numeric d;
numeric ratiox, ratioy;

def mycircle(expr x, y)=
draw (x-d,y)..(x,y+d)..(x+d,y)..(x,y-d)..cycle
enddef;

def myline(expr x, y, z, w) =
save ratioy, ratiox;
ratiox:=(z-x)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
ratioy:=(w-y)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
draw (x+d*ratiox,y+d*ratioy)--(z-d*ratiox,w-d*ratioy);
enddef;

def mybline(expr x, y, z, w) =
save ratioy, ratiox;
pickup pencircle scaled 1.5pt;
ratiox:=(z-x)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
ratioy:=(w-y)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
draw (x+d*ratiox,y+d*ratioy)--(z-d*ratiox,w-d*ratioy);
pickup pencircle scaled .5pt;
enddef;

def myarr(expr x, y, z, w) =
save ratioy, ratiox;
ratiox:=(z-x)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
ratioy:=(w-y)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
drawarrow (x+2*d*ratiox,y+2*d*ratioy)--(z-2*d*ratiox,w-2*d*ratioy);
enddef;

def xmark(expr s, x) =
draw (x,-dx)--(x,dx);
label.bot (s,(x,-dx));
enddef;

def ymark(expr s, x) =
draw (-dy,x)--(dy,x);
label.lft (s,(-dy,x));
enddef;

beginfig(1)

u:=0.5cm;
d:=0.05u;

ux:=1.5cm;
uy:=1.5cm;
%uy:=0.3cm;
dx:=0.06cm;
dy:=0.06cm;

numeric a[], b[];
numeric i;
numeric y;
numeric n;

y:=0.7;
n:=6;

%osi
drawarrow (-0.1ux,0)--(n*ux+.1ux,0);
drawarrow (0,-0.1uy)--(0,n*y*uy+.2uy);

%priamka
draw (0,0)--(n*ux,n*y*uy);


%labels
for i=1 upto n:
  draw (i*ux,-dx)--(i*ux,dx);
  label.bot (decimal(i),(i*ux,-dx));
endfor;
for i=1 upto (floor(n*y)):
  draw (-dy,i*uy)--(dy,i*uy);
  label.lft (decimal(i),(-dy,i*uy));
endfor;

  label.rt (btex $(n,ny)$ etex, (n*ux,n*y*uy));

pickup pencircle scaled 1pt;
%schody
for i=1 upto n:
  draw ((i-1)*ux,0)--((i-1)*ux,floor(y*i)*uy)--(i*ux,floor(y*i)*uy)--(i*ux,0);
endfor;

endfig;

beginfig(2)

u:=0.5cm;
d:=0.05u;

ux:=1.5cm;
uy:=1.5cm;
%uy:=0.3cm;
dx:=0.06cm;
dy:=0.06cm;

numeric a[], b[];
numeric i;
numeric y;
numeric n;

y:=0.7;
n:=6;



%priamka
draw (0,0)--(n*ux,n*y*uy);
fill (0,0)--(n*ux,n*y*uy)--(n*ux,0)--cycle withcolor 0.8white;
for i=1 upto n:
  fill ((i-1)*ux,0)--((i-1)*ux,floor(y*i)*uy)--(i*ux,floor(y*i)*uy)--(i*ux,0)--cycle withcolor white;
endfor;

%osi
drawarrow (-0.1ux,0)--(n*ux+.2ux,0);
drawarrow (0,-0.1uy)--(0,n*y*uy+.2uy);




%labels
for i=1 upto n:
  draw (i*ux,-dx)--(i*ux,dx);
  label.bot (decimal(i),(i*ux,-dx));
endfor;
for i=1 upto (floor(n*y)):
  draw (-dy,i*uy)--(dy,i*uy);
  label.lft (decimal(i),(-dy,i*uy));
endfor;

  label.rt (btex $(n,ny)$ etex, (n*ux,n*y*uy));

pickup pencircle scaled 1pt;
%schody
for i=1 upto n:
  draw ((i-1)*ux,0)--((i-1)*ux,floor(y*i)*uy)--(i*ux,floor(y*i)*uy)--(i*ux,0);
endfor;

endfig;


beginfig(3)

u:=0.5cm;
d:=0.05u;

ux:=1.5cm;
uy:=1.5cm;
%uy:=0.3cm;
dx:=0.06cm;
dy:=0.06cm;

numeric a[], b[];
numeric i;
numeric y;
numeric n;

y:=0.7;
n:=7;


%priamka
draw (0,0)--(n*ux,n*y*uy);
fill (0,0)--(n*ux,n*y*uy)--(n*ux,0)--cycle withcolor 0.8white;
for i=1 upto n:
  fill ((i-1)*ux,0)--((i-1)*ux,floor(y*i)*uy)--(i*ux,floor(y*i)*uy)--(i*ux,0)--cycle withcolor white;
endfor;

%osi
drawarrow (-0.1ux,0)--(n*ux+.2ux,0);
drawarrow (0,-0.1uy)--(0,n*y*uy+.2uy);

%convex hull
draw (0,0)--(1*ux,1*uy)--(2*ux,2*uy)--(4*ux,3*uy)--(5*ux,4*uy)--(7*ux,5*uy);


%labels
for i=1 upto n:
  draw (i*ux,-dx)--(i*ux,dx);
  label.bot (decimal(i),(i*ux,-dx));
endfor;
for i=1 upto (floor(n*y)):
  draw (-dy,i*uy)--(dy,i*uy);
  label.lft (decimal(i),(-dy,i*uy));
endfor;

  label.rt (btex $(n,ny)$ etex, (n*ux,n*y*uy));

pickup pencircle scaled 1pt;
%schody
for i=1 upto n:
  draw ((i-1)*ux,0)--((i-1)*ux,floor(y*i)*uy)--(i*ux,floor(y*i)*uy)--(i*ux,0);
endfor;

endfig;

\end