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Problem9.m

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+%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
+%}