Day 3.1

% First star
% I think I found a pretty little solution for the first star where I
% avoid doing a lot of matrix manuevering.
% Because the squares of numbers follow two separate diagonal lines
% throughout the grid, I can deduce where my input number is located.
% Afterwards a little addition/subtraction is needed to calculate the
% manhatten distance to the center of the grid.

input = 347991;

% Square number counter
x = 0;
while x^2 < input
    x = x + 1;
end

x = x - 1;

if mod(x,2) == 1
    if (x+1)^2 - input == input - (x^2+1)
        steps = x + 1;
    elseif (x+1)^2 - input < input - (x^2+1)
        row = abs(((x+1)^2 - (x-1)/2) - input);
        steps = (x+1)/2 + row;
    else
        col = abs((x^2+1 + (x-1)/2) - input);
        steps = (x+1)/2 + col;
    end
else
    if (x+1)^2 - input == input - (x^2+1)
        steps = x;
    elseif (x+1)^2 - input < input - (x^2+1)
        row = abs(((x+1)^2 - x/2) - input);
        steps = x/2 + row;
    else
        col = abs((x^2+1 + x/2) - input);
        steps = x/2 + col;
    end
end

fprintf('Number of steps: %d\n',steps)