| author |
Steve Losh <steve@stevelosh.com> |
| date |
Wed, 15 Dec 2021 23:10:57 -0500 |
| parents |
428c6288f9e9 |
| children |
(none) |
(in-package :advent)
;;;; Input ----------------------------------------------------------------
(defun mkinput (year day)
(alexandria:write-string-into-file
(losh:pbpaste)
(format nil "data/~D/~2,'0D.txt" year day)
:if-exists :supersede))
;;;; Streams ------------------------------------------------------------------
(defun ensure-stream (input)
(ctypecase input
(stream input)
(string (make-string-input-stream input))))
(defun ensure-string (input)
(ctypecase input
(stream (alexandria:read-stream-content-into-string input))
(string (copy-seq input))))
(defun ensure-keyword (input)
(values
(ctypecase input
(keyword input)
(symbol (alexandria:make-keyword input))
(string (alexandria:make-keyword (string-upcase (str:trim input)))))))
;;;; Problems -----------------------------------------------------------------
(defmacro define-problem-tests ((year day) part1 part2)
`(1am:test ,(alexandria:symbolicate 'test-
(princ-to-string year)
'/
(princ-to-string day))
(multiple-value-bind (part1 part2) (,(alexandria:symbolicate 'run))
(1am:is (equal ,part1 part1))
(1am:is (equal ,part2 part2)))))
(defmacro define-problem ((year day)
(arg &optional (reader 'identity))
(&optional part-1-answer part-2-answer)
&body body)
(multiple-value-bind (body declarations docstring)
(alexandria:parse-body body :documentation t)
(with-gensyms (file)
(let ((run (symb 'run)))
`(progn
(defun ,run (&optional ,arg)
,@(when docstring (list docstring))
,@declarations
(let ((,file (unless ,arg (open (problem-data-path ,year ,day)))))
(unwind-protect
(progn (unless ,arg
(setf ,arg (,reader (ensure-stream (or ,arg ,file)))))
,@body)
(when ,file (close ,file)))))
,@(when part-1-answer
(list `(define-problem-tests (,year ,day) ,part-1-answer ,part-2-answer)))
'run)))))
(defun problem-data-path (year day)
(make-pathname
:directory `(:relative "data" ,(aesthetic-string year))
:name (format nil "~2,'0D" day)
:type "txt"))
(defmacro defpackage* (name &body body)
`(defpackage ,name
(:use :cl :losh :iterate :advent)
,@body))
;;;; Readers ------------------------------------------------------------------
(alexandria:define-constant +whitespace-chars+
'(#\Space #\Newline #\Backspace #\Tab #\Linefeed #\Page #\Return #\Rubout)
:test #'equal)
(defun read-numbers-from-string (line)
(mapcar #'parse-integer (ppcre:all-matches-as-strings "-?\\d+" line)))
(defun read-and-collect (stream reader)
(iterate (for value :in-stream stream :using reader)
(collect value)))
(defmacro with-eof-handled ((stream eof-error-p eof-value) &body body)
(once-only (stream eof-error-p eof-value)
`(if (null (peek-char nil ,stream nil))
(if ,eof-error-p
(error 'end-of-file)
,eof-value)
(progn ,@body))))
(defun read-before (char &optional (discard-delimiter t) (stream *standard-input*) (eof-error-p t) eof-value)
"Read characters from `stream` up to, but *not* including, `char`.
A string of the characters read will be returned.
If `discard-delimiter` is true, the `char` (if any) will be consumed from the
stream. It will not be included in the results — use `read-to` for that.
EOF is only reported when an EOF is encountered immediately. Otherwise the
remaining characters will be read and returned (and EOF reported on the next
invocation).
"
(with-eof-handled (stream eof-error-p eof-value)
(iterate
(for c = (peek-char nil stream nil))
(until (null c))
(when (char= char c)
(when discard-delimiter
(read-char stream))
(finish))
(collect (read-char stream) :result-type 'string))))
(defun read-to (char &optional (stream *standard-input*) (eof-error-p t) eof-value)
"Read characters from `stream` up to and including `char`.
A string of the characters read will be returned.
EOF is only reported when an EOF is encountered immediately. Otherwise the
remaining characters will be read and returned (and EOF reported on the next
invocation).
