$title Use of dynamics sets, predecessor, successor graphs

set nodes /1*7/;
alias (i,j,nodes);

* note that pred is a 2D static set
set pred(i,j) 'i is the predecessor of j' /
    1.2*3
    2.5
    3.4
    4.5
    5.6*7
    /;

option pred:0:0:1;
display pred;

set succ(i,j) 'i is the successor of j';

succ(i,j) = yes$pred(j,i);
* note that succ is a dynamic 2D set

* generate a 1D dynamic set whose elements are the leaves of the graph
set leaves(i) 'nodes that have no successor';
leaves(i) = yes;
loop(succ(i,j),
  leaves(j) = no;
  );
* can do this just using pred

* generate a 1D dynamic set whose elements are the roots of the graph
set roots(i) 'nodes that have no predecessor';
roots(i) = yes;
loop(pred(i,j),
  roots(j) = no;
  );

if (card(roots) gt 0,
  display roots;
else
  display 'error: must have at least one root';
);