usepackage("amsmath");
import graph;
size(8cm,0);

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

pair[] ListeDesPointsCompris;
pair[] ListeDesPointsExclus;

//==================
// bool3 est un booléen à trois états : true, default et false
bool3 TestRelierOuPas(real x) {
  static real lasty;
  static bool first = true;
  real y = floor(x);
  bool memebranche = first || lasty == y;
  first = false;
  if(!memebranche) { ListeDesPointsExclus.push((x,lasty));
                     ListeDesPointsCompris.push((x,y));
                   }
  lasty=y;
  return memebranche ? true : default;
};
//==================

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

dot(ListeDesPointsCompris);
dot(ListeDesPointsExclus,UnFill);