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| 1 | +# Copyright 2013, Michael H. Goldwasser |
| 2 | +# |
| 3 | +# Developed for use with the book: |
| 4 | +# |
| 5 | +# Data Structures and Algorithms in Python |
| 6 | +# Michael T. Goodrich, Roberto Tamassia, and Michael H. Goldwasser |
| 7 | +# John Wiley & Sons, 2013 |
| 8 | +# |
| 9 | +# This program is free software: you can redistribute it and/or modify |
| 10 | +# it under the terms of the GNU General Public License as published by |
| 11 | +# the Free Software Foundation, either version 3 of the License, or |
| 12 | +# (at your option) any later version. |
| 13 | +# |
| 14 | +# This program is distributed in the hope that it will be useful, |
| 15 | +# but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 16 | +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 17 | +# GNU General Public License for more details. |
| 18 | +# |
| 19 | +# You should have received a copy of the GNU General Public License |
| 20 | +# along with this program. If not, see <http://www.gnu.org/licenses/>. |
| 21 | + |
| 22 | +class Graph: |
| 23 | + """Representation of a simple graph using an adjacency map.""" |
| 24 | + |
| 25 | + #------------------------- nested Vertex class ------------------------- |
| 26 | + class Vertex: |
| 27 | + """Lightweight vertex structure for a graph.""" |
| 28 | + __slots__ = '_element' |
| 29 | + |
| 30 | + def __init__(self, x): |
| 31 | + """Do not call constructor directly. Use Graph's insert_vertex(x).""" |
| 32 | + self._element = x |
| 33 | + |
| 34 | + def element(self): |
| 35 | + """Return element associated with this vertex.""" |
| 36 | + return self._element |
| 37 | + |
| 38 | + def __hash__(self): # will allow vertex to be a map/set key |
| 39 | + return hash(id(self)) |
| 40 | + |
| 41 | + def __str__(self): |
| 42 | + return str(self._element) |
| 43 | + |
| 44 | + #------------------------- nested Edge class ------------------------- |
| 45 | + class Edge: |
| 46 | + """Lightweight edge structure for a graph.""" |
| 47 | + __slots__ = '_origin', '_destination', '_element' |
| 48 | + |
| 49 | + def __init__(self, u, v, x): |
| 50 | + """Do not call constructor directly. Use Graph's insert_edge(u,v,x).""" |
| 51 | + self._origin = u |
| 52 | + self._destination = v |
| 53 | + self._element = x |
| 54 | + |
| 55 | + def endpoints(self): |
| 56 | + """Return (u,v) tuple for vertices u and v.""" |
| 57 | + return (self._origin, self._destination) |
| 58 | + |
| 59 | + def opposite(self, v): |
| 60 | + """Return the vertex that is opposite v on this edge.""" |
| 61 | + if not isinstance(v, Graph.Vertex): |
| 62 | + raise TypeError('v must be a Vertex') |
| 63 | + return self._destination if v is self._origin else self._origin |
| 64 | + raise ValueError('v not incident to edge') |
| 65 | + |
| 66 | + def element(self): |
| 67 | + """Return element associated with this edge.""" |
| 68 | + return self._element |
| 69 | + |
| 70 | + def __hash__(self): # will allow edge to be a map/set key |
| 71 | + return hash( (self._origin, self._destination) ) |
| 72 | + |
| 73 | + def __str__(self): |
| 74 | + return '({0},{1},{2})'.format(self._origin,self._destination,self._element) |
| 75 | + |
| 76 | + #------------------------- Graph methods ------------------------- |
| 77 | + def __init__(self, directed=False): |
| 78 | + """Create an empty graph (undirected, by default). |
| 79 | +
|
| 80 | + Graph is directed if optional paramter is set to True. |
| 81 | + """ |
| 82 | + self._outgoing = {} |
| 83 | + # only create second map for directed graph; use alias for undirected |
