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