"
(with-eof-handled (stream eof-error-p eof-value)
(iterate
(for c = (peek-char nil stream nil))
(until (null c))
(collect (read-char stream) :result-type 'string)
(until (char= char c)))))
(defun read-word (&optional (stream *standard-input*) (eof-error-p t) eof-value)
"Read the next word from `stream` and return it as a string.
A word is a sequence of non-whitespace characters. Leading whitespace will be
skipped.
"
(peek-char t stream nil)
(with-eof-handled (stream eof-error-p eof-value)
(iterate
(for c = (read-char stream nil #\space))
(until (member c +whitespace-chars+))
(collect c :result-type 'string))))
(defun read-all (stream)
"Read all forms from `stream` and return them as a fresh list."
(read-and-collect stream #'read))
(defun read-numbers (stream)
(read-numbers-from-string (alexandria:read-stream-content-into-string stream)))
(defun read-lines (stream)
"Read all lines from `stream` and return them as a fresh list of strings."
(read-and-collect stream #'read-line))
(defun read-lines-of-numbers-and-garbage (stream)
"Read the lines of numbers in `stream` into a list of lists of numbers.
Numbers can be separated by anything, even garbage.
Lines without any numbers will be discarded.
"
(iterate (for line :in-stream stream :using #'read-line)
(for numbers = (read-numbers-from-string line))
(when numbers
(collect numbers))))
(defun read-lines-of-words (stream)
(mapcar (lambda (line) (split-sequence:split-sequence #\space line))
(read-lines stream)))
(defun read-comma-separated-values (stream)
(str:split #\, (alexandria:read-stream-content-into-string stream)))
(defun read-comma-separated-integers (stream)
(mapcar #'parse-integer (read-comma-separated-values stream)))
(defun read-2d-array (stream &key key)
(iterate
(with lines = (read-lines stream))
(with result = (make-array (list (length lines) (length (first lines)))))
(for row :from 0)
(for line :in lines)
(iterate
(for col :from 0)
(for char :in-string line)
(setf (aref result row col) (if key (funcall key char) char)))
(returning result)))
(defun read-digits (stream)
(iterate (for char :in-stream stream :using #'read-char)
(for digit = (digit-char-p char))
(when digit
(collect digit))))
(defun read-chunks (stream)
"Read double-newline separated lines into a list of lists of lines."
(iterate (with current = (list))
(for line = (read-line stream nil :eof))
(if (or (eql :eof line) (string= "" line))
(progn
(collect current)
(setf current (list)))
(push line current))
(until (eql :eof line))))
;;;; Rings --------------------------------------------------------------------
(declaim (inline ring-prev ring-next ring-data))
(defstruct (ring (:constructor make-ring%))
(data)
(prev nil :type (or null ring))
(next nil :type (or null ring)))
(defmethod print-object ((ring ring) stream)
(print-unreadable-object (ring stream :type t :identity t)
(format stream "~S" (ring-list ring))))
(defun map-ring (function ring)
(if (null ring)
nil
(cons (funcall function (ring-data ring))
(loop
:for r = (ring-next ring) :then (ring-next r)
:until (eql r ring)
:collect (funcall function (ring-data r))))))
(defmacro do-ring ((el ring) &body body)
(once-only (ring)
(with-gensyms (r started)
`(if (null ,ring)
nil
(do* ((,r ,ring (ring-next ,r))
(,started nil t))
((and ,started (eql ,ring ,r)) (values))
(let ((,el (ring-data ring)))
,@body))))))
(defun ring-find (ring el)
(cond
((null ring) nil)
((eql (ring-data ring) el) ring)
(t (loop
:for r = (ring-next ring) :then (ring-next r)
:until (eql r ring)
:when (eql (ring-data r) el) :return r))))
(defun ring-list (ring)
(map-ring #'identity ring))
(defun ring-length (ring)
(let ((result 0))
(do-ring (el ring)
(declare (ignore el))
(incf result))
result))
(defun ring-move (ring n)
(check-type n fixnum)
(if (minusp n)
(loop :repeat (- n) :do (setf ring (ring-prev ring)))
(loop :repeat n :do (setf ring (ring-next ring))))
ring)
(defun ring-insert-after (ring element)
(if (null ring)
(ring element)
(let* ((p ring)
(n (ring-next ring))
(new (make-ring% :data element :prev p :next n)))
