%ProjectEuler/Octave/Problem9.m
%Matthew Ellison
% Created: 
%Modified: 03-28-19
%There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.
%{
	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/>.
%}


%Create the variable
a = 1;
b = 0;
c = 0;
found = false;

%Start the timer
startTime = clock();

%Start with the smallest possible a
while((a < 1000) && ~found)
	b = a + 1;	%b must be > a
	c = sqrt(a^2 + b^2);	%c^2 = a^2 + b^2
	%Loop through all possible b's. When the sum of a, b, c is > 1000. You done have the number. Try the next a
	while((a + b + c) < 1000)
		++b;
		c = sqrt(a^2 + b^2);
	end
	%If you haven't found the numbers yet, increment a and try again
	if((a + b + c) == 1000)
			found = true;
	else
		++a;
	end
end

%Stop the timer
endTime = clock();

%print the results
printf("The Pythagorean triplet where a + b + c = 1000 is %d %d %d\n", a, b, c)
printf("The product of those numbers is %d\n", a * b * c)
printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime))

%Cleanup the variables
clear a;
clear b;
clear c;
clear found;
clear startTime;
clear endTime;
clear ans;

%{
Results:
The Pythagorean triplet where a + b + c = 1000 is 200 375 425
The product of those numbers is 31875000
It took 0.573143 seconds to run this algorithm
%}