--- /dev/null
+# This file is part of NIT (http://www.nitlanguage.org).
+#
+# Copyright 2015 Alexandre Blondin Massé <blondin_masse.alexandre@uqam.ca>
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# Implementation of directed graphs, also called digraphs.
+#
+# Overview
+# ========
+#
+# This module provides a simple interface together with a concrete
+# implementation of directed graphs (or digraphs).
+#
+# The upper level interface is `Digraph` and contains all methods for digraphs
+# that do not depend on the underlying data structure. More precisely, if basic
+# operations such as `predecessors`, `successors`, `num_vertices`, etc. are
+# implemented, then high level operations (such as computing the connected
+# components or a shortest path between two vertices) can be easily derived.
+# Also, all methods found in `Digraph` do no modify the graph. For mutable
+# methods, one needs to check the `MutableDigraph` child class. Vertices can be
+# any `Object`, but there is no information stored in the arcs, which are
+# simple arrays of the form `[u,v]`, where `u` is the source of the arc and `v`
+# is the target.
+#
+# There is currently only one concrete implementation named `HashDigraph` that
+# makes use of the HashMap class for storing the predecessors and successors.
+# It is therefore simple to provide another implementation: One only has to
+# create a concrete specialization of either `Digraph` or `MutableDigraph`.
+#
+# Basic methods
+# =============
+#
+# To create an (empty) new graph whose keys are integers, one simply type
+# ~~~
+# import digraph
+# var g = new HashDigraph[Int]
+# ~~~
+#
+# Then we can add vertices and arcs. Note that if an arc is added whose source
+# and target are not already in the digraph, the vertices are added beforehand.
+# ~~~
+# import digraph
+# var g = new HashDigraph[Int]
+# g.add_vertex(0)
+# g.add_vertex(1)
+# g.add_arc(0,1)
+# g.add_arc(1,2)
+# assert g.to_s == "Digraph of 3 vertices and 2 arcs"
+# ~~~
+#
+# One might also create digraphs with strings in vertices, for instance to
+# represent some directed relation. However, it is currently not possible to
+# store values in the arcs.
+# ~~~
+# import digraph
+# var g = new HashDigraph[String]
+# g.add_vertex("Amy")
+# g.add_vertex("Bill")
+# g.add_vertex("Chris")
+# g.add_vertex("Diane")
+# g.add_arc("Amy", "Bill") # Amy likes Bill
+# g.add_arc("Bill", "Amy") # Bill likes Amy
+# g.add_arc("Chris", "Diane") # and so on
+# g.add_arc("Diane", "Amy") # and so on
+# ~~~
+#
+# `HashDigraph`s are mutable, i.e. one might remove arcs and/or vertices:
+# ~~~
+# import digraph
+# var g = new HashDigraph[Int]
+# g.add_arc(0,1)
+# g.add_arc(0,2)
+# g.add_arc(1,2)
+# g.add_arc(2,3)
+# g.add_arc(2,4)
+# g.remove_vertex(1)
+# g.remove_arc(2, 4)
+# assert g.to_s == "Digraph of 4 vertices and 2 arcs"
+# ~~~
+#
+# If one has installed [Graphviz](http://graphviz.org), it is easy to produce a
+# *dot* file which Graphviz process into a picture:
+# ~~~
+# import digraph
+# var g = new HashDigraph[Int]
+# g.add_arcs([[0,1],[0,2],[1,2],[2,3],[2,4]])
+# print g.to_dot
+# # Then call "dot -Tpng -o graph.png"
+# ~~~
+#
+# 
+#
+# Other methods
+# =============
+#
+# There exist other methods available for digraphs and many other will be
+# implemented in the future. For more details, one should look at the methods
+# directly. For instance, the [strongly connected components]
+# (https://en.wikipedia.org/wiki/Strongly_connected_component) of a digraph are
+# returned as a [disjoint set data structure]
+# (https://en.wikipedia.org/wiki/Disjoint-set_data_structure) (i.e. a set of
+# sets):
+# ~~~
+# import digraph
+# var g = new HashDigraph[Int]
+# g.add_arcs([[1,2],[2,1],[2,3],[3,4],[4,5],[5,3]])
+# for component in g.strongly_connected_components.to_partitions
+# do
+# print component
+# end
+# # Prints [1,2] and [3,4,5]
+# ~~~
+#
+# It is also possible to compute a shortest (directed) path between two
+# vertices:
+# ~~~
+# import digraph
+# var g = new HashDigraph[Int]
+# g.add_arcs([[1,2],[2,1],[2,3],[3,4],[4,5],[5,3]])
+# var path = g.a_shortest_path(2, 4)
+# if path != null then print path else print "No path"
+# # Prints [2,3,4]
+# path = g.a_shortest_path(4, 2)
+# if path != null then print path else print "No path"
+# # Prints "No path"
+# ~~~
+#
+# Extending the library
+# =====================
+#
+# There are at least two ways of providing new methods on digraphs. If the
+# method is standard and could be useful to other users, you should consider
+# including your implementation directly in this library.
