--------------------------------------------------
Question 1:
--------------------------------------------------
>>clear; syms x; a=solve(x^2+4)
a=
   2i
  -2i 

>>b = char('a' - 30)
b=
   C

>>ints = linspace(0,10,11);
>>c = sum(ints(mod(ints,2)==ones(1)))
c=
  25

>>data.s = { 'hi' };
>>data.s(2) = { data(1).s };
>>d = data.s{2}
d=
  'hi'


--------------------------------------------------
Question 2:
--------------------------------------------------
function stuff = prob2

% Solve for a root of x^4 - c1*x^2 -c2*x - c3

% Initialize Values

c1=5; c2=22.5; c3=1.5625;    % set constants in equation
eps = 0.001;                 % tolerance
inc = 1;                     % initial increment
maxiter = 1000;              % max iterations allowed
iters=0;                     % iterations so far

% Prompt user for initial value
% Ensure $x$ is positive and real

x = input('Enter initial value of pile depth: ');
while x <= 0 | ~isreal(x)    % while ~(x > 0 & isreal(x)) okay as well
     x = input('That value is "evil". Re-enter initial value of root: ');
end

% get initial value of $lhs$ to see if guess was good
lhs = rhs(x,c1,c2,c3);

while (abs(lhs) > eps) & (iters < maxiter)

   % decrease increment if sign changes
   if lhs*rhs(x+inc,c1,c2,c3) < 0
      inc=inc/10;
   end

   % update x, f(x), and iteration count
   x = x + inc;
   iters = iters + 1;
   lhs = rhs(x,c1,c2,c3);
end

if iters == maxiter
   disp('Too many iterations...restarting!');
   eval('prob2');       % Repeat the analysis
   return;              % return without passing values
end

% Store final value of root, value of f(x) for the root, and iterations
   stuff = [x lhs iters];

% Subfunction
function lhs = rhs(x,c1,c2,c3)
   %Computer left-hand side $lhs$ of equation
   lhs= x^4 - c1*x^2 - c2*x - c3;


--------------------------------------------------
Question 3:
--------------------------------------------------
function v = vec2set(v)
ii = 1;
while ii < length(v)
   firstelem = v(ii);
   rest_of_v = v(ii+1:end);
   rest_of_v = rest_of_v( firstelem ~= rest_of_v );
   v = [v(1:ii) rest_of_v];
   ii = ii + 1;
end


function result = set_union(x, y)
result = vec2set([x y]);


function result = set_intersect(x, y)
x = vec2set(x); y = vec2set(y);
ii = 1;
result = [];
while ii  <= length(x)
   if any(x(ii)==y)         % also acceptable: if sum(x(ii)==y)>0
      result = [result x(ii)];
   end
   ii = ii + 1;
end


% distribute.m
x = [1 2 3 1]; y = [2 2 4]; z = [0 2 1 3];

x = vec2set(x); y = vec2set(y); z = vec2set(z); 

LHS = set_union(x,set_intersect(y,z));
RHS = set_intersect(set_union(x,y),set_union(x,z));

if LHS==RHS
  disp('Success! The law worked. Hooray!');
else
  disp('Failure! The law failed. Bummer!');
end


--------------------------------------------------
Bonus Questions:
--------------------------------------------------
Bonus 1:
Daisy        Niranjan     Andy         Michael  
Rohit        Raju         Paradee      Maxim

Bonus 2:
>>data.s={'hi'};
>>data.s(2)={data(1).s};
>>sum(data.s{2}{1}(1:2))
ans =
     209

Bonus 3:
finds intersection of two vectors