twa_graph: add a merge_univ_dests() method

and call it after parsing

* spot/twa/twagraph.cc, spot/twa/twagraph.hh
(twa_graph::merge_univ_dests): New method.
* spot/parseaut/parseaut.yy: Call it.
* spot/twaalgos/dot.cc: Improve output, now that
several edges can use the same universal destination.
* tests/core/alternating.test, tests/core/complete.test,
tests/core/parseaut.test, tests/python/_altscc.ipynb,
tests/python/alternating.py, tests/python/alternation.ipynb: Adjust
test case.
* doc/org/tut24.org: Adjust example.

spot/parseaut/parseaut.yy

@@ -2423,6 +2423,8 @@ namespace spot
     fix_acceptance(r);
     fix_initial_state(r);
     fix_properties(r);
+    if (r.h->aut && r.h->aut->is_alternating())
+      r.h->aut->merge_univ_dests();
     return r.h;
   };
 

spot/twa/twagraph.cc

@@ -43,10 +43,66 @@ namespace spot
     delete namer;
   }
 
+    /// \brief Merge universal destinations
+    ///
+    /// If several states have the same universal destination, merge
+    /// them all.  Also remove unused destination, and any redundant
+    /// state in each destination.
+  void twa_graph::merge_univ_dests()
+  {
+    auto& g = get_graph();
+    auto& dests = g.dests_vector();
+    auto& edges = g.edge_vector();
+
+    std::vector<unsigned> old_dests;
+    std::swap(dests, old_dests);
+    std::vector<unsigned> seen(old_dests.size(), -1U);
+    std::map<std::vector<unsigned>, unsigned> uniq;
+
+    auto fixup = [&](unsigned& in_dst)
+      {
+        unsigned dst = in_dst;
+        if ((int) dst >= 0)       // not a universal edge
+          return;
+        dst = ~dst;
+        unsigned& nd = seen[dst];
+        if (nd == -1U)
+          {
+            std::vector<unsigned>
+              tmp(old_dests.data() + dst + 1,
+                  old_dests.data() + dst + 1 + old_dests[dst]);
+            std::sort(tmp.begin(), tmp.end());
+            tmp.erase(std::unique(tmp.begin(), tmp.end()), tmp.end());
+            auto p = uniq.emplace(tmp, 0);
+            if (!p.second)
+              {
+                nd = p.first->second;
+              }
+            else
+              {
+                nd = g.new_univ_dests(tmp.begin(), tmp.end());
+                p.first->second = nd;
+              }
+          }
+        in_dst = nd;
+      };
+
+    unsigned tend = edges.size();
+    for (unsigned t = 1; t < tend; t++)
+      {
+        if (g.is_dead_edge(t))
+          continue;
+        fixup(edges[t].dst);
+      }
+    fixup(init_number_);
+  }
+
   void twa_graph::merge_edges()
   {
     set_named_prop("highlight-edges", nullptr);
     g_.remove_dead_edges_();
+    if (is_alternating())
+      merge_univ_dests();
 
     typedef graph_t::edge_storage_t tr_t;
     g_.sort_edges_([](const tr_t& lhs, const tr_t& rhs)

spot/twa/twagraph.hh

@@ -521,6 +521,11 @@ namespace spot
     /// extremities and acceptance.
     void merge_edges();
 
+    /// \brief marge common universal destination
+    ///
+    /// This is already called by merge_edges().
+    void merge_univ_dests();
+
     /// \brief Remove all dead states
     ///
     /// Dead states are all the states that cannot be part of

spot/twaalgos/dot.cc

@@ -360,10 +360,14 @@ namespace spot
         return bdd_format_formula(aut_->get_dict(), label);
       }
 
+      std::set<int> done;
+
       void
       print_dst(int dst, const char* style = nullptr)
       {
-        os_ << "    " << dst << " [label=<>,width=0,height=0,shape=none]\n";
+        if (!done.emplace(dst).second)
+          return;
+        os_ << "    " << dst << " [label=<>,shape=point]\n";
         for (unsigned d: aut_->univ_dests(dst))
           {
             os_ << "    " << dst << " -> " << d;
@@ -465,7 +469,7 @@ namespace spot
           }
         else
           {
-            os_ << " [dir=none]\n";
+            os_ << " [arrowhead=onormal]\n";
             print_dst(init);
           }
       }
@@ -626,11 +630,10 @@ namespace spot
                 os_ << ", " << highlight;
               }
           }
-        // No arrow tip of the common part of a universal transition
-        if ((int)t.dst < 0)
-          os_ << ", dir=none";
+        if (aut_->is_univ_dest(t.dst))
+          os_ << ", arrowhead=onormal";
         os_ << "]\n";
-        if ((int)t.dst < 0)     // Universal destination
+        if (aut_->is_univ_dest(t.dst))
           print_dst(t.dst, highlight.c_str());
       }