+#
+# Otherwise, for personal use, you should simply define a new class inheriting
+# from `HashDigraph` and add the new services.
+module digraph
+
+# Interface for digraphs
+interface Digraph[V: Object]
+
+ ## ---------------- ##
+ ## Abstract methods ##
+ ## ---------------- ##
+
+ # The number of vertices in this graph.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_vertex(0)
+ # g.add_vertex(1)
+ # assert g.num_vertices == 2
+ # g.add_vertex(0)
+ # assert g.num_vertices == 2
+ # ~~~
+ fun num_vertices: Int is abstract
+
+ # The number of arcs in this graph.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(0, 1)
+ # assert g.num_arcs == 1
+ # g.add_arc(0, 1)
+ # assert g.num_arcs == 1
+ # g.add_arc(2, 3)
+ # assert g.num_arcs == 2
+ # ~~~
+ fun num_arcs: Int is abstract
+
+ # Returns true if and only if `u` exists in this graph.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_vertex(1)
+ # assert g.has_vertex(1)
+ # assert not g.has_vertex(0)
+ # g.add_vertex(1)
+ # assert g.has_vertex(1)
+ # assert not g.has_vertex(0)
+ # ~~~
+ fun has_vertex(u: V): Bool is abstract
+
+ # Returns true if and only if `(u,v)` is an arc in this graph.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(0, 1)
+ # g.add_arc(1, 2)
+ # assert g.has_arc(0, 1)
+ # assert g.has_arc(1, 2)
+ # assert not g.has_arc(0, 2)
+ # ~~~
+ fun has_arc(u, v: V): Bool is abstract
+
+ # Returns the predecessors of `u`.
+ #
+ # If `u` does not exist, then it returns null.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(0, 1)
+ # g.add_arc(1, 2)
+ # g.add_arc(0, 2)
+ # assert g.predecessors(2).has(0)
+ # assert g.predecessors(2).has(1)
+ # assert not g.predecessors(2).has(2)
+ # ~~~
+ fun predecessors(u: V): Collection[V] is abstract
+
+ # Returns the successors of `u`.
+ #
+ # If `u` does not exist, then an empty collection is returned.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(0, 1)
+ # g.add_arc(1, 2)
+ # g.add_arc(0, 2)
+ # assert not g.successors(0).has(0)
+ # assert g.successors(0).has(1)
+ # assert g.successors(0).has(2)
+ # ~~~
+ fun successors(u: V): Collection[V] is abstract
+
+ # Returns an iterator over the vertices of this graph.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(0, 1)
+ # g.add_arc(0, 2)
+ # g.add_arc(1, 2)
+ # var vs = new HashSet[Int]
+ # for v in g.vertices_iterator do vs.add(v)
+ # assert vs == new HashSet[Int].from([0,1,2])
+ # ~~~
+ fun vertices_iterator: Iterator[V] is abstract
+
+ ## -------------------- ##
+ ## Non abstract methods ##
+ ## -------------------- ##
+
+ ## ------------- ##
+ ## Basic methods ##
+ ## ------------- ##
+
+ # Returns true if and only if this graph is empty.
+ #
+ # An empty graph is a graph without vertex and arc.
+ #
+ # ~~~
+ # import digraph
+ # assert (new HashDigraph[Int]).is_empty
+ # ~~~
+ fun is_empty: Bool do return num_vertices == 0 and num_arcs == 0
+
+ # Returns an array containing the vertices of this graph.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_vertices([0,2,4,5])
+ # assert g.vertices.length == 4
+ # ~~~
+ fun vertices: Array[V] do return [for u in vertices_iterator do u]
+
+ # Returns an iterator over the arcs of this graph
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(0, 1)
+ # g.add_arc(0, 2)
+ # g.add_arc(1, 2)
+ # for arc in g.arcs_iterator do
+ # assert g.has_arc(arc[0], arc[1])
+ # end
+ # ~~~
+ fun arcs_iterator: Iterator[Array[V]] do return new ArcsIterator[V](self)
+
+ # Returns the arcs of this graph.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 3)
+ # g.add_arc(2, 3)
+ # assert g.arcs.length == 2
+ # ~~~
+ fun arcs: Array[Array[V]] do return [for arc in arcs_iterator do arc]
+
+ # Returns the incoming arcs of vertex `u`.
