%ProjectEuler/Problem9.m
%This is a script to answer Problem 9 for Project Euler
%There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

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

%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) && ~found)
		%If the sum == 1000 you found the numbers
		if((a + b + c) == 1000)
			found = true;
		%Otherwise try the next b and recalculate c
		else
			++b;
			c = sqrt(a^2 + b^2);
		end
	end
	%If you haven't found the numbers yet, increment a and try again
	if(~found)
		++a;
	end
end

%print the result
a * b * c

%Cleanup the variables
clear a;
clear b;
clear c;
clear found;