197 lines
7.3 KiB
EmacsLisp
197 lines
7.3 KiB
EmacsLisp
;;; tree.el --- Working with Trees -*- lexical-binding: t -*-
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;; Author: William Carroll <wpcarro@gmail.com>
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;; Version: 0.0.1
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;; URL: https://git.wpcarro.dev/wpcarro/briefcase
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;; Package-Requires: ((emacs "25.1"))
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;;; Commentary:
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;; Some friendly functions that hopefully will make working with trees cheaper
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;; and therefore more appealing!
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;;
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;; Tree terminology:
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;; - leaf: node with zero children.
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;; - root: node with zero parents.
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;; - depth: measures a node's distance from the root node. This implies the
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;; root node has a depth of zero.
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;; - height: measures the longest traversal from a node to a leaf. This implies
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;; that a leaf node has a height of zero.
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;; - balanced?
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;;
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;; Tree variants:
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;; - binary: the maximum number of children is two.
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;; - binary search: the maximum number of children is two and left sub-trees are
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;; lower in value than right sub-trees.
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;; - rose: the number of children is variable.
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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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(require 'list)
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(require 'set)
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(require 'tuple)
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(require 'series)
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(require 'random)
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(require 'maybe)
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; Library
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(cl-defstruct tree xs)
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(cl-defstruct node value children)
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(cl-defun tree-node (value &optional children)
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"Create a node struct of VALUE with CHILDREN."
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(make-node :value value
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:children children))
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(defun tree-reduce-breadth (acc f xs)
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"Reduce over XS breadth-first applying F to each x and ACC (in that order).
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Breadth-first traversals guarantee to find the shortest path in a graph.
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They're typically more difficult to implement than DFTs and may also incur
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higher memory costs on average than their depth-first counterparts.")
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;; TODO: Support :order as 'pre | 'in | 'post.
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;; TODO: Troubleshoot why I need defensive (nil? node) check.
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(defun tree-reduce-depth (acc f node)
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"Reduce over NODE depth-first applying F to each NODE and ACC.
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F is called with each NODE, ACC, and the current depth.
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Depth-first traversals have the advantage of typically consuming less memory
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than their breadth-first equivalents would have. They're also typically
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easier to implement using recursion. This comes at the cost of not
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guaranteeing to be able to find the shortest path in a graph."
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(cl-labels ((do-reduce-depth
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(acc f node depth)
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(let ((acc-new (funcall f node acc depth)))
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(if (or (maybe-nil? node)
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(tree-leaf? node))
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acc-new
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(list/reduce
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acc-new
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(lambda (node acc)
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(tree-do-reduce-depth
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acc
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f
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node
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(number/inc depth)))
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(node-children node))))))
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(do-reduce-depth acc f node 0)))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; Helpers
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defun tree-height (xs)
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"Return the height of tree XS.")
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;; TODO: Troubleshoot why need for (nil? node). Similar misgiving
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;; above.
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(defun tree-leaf-depths (xs)
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"Return a list of all of the depths of the leaf nodes in XS."
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(list/reverse
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(tree-reduce-depth
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'()
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(lambda (node acc depth)
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(if (or (maybe-nil? node)
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(tree-leaf? node))
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(list/cons depth acc)
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acc))
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xs)))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; Generators
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; TODO: Consider parameterizing height, forced min-max branching, random
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;; distributions, etc.
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;; TODO: Bail out before stack overflowing by consider branching, current-depth.
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(cl-defun tree-random (&optional (value-fn (lambda (_) nil))
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(branching-factor 2))
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"Randomly generate a tree with BRANCHING-FACTOR using VALUE-FN to compute the
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node values. VALUE-FN is called with the current-depth of the node. Useful for
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generating test data. Warning this function can overflow the stack."
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(cl-labels ((do-random
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(d vf bf)
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(make-node
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:value (funcall vf d)
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:children (->> (series/range 0 (number/dec bf))
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(list/map
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(lambda (_)
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(when (random-boolean?)
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(do-random d vf bf))))))))
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(do-random 0 value-fn branching-factor)))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; Predicates
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defun tree-instance? (tree)
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"Return t if TREE is a tree struct."
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(node-p tree))
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(defun tree-leaf? (node)
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"Return t if NODE has no children."
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(maybe-nil? (node-children node)))
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(defun tree-balanced? (n xs)
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"Return t if the tree, XS, is balanced.
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A tree is balanced if none of the differences between any two depths of two leaf
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nodes in XS is greater than N."
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(> n (->> xs
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tree-leaf-depths
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set/from-list
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set/count
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number/dec)))
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; Tests
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defconst tree-enable-testing? t
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"When t, test suite runs.")
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;; TODO: Create set of macros for a proper test suite including:
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;; - describe (arbitrarily nestable)
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;; - it (arbitrarily nestable)
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;; - line numbers for errors
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;; - accumulated output for synopsis
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;; - do we want describe *and* it? Why not a generic label that works for both?
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(when tree-enable-testing?
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(let ((tree-a (tree-node 1
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(list (tree-node 2
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(list (tree-node 5)
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(tree-node 6)))
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(tree-node 3
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(list (tree-node 7)
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(tree-node 8)))
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(tree-node 4
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(list (tree-node 9)
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(tree-node 10))))))
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(tree-b (tree-node 1
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(list (tree-node 2
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(list (tree-node 5)
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(tree-node 6)))
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(tree-node 3)
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(tree-node 4
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(list (tree-node 9)
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(tree-node 10)))))))
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;; instance?
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(prelude/assert (tree-instance? tree-a))
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(prelude/assert (tree-instance? tree-b))
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(prelude/refute (tree-instance? '(1 2 3)))
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(prelude/refute (tree-instance? "oak"))
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;; balanced?
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(prelude/assert (tree-balanced? 1 tree-a))
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(prelude/refute (tree-balanced? 1 tree-b))
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(message "Tests pass!")))
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(provide 'tree)
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;;; tree.el ends here
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