+ #
+ # If `u` is not in this graph, an empty array is returned.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 3)
+ # g.add_arc(2, 3)
+ # for arc in g.incoming_arcs(3) do
+ # assert g.is_predecessor(arc[0], arc[1])
+ # end
+ # ~~~
+ fun incoming_arcs(u: V): Collection[Array[V]]
+ do
+ if has_vertex(u) then
+ return [for v in predecessors(u) do [v, u]]
+ else
+ return new Array[Array[V]]
+ end
+ end
+
+ # Returns the outgoing arcs of vertex `u`.
+ #
+ # If `u` is not in this graph, an empty array is returned.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 3)
+ # g.add_arc(2, 3)
+ # g.add_arc(1, 2)
+ # for arc in g.outgoing_arcs(1) do
+ # assert g.is_successor(arc[1], arc[0])
+ # end
+ # ~~~
+ fun outgoing_arcs(u: V): Collection[Array[V]]
+ do
+ if has_vertex(u) then
+ return [for v in successors(u) do [u, v]]
+ else
+ return new Array[Array[V]]
+ end
+ end
+
+ ## ---------------------- ##
+ ## String representations ##
+ ## ---------------------- ##
+
+ redef fun to_s
+ do
+ var vertex_word = "vertices"
+ var arc_word = "arcs"
+ if num_vertices <= 1 then vertex_word = "vertex"
+ if num_arcs <= 1 then arc_word = "arc"
+ return "Digraph of {num_vertices} {vertex_word} and {num_arcs} {arc_word}"
+ end
+
+ # Returns a GraphViz string representing this digraph.
+ fun to_dot: String
+ do
+ var s = "digraph \{\n"
+ # Writing the vertices
+ for u in vertices_iterator do
+ s += " \"{u.to_s.escape_to_dot}\" "
+ s += "[label=\"{u.to_s.escape_to_dot}\"];\n"
+ end
+ # Writing the arcs
+ for arc in arcs do
+ s += " {arc[0].to_s.escape_to_dot} "
+ s += "-> {arc[1].to_s.escape_to_dot};"
+ end
+ s += "\}"
+ return s
+ end
+
+ ## ------------ ##
+ ## Neighborhood ##
+ ## ------------ ##
+
+ # Returns true if and only if `u` is a predecessor of `v`.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 3)
+ # assert g.is_predecessor(1, 3)
+ # assert not g.is_predecessor(3, 1)
+ # ~~~
+ fun is_predecessor(u, v: V): Bool do return has_arc(u, v)
+
+ # Returns true if and only if `u` is a successor of `v`.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 3)
+ # assert not g.is_successor(1, 3)
+ # assert g.is_successor(3, 1)
+ # ~~~
+ fun is_successor(u, v: V): Bool do return has_arc(v, u)
+
+ # Returns the number of arcs whose target is `u`.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 3)
+ # g.add_arc(2, 3)
+ # assert g.in_degree(3) == 2
+ # assert g.in_degree(1) == 0
+ # ~~~
+ fun in_degree(u: V): Int do return predecessors(u).length
+
+ # Returns the number of arcs whose source is `u`.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 2)
+ # g.add_arc(1, 3)
+ # g.add_arc(2, 3)
+ # assert g.out_degree(3) == 0
+ # assert g.out_degree(1) == 2
+ # ~~~
+ fun out_degree(u: V): Int do return successors(u).length
+
+ # ------------------ #
+ # Paths and circuits #
+ # ------------------ #
+
+ # Returns true if and only if `vertices` is a path of this digraph.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 2)
+ # g.add_arc(2, 3)
+ # g.add_arc(3, 4)
+ # assert g.has_path([1,2,3])
+ # assert not g.has_path([1,3,3])
+ # ~~~
+ fun has_path(vertices: SequenceRead[V]): Bool
+ do
+ for i in [0..vertices.length - 1[ do
+ if not has_arc(vertices[i], vertices[i + 1]) then return false
+ end
+ return true
+ end
+
+ # Returns true if and only if `vertices` is a circuit of this digraph.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 2)
+ # g.add_arc(2, 3)
+ # g.add_arc(3, 1)
+ # assert g.has_circuit([1,2,3,1])
+ # assert not g.has_circuit([1,3,2,1])
+ # ~~~
+ fun has_circuit(vertices: SequenceRead[V]): Bool
+ do
+ return vertices.is_empty or (has_path(vertices) and vertices.first == vertices.last)
+ end
+
+ # Returns a shortest path from vertex `u` to `v`.
