%----------------------------------------------------------------------------
% Exercise 1
% CS100M, due in lecture Tues 9/5
%----------------------------------------------------------------------------
% Follow the submission guidelines in the Exercises page on the
% website. Remember that these exercises are intended for practice and
% NOT points.
%----------------------------------------------------------------------------
% Part 1
% ------
% Write an algorithm for tying shoe laces. Assume the "user" of your
% algorithm is a very stupid robot "who" will do everything you command.
% You may use only English words. You don't have to go beserk with "code,"
% but you do have to be extremely explicit. The best algorithm (style, 
% content, look, approach, etc) will win a prize -- an autographed
% copy of my Unix textbook. However, I do ask that you allow your work
% to become publically available if you win.
%----------------------------------------------------------------------------
% Part 2
% ------
% Run the following code in MATLAB. You might discover some frustrating
% behavior. See if you can fix the code. Resubmit the corrected code
% with your changes highlighted. As part of the commentary, explain
% why you made the change(s). Feel free to enhance the code to add
% more features. Superior programs might earn bonus points.
%
% If you cannot spot the bug, don't worry. We'll give you full credit
% if you try. Be sure to explain what you tried in commentary, even if
% the approaches didn't work.
%----------------------------------------------------------------------------

%%%%%%%%%%%%%%%%%%%%
% Bisection method %
% 8/31/2001        %
% DIS              %
%%%%%%%%%%%%%%%%%%%%

% Note: I'm kind of throwing in comments.
% We'll show a better system for comment style later.
% To run,
% + set your path with the command window
% + enter $bisection$ after the prompt >>
%   (don't enter the $-signs -- I'm using them to indicate
%    command entry)
% The program will produce an answer printed in the command window.

% starting interval
right=5;
left=0;

% count on how many iterations to rech root
iterations = 0;

% coefficients for equation to solve: a2*x^2 + a1*x + a0 = 0
a0=4;
a1=-4;
a2=1;

% value that's "close enough" to zero
eps = 0.001;

% need value of function to get iteration going
f_mid = 1;

% the following loops solves for the root
while abs(f_mid - 0.0) > eps

    mid = (left + right)/2.0;
    f_left  = a2*left^2  + a1*left  + a0;
    f_right = a2*right^2 + a1*right + a0;
    f_mid   = a2*mid^2   + a1*mid   + a0;

    % Xm is to the left of root
      if f_mid * f_right < 0
         left = mid;

    % Xm is to the right of the root
      elseif f_mid * f_left < 0
         right = mid;

    % either finished or something is wrong
      else 
	  disp('done calculating')  
      end

    % increment count of iterations
      iterations = iterations + 1;
end

% print computed root
  disp( ['the root is ' num2str(mid)] )
  disp( ['done with ' num2str(iterations)] )