(setf (ring-next p) new
(ring-prev n) new)
new)))
(defun ring-insert-before (ring element)
(if (null ring)
(ring element)
(let* ((p (ring-prev ring))
(n ring)
(new (make-ring% :data element :prev p :next n)))
(setf (ring-next p) new
(ring-prev n) new)
new)))
(defun ring-cut (ring &key prev)
(assert (not (null ring)) (ring) "Cannot cut from empty ring ~S" ring)
(let ((n (ring-next ring)))
(if (eql ring n)
nil
(let ((p (ring-prev ring)))
(setf (ring-next p) n
(ring-prev n) p
(ring-next ring) nil
(ring-prev ring) nil)
(if prev p n)))))
(define-modify-macro ring-findf (el) ring-find)
(define-modify-macro ring-cutf (&rest keywords) ring-cut)
(define-modify-macro ring-movef (n) ring-move)
(define-modify-macro ring-nextf () ring-next)
(define-modify-macro ring-prevf () ring-prev)
(define-modify-macro ring-insertf-after (element) ring-insert-after)
(define-modify-macro ring-insertf-before (element) ring-insert-before)
(defun ring (&rest elements)
(if (null elements)
nil
(iterate
(with start)
(for element :in elements)
(for prev = ring)
(for ring = (if-first-time
(setf start (make-ring% :data element))
(make-ring% :data element :prev prev)))
(when prev
(setf (ring-next prev) ring
(ring-prev ring) prev))
(finally (setf (ring-next ring) start
(ring-prev start) ring)
(return start)))))
;;;; Miscellaneous ------------------------------------------------------------
(defun hash-table= (h1 h2 &optional (test #'eql))
"Return whether `h1` and `h2` have the same keys and values.
The consequences are undefined if `h1` and `h2` use different key tests.
`test` is used to compare values.
"
(and (= (hash-table-count h1)
(hash-table-count h2))
(iterate (for (k v) :in-hashtable h1)
(always (funcall test v (gethash k h2))))))
(defun hamming-distance (sequence1 sequence2 &key (test #'eql))
"Return the Hamming distance between `sequence1` and `sequence2`."
;; todo assert length=?
(let ((result 0))
(map nil (lambda (x y)
(unless (funcall test x y)
(incf result)))
sequence1
sequence2)
result))
(defun unique (list &key (test #'eql))
"Return a fresh list of the unique elements in `LIST`.
This differs from REMOVE-DUPLICATES in that *all* duplicate elements will be
removed, not just all-but-the-last.
This is O(n²).
Example:
(remove-duplicates '(3 1 3 2 3))
; => (1 2 3)
(unique '(3 1 3 2 3))
; => (1 2)
"
(iterate
(for a :in list)
(for i :from 0)
(unless (iterate (for b :in list)
(for j :from 0)
(unless (= i j)
(thereis (funcall test a b))))
(collect a))))
(defun extremum+ (sequence predicate)
"Like ALEXANDRIA:EXTREMUM but also return the position as a second value."
(iterate
(with value = nil)
(with position = nil)
(for i :from 0)
(for v :in-whatever sequence)
(if-first-time
(setf value v
position i)
(when (funcall predicate v value)
(setf value v
position i)))
(finally (return (values value position)))))
(defun extremums (sequence predicate &key (key #'identity))
"Like ALEXANDRIA:EXTREMUM but return *all* values in case of a tie."
(iterate
(with results = nil)
(with prev = nil)
(for v :in-whatever sequence)
(for k = (funcall key v))
(if-first-time
(progn (push v results)
(setf prev k))
(cond
((funcall predicate k prev) (setf results (list v)
prev k))
((funcall predicate prev k) nil) ; noop
(t (progn (push v results)
(setf prev k)))))
(finally (return results))))
(defun char-invertcase (char)
"Return `char` with its case inverted, if possible."
(if (lower-case-p char)
(char-upcase char)
(char-downcase char)))
(defun-inline x (point)
(realpart point))
(defun-inline y (point)
(imagpart point))
(defun manhattan-distance (point1 &optional (point2 #c(0 0)))
"Return the Manhattan distance between the two points on the complex plane."
(+ (abs (- (x point1)
(x point2)))
(abs (- (y point1)
(y point2)))))
(defun manhattan-neighbors (point)
"Return points adjacent to point (excluding diagonals) on the complex plane."
(list (+ point #c(0 1))
(+ point #c(1 0))
(+ point #c(0 -1))
(+ point #c(-1 0))))
(defun manhattan-neighborhood (point)
"Return point and points adjacent to point (excluding diagonals) on the complex plane."