+ #
+ # If no path exists between `u` and `v`, it returns `null`.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 2)
+ # g.add_arc(2, 3)
+ # g.add_arc(3, 4)
+ # assert g.a_shortest_path(1, 4).length == 4
+ # g.add_arc(1, 3)
+ # assert g.a_shortest_path(1, 4).length == 3
+ # assert g.a_shortest_path(4, 1) == null
+ # ~~~
+ fun a_shortest_path(u, v: V): nullable Sequence[V]
+ do
+ var queue = new List[V].from([u]).as_fifo
+ var pred = new HashMap[V, nullable V]
+ var visited = new HashSet[V]
+ var w: nullable V = null
+ pred[u] = null
+ while not queue.is_empty do
+ w = queue.take
+ if not visited.has(w) then
+ visited.add(w)
+ if w == v then break
+ for wp in successors(w) do
+ if not pred.keys.has(wp) then
+ queue.add(wp)
+ pred[wp] = w
+ end
+ end
+ end
+ end
+ if w != v then
+ return null
+ else
+ var path = new List[V]
+ path.add(v)
+ w = v
+ while pred[w] != null do
+ path.unshift(pred[w].as(not null))
+ w = pred[w]
+ end
+ return path
+ end
+ end
+
+ # Returns the distance between `u` and `v`
+ #
+ # If no path exists between `u` and `v`, it returns null. It is not
+ # symmetric, i.e. we may have `dist(u, v) != dist(v, u)`.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 2)
+ # g.add_arc(2, 3)
+ # g.add_arc(3, 4)
+ # assert g.distance(1, 4) == 3
+ # g.add_arc(1, 3)
+ # assert g.distance(1, 4) == 2
+ # assert g.distance(4, 1) == null
+ # ~~~
+ fun distance(u, v: V): nullable Int
+ do
+ var queue = new List[V].from([u]).as_fifo
+ var dist = new HashMap[V, Int]
+ var visited = new HashSet[V]
+ var w: nullable V
+ dist[u] = 0
+ while not queue.is_empty do
+ w = queue.take
+ if not visited.has(w) then
+ visited.add(w)
+ if w == v then break
+ for wp in successors(w) do
+ if not dist.keys.has(wp) then
+ queue.add(wp)
+ dist[wp] = dist[w] + 1
+ end
+ end
+ end
+ end
+ return dist.get_or_null(v)
+ end
+
+ # -------------------- #
+ # Connected components #
+ # -------------------- #
+
+ # Returns the weak connected components of this digraph.
+ #
+ # The weak connected components of a digraph are the usual
+ # connected components of its associated undirected graph,
+ # i.e. the graph obtained by replacing each arc by an edge.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 2)
+ # g.add_arc(2, 3)
+ # g.add_arc(4, 5)
+ # assert g.weakly_connected_components.number_of_subsets == 2
+ # ~~~
+ fun weakly_connected_components: DisjointSet[V]
+ do
+ var components = new DisjointSet[V]
+ components.add_all(vertices)
+ for arc in arcs_iterator do
+ components.union(arc[0], arc[1])
+ end
+ return components
+ end
+
+ # Returns the strongly connected components of this digraph.
+ #
+ # Two vertices `u` and `v` belong to the same strongly connected
+ # component if and only if there exists a path from `u` to `v`
+ # and there exists a path from `v` to `u`.
+ #
+ # This is computed in linear time (Tarjan's algorithm).
