lib/graph: add `Digraph::eulerian_path`

Signed-off-by: Jean Privat <jean@pryen.org>

diff --git a/lib/graph/digraph.nit b/lib/graph/digraph.nit
index e6af185..e574dc4 100644 (file)
--- a/lib/graph/digraph.nit
+++ b/lib/graph/digraph.nit
@@ -506,6 +506,22 @@ interface Digraph[V: Object]
                end
        end
 
+       # Build a path (or circuit) from the vertex `start` that visits every edge exactly once.
+       #
+       # ~~~
+       # var g = new HashDigraph[Int]
+       # g.add_arc(1, 2)
+       # g.add_arc(2, 3)
+       # g.add_arc(3, 4)
+       # assert g.eulerian_path(1) == [1, 2, 3, 4]
+       # ~~~
+       fun eulerian_path(start: V): Array[V]
+       do
+               var visited = new HashDigraph[V]
+               visited.add_graph(self)
+               return visited.remove_eulerian_path(start)
+       end
+
        # Returns the distance between `u` and `v`
        #
        # If no path exists between `u` and `v`, it returns null. It is not
@@ -823,6 +839,29 @@ abstract class MutableDigraph[V: Object]
                        end
                end
        end
+
+       # Build a path (or circuit) that removes every edge exactly once.
+       #
+       # See `eulerian_path` for details
+       fun remove_eulerian_path(start: V): Array[V]
+       do
+               var stack = new Array[V]
+               var path = new Array[V]
+               var current = start
+               loop
+                       if out_degree(current) == 0 then
+                               path.unshift current
+                               if stack.is_empty then break
+                               current = stack.pop
+                       else
+                               stack.add current
+                               var n = successors(current).first
+                               remove_arc(current, n)
+                               current = n
+                       end
+               end
+               return path
+       end
 end
 # A directed graph represented by hash maps
 class HashDigraph[V: Object]