%ProjectEuler/Octave/Problem20.m
%Matthew Ellison
% Created: 03-14-19
%Modified: 03-28-19
%What is the sum of the digits of 100!?
%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


%The number that will hold 100!
syms num;
syms x;	%A helper that will allow us to do easy math with the symbolics
num = 1 * x;
num = subs(num, x, 1);
%Setup the rest of our variables
sumOfNums = 0;	%Holds the sum of the digits of num
TOP_NUM = 100;	%The number that we are trying to factorial

%Start the timer
startTime = clock();

%Run through every number from 1 to 100 and multiply it by the current number
for cnt = 1 : TOP_NUM
	num = num * x;
	num = subs(num, x, cnt);
end

%Get a string of the numebr because it is easier to pull appart the individual characters for the sum
numString = char(num);
%Run through every character in the string, convert it back to an integer and add it to the running sum
for cnt = 1 : size(numString)(2)
	sumOfNums += str2num(numString(cnt));
end

%Stop the timer
endTime = clock();

%Print the results
printf("100! = %s\n", numString)
printf("The sum of the digits is: %d\n", sumOfNums)
printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime))

%{
100! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
The sum of the digits is: 648
It took 6.356117 seconds to run this algorithm
%}