1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
|
;;; graph.el --- Working with in-memory graphs -*- lexical-binding: t -*-
;; Author: William Carroll <wpcarro@gmail.com>
;;; Commentary:
;;
;; Remember that there are optimal three ways to model a graph:
;; 1. Edge List
;; 2. Vertex Table (a.k.a. Neighbors Table)
;; 3. Adjacency Matrix
;;
;; I may call these "Edges", "Neighbors", "Adjacencies" to avoid verbose naming.
;; For now, I'm avoiding dealing with Adjacency Matrices as I don't have an
;; immediate use-case for them. This is subject to change.
;;
;; There are also hybrid representations of graphs that combine the three
;; aforementioned models. I believe Erlang's digraph module models graphs in
;; Erlang Term Storage (i.e. ETS) this way.
;; TODO: Verify this claim.
;;
;; Graphs can be weighted or unweighted. They can also be directed or
;; undirected.
;; TODO: Create a table explaining all graph variants.
;;
;; TODO: Figure out the relationship of this module and tree.el, which should in
;; principle overlap.
;;; Code:
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Dependencies
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(require 'prelude)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Library
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; For now, I'll support storing *either* neighbors or edges in the graph struct
;; as long as both aren't set, since that introduces consistency issues. I may
;; want to handle that use-case in the future, but not now.
(cl-defstruct graph neighbors edges)
;; TODO: How do you find the starting point for a topo sort?
(defun graph/sort (xs)
"Return a topological sort of XS.")
(defun graph/from-edges (xs)
"Create a graph struct from the Edge List, XS.
The user must pass in a valid Edge List since asserting on the shape of XS might
be expensive."
(make-graph :edges xs))
(defun graph/from-neighbors (xs)
"Create a graph struct from a Neighbors Table, XS.
The user must pass in a valid Neighbors Table since asserting on the shape of
XS might be expensive."
(make-graph :neighbors xs))
(defun graph/instance? (xs)
"Return t if XS is a graph struct."
(graph-p xs))
;; TODO: Model each of the mapping functions into an isomorphism.
(defun graph/edges->neighbors (xs)
"Map Edge List, XS, into a Neighbors Table."
(prelude-assert (graph/instance? xs)))
(defun graph/neighbors->edges (xs)
"Map Neighbors Table, XS, into an Edge List."
(prelude-assert (graph/instance? xs)))
;; Below are three different models of the same unweighted, directed graph.
(defvar graph/edges
'((a . b) (a . c) (a . e)
(b . c) (b . d)
(c . e)
(d . f)
(e . d) (e . f)))
(defvar graph/neighbors
((a b c e)
(b c d)
(c e)
(d f)
(e d g)
(f)))
(provide 'graph)
;;; graph.el ends here
|
