function Nim3PilesFun(N1,N2,N3)
% This is a function for 3 piles Nim game. 
% N1, N2, N3 are original numbers of objects in each pile.
% Player can take any number of objects from one pile.
% The player who takes the last object lose. 
disp ('   ');
disp('************ Game Start ***********');
disp(' ');
fprintf('***** You can remove any number of objects from one pile *****');
disp(' ');
disp('***** The player who takes the last object win. *****');
disp('***** Enter -1 to end the game. *****');
fprintf('The original piles are [%i,%i,%i]', N1,N2,N3);
disp ('   ');
% set current number of objects in the pile 
C1 = N1;
C2 = N2;
C3 = N3;
while (C1>0 || C2>0 || C3>0 )
    % player move
    P = input('Please enter your move (for example use [3,5,6] to indicate your move)? '); % player's move
    if(P == -1)%quit the game by player
        C1=0;
        C2=0;
        C3=0;
    else
        if (P(1)> C1 || P(2)> C2 || P(3)> C3) %enter any number more than existing objects in the pile
            disp('Illegal move! You can not remove more objects than what in the pile');
        else
            
            C1 = P(1);
            C2 = P(2);
            C3 = P(3);
          
            if( C1==0 && C2==0 && C3==0) % player made the last move
                 disp('You made the last move. You won!'); 
            else % computer need to make a move
                
                if(C1==0 && C2==0) % if only one pile left, take all objects from the pile
                     C3=0;
                elseif(C2==0 && C3==0) 
                     C1=0;
                elseif(C1==0 && C3==0) 
                     C2=0;
                else  % if there is more than one piles left,    
                     
                    [R1,R2,R3] = NimSum(C1,C2,C3);
                    C1= bin2dec(R1);
                    C2= bin2dec(R2);
                    C3= bin2dec(R3);
       
                end
                 %after computer move
                if(C1==0 && C2==0 && C3==0)
                   disp('Computer made the last move. Computer won!');
                else
                    fprintf('The computer made a move and the remaining piles are [%i,%i,%i]', C1,C2,C3);
                    disp(' ');
                end
            end
        end
    end   
    
end  

function [r1,r2,r3] = NimSum(c1,c2,c3)
b1 = dec2bin(c1);
b2 = dec2bin(c2);
b3 = dec2bin(c3);

a = fliplr(b1);
b = fliplr(b2);
c = fliplr(b3);
La = length(a);
Lb = length(b);
Lc = length(c);
L = max(La,max(Lb,Lc));
Lmin = min(La,min(Lb,Lc));
S = size(L);
M = size(L);

for i=L:-1:1
    Ea = GetElement(a,La,i);
    Eb = GetElement(b,Lb,i);
   Ec = GetElement(c,Lc,i);
     
    S(i) = Ea+ Eb+Ec;
    
    if ( mod(S(i),2) ~= 0)
        M(i)=1;
    else
        M(i)=0;
    end
    
end  

Msum=0;
for i=L:-1:1
    Msum=Msum+ M(i); 
end

changed=0;
if (Msum ~= 0) %N Position, can force to P position
  for l=L:-1:Lmin  % start with number with largest number
    if(La == l && changed==0)
        [a,changed] = RemoveObjects(a,l,M);
    end     
    if(changed==0 && Lb == l)
        [b,changed]  = RemoveObjects(b,l,M);
    end      
    if(changed==0 && Lc == l )
        [c,changed] = RemoveObjects(c,l,M);
    end
    
  end  
    r1 = fliplr(a);
    r2 = fliplr(b);
    r3 = fliplr(c);
    
else % at P postion and make any move
    if(c1~=0 && changed ==0)
        if(c1 > 1)
            r1= dec2bin(c1-randi(c1-1));
        else
            r1= '0';
        end    
        r2=b2;
        r3=b3
    elseif(c2~=0 && changed ==0)
        if(c2>1)
            r2= dec2bin(c2-randi(c2-1));
        else
            r2='0';
        end    
        r1=b1;
        r3=b3;
    elseif(c3~=0 && changed ==0)
        if(c3>1)
            r3= dec2bin(c3-randi(c3-1));
        else
            r3='0';
        end    
        r1=b1;
        r2=b2;   
    end
        
end



   %nested function
    function e= GetElement(x,L,i)
        if(i<=L)
           e = str2double(x(i));
        else 
           e =str2double('0');
        end   
        
    end
    function [r, changed]= RemoveObjects(x,L,m)
         r=size(L);
         removed=0;
         changed=0;
         for j=L:-1:1 
              y= str2double(x(j));
            if (m(j)==1 && y==1)
                x(j)= '0';
                removed=1;
                changed=1;
            elseif( j<L && m(j)==1 && y==0 && removed == 1 )   
                x(j)='1';
                changed=1;
             
            end
         end  
         r=x;
         
    end
    
end
end