import graph;

import graph;
unitsize(1cm);

real Floor(real x) {return floor(x);}

pair[] Close;
pair[] Open;

bool3 branch(real x) {
static real lasty;
static bool first=true;
real y=floor(x);
bool samebranch=first || lasty == y;
first=false;
if(samebranch) lasty=x;
else {
Close.push((x,lasty));
Open.push((x,y));
}
lasty=y;
return samebranch ? true : default;
};

draw(graph(Floor,-5.5,5.5,500,branch));
axes("$x$",rotate(0)*"$\lfloor x\rfloor$",red);

dot(Close);
dot(Open,UnFill);