92 lines
2.8 KiB
EmacsLisp
92 lines
2.8 KiB
EmacsLisp
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;;; graph.el --- Working with in-memory graphs -*- lexical-binding: t -*-
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;; Author: William Carroll <wpcarro@gmail.com>
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;;; Commentary:
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;;
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;; Remember that there are optimal three ways to model a graph:
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;; 1. Edge List
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;; 2. Vertex Table (a.k.a. Neighbors Table)
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;; 3. Adjacency Matrix
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;;
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;; I may call these "Edges", "Neighbors", "Adjacencies" to avoid verbose naming.
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;; For now, I'm avoiding dealing with Adjacency Matrices as I don't have an
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;; immediate use-case for them. This is subject to change.
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;;
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;; There are also hybrid representations of graphs that combine the three
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;; aforementioned models. I believe Erlang's digraph module models graphs in
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;; Erlang Term Storage (i.e. ETS) this way.
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;; TODO: Verify this claim.
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;;
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;; Graphs can be weighted or unweighted. They can also be directed or
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;; undirected.
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;; TODO: Create a table explaining all graph variants.
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;;
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;; TODO: Figure out the relationship of this module and tree.el, which should in
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;; principle overlap.
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;;; Code:
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; Dependencies
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(require 'prelude)
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; Library
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; For now, I'll support storing *either* neighbors or edges in the graph struct
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;; as long as both aren't set, since that introduces consistency issues. I may
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;; want to handle that use-case in the future, but not now.
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(cl-defstruct graph neighbors edges)
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;; TODO: How do you find the starting point for a topo sort?
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(defun graph/sort (xs)
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"Return a topological sort of XS.")
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(defun graph/from-edges (xs)
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"Create a graph struct from the Edge List, XS.
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The user must pass in a valid Edge List since asserting on the shape of XS might
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be expensive."
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(make-graph :edges xs))
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(defun graph/from-neighbors (xs)
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"Create a graph struct from a Neighbors Table, XS.
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The user must pass in a valid Neighbors Table since asserting on the shape of
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XS might be expensive."
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(make-graph :neighbors xs))
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(defun graph/instance? (xs)
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"Return t if XS is a graph struct."
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(graph-p xs))
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;; TODO: Model each of the mapping functions into an isomorphism.
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(defun graph/edges->neighbors (xs)
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"Map Edge List, XS, into a Neighbors Table."
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(prelude/assert (graph/instance? xs)))
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(defun graph/neighbors->edges (xs)
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"Map Neighbors Table, XS, into an Edge List."
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(prelude/assert (graph/instance? xs)))
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;; Below are three different models of the same unweighted, directed graph.
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(defvar graph/edges
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'((a . b) (a . c) (a . e)
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(b . c) (b . d)
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(c . e)
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(d . f)
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(e . d) (e . f)))
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(defvar graph/neighbors
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((a b c e)
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(b c d)
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(c e)
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(d f)
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(e d g)
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(f)))
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(provide 'graph)
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;;; graph.el ends here
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