%% Lecture 7
%
% Last week.
% (lecture) functions that take the name of another function as an argument.
% (lab)     NIM

% This week, touching on NIM, and a key computer science topic: recursion,
%
% The game of NIM.  
%

% In the lab:  I asked you to write a "playGame" 

% function winner = playGame(strategy1, strategy2, n)
%  and this required a loop:
%
%  currentPlayer = 1;
%  while n > 1
%   if currentPlayer == 1
%      n = feval(strategy1,n);
%      currentPlayer = 2;
%   else
%      n = feval(strategy2,n);
%      currentPlayer = 1;
%   end
%  end

% instead, what if we take the more direct approach:

the first step is to just do strategy1 on n coins:

n = feval(strategy1,n);

then, we have a number of coins, 2 strategies.  
Wouldn't it be great if there was some way to compute 
    what else would happen?
    
    

function winner = playGame(strategy1, strategy2,n)
  if n == 1, winner = 2,
  else
      n = feval(strategy1,n);
      winner = 3-playGame(strategy2, strategy1, n);
  end
  
  % KEY is that the game must be the same.
  % and you must define the stopping condition.
  %   (usually best to work up!).

% Another game, Towers of Hanoi.
%
% Given the poles, and rings stacked in order of size on 1 pole,
%  how can we move them to be stacked in order on another pole, 
%   when we only move one at a time, and when a bigger ring can never 
%   be on top of a smaller one?

% Play the game w/ 4 rings?
%
%
Solve(N, Src, Aux, Dst)
    if N is 0 
      exit
    else
      Solve(N-1, Src, Dst, Aux)
      Move from Src to Dst
      Solve(N-1, Aux, Src, Dst)
      
% Now, think about poor Gauss, and what he is doing for this?