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(1, 2)
+ # g.add_arc(2, 3)
+ # g.add_arc(3, 1)
+ # g.add_arc(3, 4)
+ # g.add_arc(4, 5)
+ # g.add_arc(5, 6)
+ # g.add_arc(6, 5)
+ # assert g.strongly_connected_components.number_of_subsets == 3
+ # ~~~
+ fun strongly_connected_components: DisjointSet[V]
+ do
+ var tarjanAlgorithm = new TarjanAlgorithm[V](self)
+ return tarjanAlgorithm.strongly_connected_components
+ end
+end
+
+# Computing the strongly connected components using Tarjan's algorithm
+private class TarjanAlgorithm[V: Object]
+ # The graph whose strongly connected components will be computed
+ var graph: Digraph[V]
+ # The strongly connected components computed in Tarjan's algorithm
+ var sccs = new DisjointSet[V]
+ # An index used for Tarjan's algorithm
+ var index = 0
+ # A stack used for Tarjan's algorithm
+ var stack: Queue[V] = (new Array[V]).as_lifo
+ # A map associating with each vertex its index
+ var vertex_to_index = new HashMap[V, Int]
+ # A map associating with each vertex its ancestor in Tarjan's algorithm
+ var ancestor = new HashMap[V, Int]
+ # True if and only if the vertex is in the stack
+ var in_stack = new HashSet[V]
+
+ # Returns the strongly connected components of a graph
+ fun strongly_connected_components: DisjointSet[V]
+ do
+ for u in graph.vertices_iterator do sccs.add(u)
+ for v in graph.vertices_iterator do
+ visit(v)
+ end
+ return sccs
+ end
+
+ # The recursive part of Tarjan's algorithm
+ fun visit(u: V)
+ do
+ vertex_to_index[u] = index
+ ancestor[u] = index
+ index += 1
+ stack.add(u)
+ in_stack.add(u)
+ for v in graph.successors(u) do
+ if not vertex_to_index.keys.has(v) then
+ visit(v)
+ ancestor[u] = ancestor[u].min(ancestor[v])
+ else if in_stack.has(v) then
+ ancestor[u] = ancestor[u].min(vertex_to_index[v])
+ end
+ end
+ if vertex_to_index[u] == ancestor[u] then
+ var v
+ loop
+ v = stack.take
+ in_stack.remove(v)
+ sccs.union(u, v)
+ if u == v then break
+ end
+ end
+ end
+end
+
+# Arcs iterator
+class ArcsIterator[V: Object]
+ super Iterator[Array[V]]
+
+ # The graph whose arcs are iterated over
+ var graph: Digraph[V]
+ # Attributes
+ #
+ private var sources_iterator: Iterator[V] is noinit
+ private var targets_iterator: Iterator[V] is noinit
+ init
+ do
+ sources_iterator = graph.vertices_iterator
+ if sources_iterator.is_ok then
+ targets_iterator = graph.successors(sources_iterator.item).iterator
+ if not targets_iterator.is_ok then update_iterators
+ end
+ end
+
+ redef fun is_ok do return sources_iterator.is_ok and targets_iterator.is_ok
+
+ redef fun item do return [sources_iterator.item, targets_iterator.item]
+
+ redef fun next
+ do
+ targets_iterator.next
+ update_iterators
+ end
+
+ private fun update_iterators
+ do
+ while not targets_iterator.is_ok and sources_iterator.is_ok
+ do
+ sources_iterator.next
+ if sources_iterator.is_ok then
+ targets_iterator = graph.successors(sources_iterator.item).iterator
+ end
+ end
+ end
+end
+
+# Mutable digraph
+abstract class MutableDigraph[V: Object]
+ super Digraph[V]
+
+ ## ---------------- ##
+ ## Abstract methods ##
+ ## ---------------- ##
+
+ # Adds the vertex `u` to this graph.
+ #
+ # If `u` already belongs to the graph, then nothing happens.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_vertex(0)
+ # assert g.has_vertex(0)
+ # assert not g.has_vertex(1)
+ # g.add_vertex(1)
+ # assert g.num_vertices == 2
+ # ~~~
+ fun add_vertex(u: V) is abstract
+
+ # Removes the vertex `u` from this graph and all its incident arcs.
+ #
+ # If the vertex does not exist in the graph, then nothing happens.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_vertex(0)
+ # g.add_vertex(1)
+ # assert g.has_vertex(0)
+ # g.remove_vertex(0)
+ # assert not g.has_vertex(0)
+ # ~~~
+ fun remove_vertex(u: V) is abstract
+
+ # Adds the arc `(u,v)` to this graph.