| 84 | + self._incoming = {} if directed else self._outgoing |
| 85 | + |
| 86 | + def _validate_vertex(self, v): |
| 87 | + """Verify that v is a Vertex of this graph.""" |
| 88 | + if not isinstance(v, self.Vertex): |
| 89 | + raise TypeError('Vertex expected') |
| 90 | + if v not in self._outgoing: |
| 91 | + raise ValueError('Vertex does not belong to this graph.') |
| 92 | + |
| 93 | + def is_directed(self): |
| 94 | + """Return True if this is a directed graph; False if undirected. |
| 95 | +
|
| 96 | + Property is based on the original declaration of the graph, not its contents. |
| 97 | + """ |
| 98 | + return self._incoming is not self._outgoing # directed if maps are distinct |
| 99 | + |
| 100 | + def vertex_count(self): |
| 101 | + """Return the number of vertices in the graph.""" |
| 102 | + return len(self._outgoing) |
| 103 | + |
| 104 | + def vertices(self): |
| 105 | + """Return an iteration of all vertices of the graph.""" |
| 106 | + return self._outgoing.keys() |
| 107 | + |
| 108 | + def edge_count(self): |
| 109 | + """Return the number of edges in the graph.""" |
| 110 | + total = sum(len(self._outgoing[v]) for v in self._outgoing) |
| 111 | + # for undirected graphs, make sure not to double-count edges |
| 112 | + return total if self.is_directed() else total // 2 |
| 113 | + |
| 114 | + def edges(self): |
| 115 | + """Return a set of all edges of the graph.""" |
| 116 | + result = set() # avoid double-reporting edges of undirected graph |
| 117 | + for secondary_map in self._outgoing.values(): |
| 118 | + result.update(secondary_map.values()) # add edges to resulting set |
| 119 | + return result |
| 120 | + |
| 121 | + def get_edge(self, u, v): |
| 122 | + """Return the edge from u to v, or None if not adjacent.""" |
| 123 | + self._validate_vertex(u) |
| 124 | + self._validate_vertex(v) |
| 125 | + return self._outgoing[u].get(v) # returns None if v not adjacent |
| 126 | + |
| 127 | + def degree(self, v, outgoing=True): |
| 128 | + """Return number of (outgoing) edges incident to vertex v in the graph. |
| 129 | +
|
| 130 | + If graph is directed, optional parameter used to count incoming edges. |
| 131 | + """ |
| 132 | + self._validate_vertex(v) |
| 133 | + adj = self._outgoing if outgoing else self._incoming |
| 134 | + return len(adj[v]) |
| 135 | + |
| 136 | + def incident_edges(self, v, outgoing=True): |
| 137 | + """Return all (outgoing) edges incident to vertex v in the graph. |
| 138 | +
|
| 139 | + If graph is directed, optional parameter used to request incoming edges. |
| 140 | + """ |
| 141 | + self._validate_vertex(v) |
| 142 | + adj = self._outgoing if outgoing else self._incoming |
| 143 | + for edge in adj[v].values(): |
| 144 | + yield edge |
| 145 | + |
| 146 | + def insert_vertex(self, x=None): |
| 147 | + """Insert and return a new Vertex with element x.""" |
| 148 | + v = self.Vertex(x) |
| 149 | + self._outgoing[v] = {} |
| 150 | + if self.is_directed(): |
| 151 | + self._incoming[v] = {} # need distinct map for incoming edges |
| 152 | + return v |
| 153 | + |
| 154 | + def insert_edge(self, u, v, x=None): |
| 155 | + """Insert and return a new Edge from u to v with auxiliary element x. |
| 156 | +
|
| 157 | + Raise a ValueError if u and v are not vertices of the graph. |
| 158 | + Raise a ValueError if u and v are already adjacent. |
| 159 | + """ |
| 160 | + if self.get_edge(u, v) is not None: # includes error checking |
| 161 | + raise ValueError('u and v are already adjacent') |
| 162 | + e = self.Edge(u, v, x) |
| 163 | + self._outgoing[u][v] = e |
| 164 | + self._incoming[v][u] = e |
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