//3-VARIABLE KMAP
//this function returns the a string containing the minimized expression for the given 3 variable kmap
//this function requires 
//noof.sci 
//noof0.sci
function bi = kmap3(k)
    n=4;
    m=2
k(:,:,2)=zeros(m,n);
    var=['Cn' 'Bn' 'An'];
    p1=['Cn''' 'Cn'];
    p2=['Bn''An''';'Bn''An';'BnAn';'BnAn'''];
    cmn4=4;
    cmn2=2;
    temp=1;
    disp(k(:,:,1));
bi = ' ';
//checking all the 8 1's cases 
    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
//checking all the 4 1's cases 
    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
    //checking all the 2 1's cases 
    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
    //checking if any single isolated 1's are left 
    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 "]);
endfunction