(list point
(+ point #c(0 1))
(+ point #c(1 0))
(+ point #c(0 -1))
(+ point #c(-1 0))))
(defgeneric emptyp (collection)
(:documentation "Return whether `collection` is empty."))
(defmethod emptyp ((list list))
(null list))
(defmethod emptyp ((vector vector))
(zerop (length vector)))
(defmethod emptyp ((hash-table hash-table))
(zerop (hash-table-count hash-table)))
(defmethod emptyp ((digraph digraph:digraph))
(digraph:emptyp digraph))
(defmethod emptyp ((hset hash-set))
(hset-empty-p hset))
(defun-inline nth-digit (n integer &optional (radix 10))
"Return the `n`th digit of `integer` in base `radix`, counting from the right."
(mod (truncate integer (expt radix n)) radix))
(defun-inlineable integral-image (width height value-function)
;; https://en.wikipedia.org/wiki/Summed-area_table
(let ((image (make-array (list width height)))
(last-row (1- height))
(last-col (1- width)))
(dotimes (x width)
(dotimes (y height)
(setf (aref image x y)
(+ (funcall value-function x y)
(if (= x last-col) 0 (aref image (1+ x) y))
(if (= y last-row) 0 (aref image x (1+ y)))
(if (or (= x last-col) (= y last-row))
0
(- (aref image (1+ x) (1+ y))))))))))
(defun positions-if (predicate sequence &key (start 0) end key)
"Return a fresh list of all positions in `sequence` that satisfy `predicate`.
Like `cl:position-if`, but returns a list of all the results.
Example:
(positions-if #'upper-case-p \"aBCdeF\")
; =>
(1 2 5)
"
(let ((pos start))
(nreverse (reduce (lambda (result value)
(prog1 (if (funcall predicate value)
(cons pos result)
result)
(incf pos)))
sequence
:start start
:end end
:key key
:initial-value nil))))
(defun positions (item sequence &key (start 0) end key (test #'eql))
"Return a fresh list of all positions of `item` in `sequence`.
Like `cl:position`, but returns a list of all the results.
Example:
(positions 3 #(\"foo\" \"a\" \"b\" \"bar\") :key #'length)
; =>
(0 3)
"
(let ((pos start))
(nreverse (reduce (lambda (result value)
(prog1 (if (funcall test item value)
(cons pos result)
result)
(incf pos)))
sequence
:start start
:end end
:key key
:initial-value nil))))
(defun digits (n &key (radix 10) from-end (result-type 'list))
"Return a fresh list of the digits of `n` in base `radix`.
By default, the digits are returned high-order first, as you would read them.
Use `from-end` to get them low-order first:
(digits 123) ; => (1 2 3)
(digits 123 :from-end t) ; => (3 2 1)
"
(let ((result (iterate
(for (values remaining digit) = (truncate n radix))
(collect digit)
(setf n remaining)
(until (zerop n)))))
(coerce (if from-end
result
(nreverse result))
result-type)))
(defun digits->number (digits &key from-end (radix 10) key)
"Concatenate `digits` to return an integer in base `radix`.
If `from-end` is `t`, start at the end of the list.
If `key` is given, call it on the digits first.
"
(if (not (emptyp digits))
(if from-end
(iterate (for digit :in digits)
(for multiplier :first 1 :then (* radix multiplier))
(summing (* multiplier (if key (funcall key digit) digit))))
(reduce (lambda (total digit)
(+ (* total radix) (if key (funcall key digit) digit)))
digits :initial-value 0))
0))
(defun fresh-vector (sequence)
(if (typep sequence 'vector)
(copy-seq sequence)
(coerce sequence 'vector)))
(defun first-character (string)
"Return the first character of `string`."
(char string 0))
(defmacro let-result ((symbol initform) &body body)
"Bind `symbol` to initform, execute `body`, and return `symbol`.
