%Stop the timer
endTime = clock();

%Print the results
printf("The sum of all numbers that are the sum of their digit's factorials is %d\n", totalSum);
printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime))

end

%{
Results:
The sum of all numbers that are the sum of their digit's factorials is 40730
It took 1988.403809 seconds to run this algorithm
%}