+ #
+ # If there is already an arc from `u` to `v` in this graph, then
+ # nothing happens. If vertex `u` or vertex `v` do not exist in the
+ # graph, they are added.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(0, 1)
+ # g.add_arc(1, 2)
+ # assert g.has_arc(0, 1)
+ # assert g.has_arc(1, 2)
+ # assert not g.has_arc(1, 0)
+ # g.add_arc(1, 2)
+ # assert g.num_arcs == 2
+ # ~~~
+ fun add_arc(u, v: V) is abstract
+
+ # Removes the arc `(u,v)` from this graph.
+ #
+ # If the arc does not exist in the graph, then nothing happens.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_arc(0, 1)
+ # assert g.num_arcs == 1
+ # g.remove_arc(0, 1)
+ # assert g.num_arcs == 0
+ # g.remove_arc(0, 1)
+ # assert g.num_arcs == 0
+ # ~~~
+ fun remove_arc(u, v: V) is abstract
+
+ ## -------------------- ##
+ ## Non abstract methods ##
+ ## -------------------- ##
+
+ # Adds all vertices of `vertices` to this digraph.
+ #
+ # If vertices appear more than once, they are only added once.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # g.add_vertices([0,1,2,3])
+ # assert g.num_vertices == 4
+ # g.add_vertices([2,3,4,5])
+ # assert g.num_vertices == 6
+ # ~~~
+ fun add_vertices(vertices: Collection[V])
+ do
+ for u in vertices do add_vertex(u)
+ end
+
+ # Adds all arcs of `arcs` to this digraph.
+ #
+ # If arcs appear more than once, they are only added once.
+ #
+ # ~~~
+ # import digraph
+ # var g = new HashDigraph[Int]
+ # var arcs = [[0,1], [1,2], [1,2]]
+ # g.add_arcs(arcs)
+ # assert g.num_arcs == 2
+ # ~~~
+ fun add_arcs(arcs: Collection[Array[V]])
+ do
+ for a in arcs do add_arc(a[0], a[1])
+ end
+end
+# A directed graph represented by hash maps
+class HashDigraph[V: Object]
+ super MutableDigraph[V]
+
+ # Attributes
+ #
+ private var incoming_vertices_map = new HashMap[V, Array[V]]
+ private var outgoing_vertices_map = new HashMap[V, Array[V]]
+ private var number_of_arcs = 0
+
+ redef fun num_vertices do return outgoing_vertices_map.keys.length end
+
+ redef fun num_arcs do return number_of_arcs end
+
+ redef fun add_vertex(u)
+ do
+ if not has_vertex(u) then
+ incoming_vertices_map[u] = new Array[V]
+ outgoing_vertices_map[u] = new Array[V]
+ end
+ end
+
+ redef fun has_vertex(u) do return outgoing_vertices_map.keys.has(u)
+
+ redef fun remove_vertex(u)
+ do
+ if has_vertex(u) then
+ for v in successors(u) do
+ remove_arc(u, v)
+ end
+ for v in predecessors(u) do
+ remove_arc(v, u)
+ end
+ incoming_vertices_map.keys.remove(u)
+ outgoing_vertices_map.keys.remove(u)
+ end
+ end
+
+ redef fun add_arc(u, v)
+ do
+ if not has_vertex(u) then add_vertex(u)
+ if not has_vertex(v) then add_vertex(v)
+ if not has_arc(u, v) then
+ incoming_vertices_map[v].add(u)
+ outgoing_vertices_map[u].add(v)
+ number_of_arcs += 1
+ end
+ end
+
+ redef fun has_arc(u, v)
+ do
+ return outgoing_vertices_map[u].has(v)
+ end
+
+ redef fun remove_arc(u, v)
+ do
+ if has_arc(u, v) then
+ outgoing_vertices_map[u].remove(v)
+ incoming_vertices_map[v].remove(u)
+ number_of_arcs -= 1
+ end
+ end
+
+ redef fun predecessors(u): Array[V]
+ do
+ if incoming_vertices_map.keys.has(u) then
+ return incoming_vertices_map[u].clone
+ else
+ return new Array[V]
+ end
+ end
+
+ redef fun successors(u): Array[V]
+ do
+ if outgoing_vertices_map.keys.has(u) then
+ return outgoing_vertices_map[u].clone
+ else
+ return new Array[V]
+ end
+ end
+
+ redef fun vertices_iterator: Iterator[V] do return outgoing_vertices_map.keys.iterator
+end
nitlanguage / nit.git / commitdiff