% part_c
%
% Estimates the expected return times to state i for n=5,i =1,2,3,4,5


function return_times = part_c(number_of_iterations)
% Input Variables
%   number_of_iterations	Number of times to run to find return time

% Initialize
estimate = 0;
return_times = zeros(5,1);

% Run for i = 1,2,3,4,5
for i = 1:5
  for loop = 1:number_of_iterations
    x = i;  % start at state i
    u = rand(1);  % Generate a uniform random variable
    x = part_a(x,u,5);  % take a step in the Markov chain
    estimate = estimate + 1;
    while (x ~= i)
      u = rand(1);  % Generate a uniform random variable
      x = part_a(x,u,5);  % take a step in the Markov chain
      estimate = estimate + 1;
    end
  end
  return_times(i) = estimate / number_of_iterations;
end