function NewQas=UpdateQ(JStartEnd,Qas,MoveVec)



%   This program updates the value table (as it depends on possible plays)
%
%   PlayNim also includes definitions of JStartEnd and Qas
% Input:
%     MoveVec: is the sequence of board positions that comprised the game.
%             Each element is an integer index which yields the state
%           of the game and can be found in NimScript.m
%            as NimColumn{CurrentBoardPosition}.

%     JStartEnd: This is comprised of rows of two elements indicating all the possible
%         transitions in the game. A typical row might be  [1 4] indicating that
%             one can move from board position 1 to board 4. It represents
%             the topology of the game.
%
%     Qas: This is comprised of rows of two elements. The first element of
%            each is the value of the corresponding row of JStartEnd.
%           The second element represents the number of times that the
%           choice  given by the row JStartEnd has been taken.
%
% Output:
%
%    NewQas is the updated version of the values, after compensating for the last
%                   round of rewards
%
%%     Algorithm   is of the TD type
%
%     Q_k+1=Q_k+alpha(r-Q_k)
%
%    r is the reward that is eventually delivered
%      at present: there is no discounting
%
%       I have made the reward so that the last move is a loser (-1),
%                       next to last is a winner(+1), next to next to last
%                       is loser, .... etc
%
%       This is created in the array ToAdd
%
%    alpha is  the learning rate;

%% Take MoveVec and write it as pairs ==>     MoveStartEnd
%   Create Reward vector              ==>     ToAdd
alpha=.1;
sMoveVec= length(MoveVec);
for j=2:sMoveVec
    MoveStartEnd(j-1,1:2)= [MoveVec(j-1), MoveVec(j)];   % This is a table of the moves
    ToAdd(j-1) = (-1)^(sMoveVec-j+1);                    % This is the undiscounted reward
end

%%
%   Add a weigthed version of ToAdd (average it in) to the old state values
%     to get the new state values
%
%  the more the value TDError below is non-zero, the more that learning is
%      taking place
%
sMoveStartEnd= length(MoveStartEnd);
NewQas= Qas;                    %  The new  values

for j=1:sMoveStartEnd
    Start = MoveStartEnd(j,1); %
    End   = MoveStartEnd(j,2); % Look for these in Qas

    MoveInd = find( (JStartEnd(:,1)== Start) & (JStartEnd(:,2)== End));
    NumAlreadyp1 = Qas(MoveInd,2)+1;

    TDError = ToAdd(j)-Qas(MoveInd,1);                             % CHANGE ME

    MoveNxtInd = find( JStartEnd(:,1)== End);

    if length(MoveNxtInd)>0
        TDError= -max(Qas(MoveNxtInd,1)) -Qas(MoveInd,1);          % CHANGE ME
    end
    
    NewQas(MoveInd,1) = NewQas(MoveInd,1) + (1/NumAlreadyp1)*TDError;   % CHANGE ME
    
    NewQas(MoveInd,2)=  NumAlreadyp1;    % update the number of times this move was made
end


% NewQas= Qas + alpha*(ToAdd-Qas);
%%