//3-VARIABLE KMAP
//uses noof.sci and noof0.sci
//above two functions should be executed before executing this function .
function bi = kmap3abx(k)
    n=4;
    m=2

//k=[0 0 0 1;
  // 0 1 1 1];
k(:,:,2)=zeros(m,n);
    var=['x' 'A' 'B'];
    //var=['w' 'x' 'y' 'z'];
    p1=['x''' 'x'];
    p2=['A''B''';'A''B';'AB';'AB'''];
    cmn4=4;
    cmn2=2;
    temp=1;
   // printf('The minimal ecpression of the given Kmap ');
    disp(k(:,:,1));
    //disp("is :");
    //printf('f');
   // printf("=");
 
 bi = ' ';
    //8 cells
    for i=1:m        
        for j=1:n
            if(k(i,j)~=1 & k(i,j)~=2)
                temp=0;
                break;
             end
        end
    end
    if(temp==1)
        bi = strcat([bi "1"]);
        return;
    end
    //4 cells
    z1=ones(1,4);
    z2=ones(4,1);
    z3=ones(2,2);
    temp1=['0' '1'];
    temp2=['00';'01';'11';'10'];
    for t=1:m
            z=k(t,:,1);
            no=noof(k(t,:,2));
            if(noof0(z)==0 & no<cmn4 & noof(z)>0)
                k(t,:,2)=z1;
                a=strsplit(temp1(1,t));
                for in=1:max(size(a))
                    if(a(in)=='0')
                        bi = strcat([bi var(in) '''']);
                     end
                     if(a(in)=='1')
                         bi = strcat([bi var(in)]);
                     end
                 end
                 bi = strcat([bi " + "]);
              end
    end
    for i=1:m-1
        for j=1:n
           t1=i+1;
           if(j==n)
                t2=1;
            else
                t2=j+1;
            end
            z4=[k(i,j,1) k(i,t2,1);k(t1,j,1) k(t1,t2,1)];
            z5=[k(i,j,2) k(i,t2,2);k(t1,j,2) k(t1,t2,2)];
            no=noof(z5);
            if(noof0(z4)==0 & no<cmn4 & noof(z4)>0)
                k(i,j,2)=1;
                k(i,t2,2)=1;
                k(t1,j,2)=1;
                k(t1,t2,2)=1;
                a=strsplit(temp2(j,1));
                b=strsplit(temp2(t2,1));
                c=strcmp(a,b);
                for in=1:max(size(c))
                    if(c(in)==0 & a(in)=='0')
                        bi = strcat([bi var(1+in) '''' ]);
                     end
                     if(c(in)==0 & a(in)=='1')
                         bi = strcat([bi var(1+in)]);
                     end
                 end
                 bi = strcat([bi " + "]);

            end
        end
    end
    //2 cells
    z6=[1 1];
    z7=z6';
    for i=1:m
        for j=1:n
                t1=i+1;
                if(j==n)
                    t2=1;
                else
                    t2=j+1;
                 end
            z8=[k(i,j,1) k(i,t2,1)];
            z9=[k(i,j,2) k(i,t2,2)];
            no1=noof(z9);
            if(noof0(z8)==0 & no1<cmn2 & noof(z8)>0)
              k(i,j,2)=1;
              k(i,t2,2)=1;
              bi = strcat([bi p1(1,i)]);
              a=strsplit(temp2(j,1));
              b=strsplit(temp2(t2,1));
              c=strcmp(a,b);
                for in=1:max(size(c))
                    if(c(in)==0 & a(in)=='0')
                        bi = strcat([bi var(1+in) '''']);
                        bi = strcat([bi " + "]);
                     end
                     if(c(in)==0 & a(in)=='1')
                         bi = strcat([bi var(1+in)]);
                           bi = strcat([bi " + "]);
                     end
                 end
            end
        end
    end
    for i=1:m-1
        for j=1:n
           t1=i+1;
           if(j==n)
                t2=1;
            else
                t2=j+1;
            end
            z10=[k(i,j,1);k(t1,j,1)];
            z11=[k(i,j,2);k(t1,j,2)];
            no2=noof(z11);
            if(noof0(z10)==0 & no2<cmn2 & noof(z10)>0)
              k(i,j,2)=1;
              k(t1,j,2)=1;
              bi = strcat([bi p2(j,1)]);
              bi = strcat([bi " + "]);
            end
        end
    end
    //single cell
    for i=1:m
        for j=1:n
            if(k(i,j,2)==0 & k(i,j,1)==1)
                bi = strcat([bi p1(1,i)]);
                bi = strcat([bi p2(j,1)]);
                bi = strcat([bi " + "]);
            end
        end
    end
   bi = strcat([bi " 0 "]);
    //disp(" ")

endfunction