This is useful for creating a object, doing some work on it, and returning the
object. For example:
(let-result (table (make-hash-table))
(setf (gethash 0 table) 'foo))
; ==>
(let ((table (make-hash-table)))
(setf (gethash 0 table) 'foo)
table)
"
`(let ((,symbol ,initform))
,@body
,symbol))
(defmacro let-complex (bindings &body body)
`(let* (,@(iterate
(for binding :in bindings)
(for (x y val) = (etypecase binding
(symbol (list
(alexandria:symbolicate binding 'x)
(alexandria:symbolicate binding 'y)
binding))
(cons binding)))
(for v = (gensym))
(collect `(,v ,val))
(collect `(,x (realpart ,v)))
(collect `(,y (imagpart ,v)))))
,@body))
(defun queue-thunk (&rest elements)
(lambda () (pop elements)))
(defun bytes->hex (bytes)
(format nil "~(~{~2,'0X~}~)" (coerce bytes 'list)))
(defun bytes->integer (bytes)
(iterate
(for byte :in (coerce bytes 'list))
(for result :seed 0 :then (+ (ash result 8) byte))
(returning result)))
(defun bounds (coords)
"Return the left, right, bottom, and top bounds of `coords`."
(multiple-value-bind (bottom top) (losh:extrema #'< coords :key #'y)
(multiple-value-bind (left right) (losh:extrema #'< coords :key #'x)
(values (x left)
(x right)
(y bottom)
(y top)))))
(defun flip-vertically (image-array)
(destructuring-bind (width height) (array-dimensions image-array)
(dotimes (y (truncate height 2))
(dotimes (x width)
(rotatef (aref image-array x y)
(aref image-array x (- height y 1)))))))
(defun draw-bitmap (pixels path &key flip-vertically)
"Draw `pixels` to `path`.
`pixels` must be a sequence of `(position . color)` conses.
"
(multiple-value-bind (left right bottom top) (bounds (mapcar #'car pixels))
(let ((origin (complex left bottom))
(image (make-array (list (1+ (- right left))
(1+ (- top bottom)))
:initial-element 0)))
(iterate
(for (pos . color) :in-whatever pixels)
(for pixel = (- pos origin))
(setf (aref image (x pixel) (y pixel)) color))
(when flip-vertically
(flip-vertically image))
(netpbm:write-to-file path image
:if-exists :supersede
:format :pbm))))
(defun gethash-arbitrary (hash-table)
(maphash (lambda (k v)
(return-from gethash-arbitrary (values k v t)))
hash-table)
(values nil nil nil))
(defun pophash (hash-table &optional (key nil key?))
(multiple-value-bind (k v found) (if key?
(multiple-value-bind (v found)
(gethash key hash-table)
(values key v found))
(gethash-arbitrary hash-table))
(if found
(progn (remhash k hash-table)
(values k v t))
(values nil nil nil))))
(defun ensure-edge (digraph pred succ)
(digraph:insert-vertex digraph pred)
(digraph:insert-vertex digraph succ)
(digraph:insert-edge digraph pred succ))
(defun bisect-integers-left (predicate low high)
"Bisect the integers `[low, high]` with `predicate` and return the LEFT element.
You can think of this function as partitioning the integers from `low` to
`high` (inclusive) into two halves: those that satisfy `(predicate x)` and
those that don't, and then selecting the element on the LEFT side of the
split:
satisfying not statisfying
[.......... ...............]
^
|
result
If no integers in the range satisfy the predicate, `nil` will be returned.
Examples:
(bisect-integers-left (lambda (x) (< x 3)) 0 9) ; => 2
; sat not-sat
; [012|345789]
; ^
; result
(bisect-integers-left (lambda (x) (<= x 7)) 0 9) ; => 7
; sat not-sat
; [0123457|89]
; ^
; result
(bisect-integers-left (lambda (x) (<= x 100)) 0 9) ; => 9
; sat not-sat
; [012345789|]
; ^
; result
(bisect-integers-left (lambda (x) (< x -1)) 0 9) ; => nil
; sat not-sat
; [|012345789]
; no result
"
(assert (<= low high))
(when (funcall predicate low)
(recursively ((low low)
(high high))
(if (= low high)
low
(let ((mid (+ low (ceiling (- high low) 2))))
(if (funcall predicate mid)
(recur mid high)
(recur low (1- mid))))))))
(defun bisect-integers-right (predicate low high)
"Bisect the integers `[low, high]` with `predicate` and return the RIGHT element.
You can think of this function as partitioning the integers from `low` to
`high` (inclusive) into two halves: those that satisfy `(predicate x)` and
those that don't, and then selecting the element on the RIGHT side of the
split:
satisfying not statisfying
[.......... ...............]
^
|
result
If all integers in the range satisfy the predicate, `nil` will be returned.
Examples:
(bisect-integers-right (lambda (x) (< x 3)) 0 9) ; => 3
; sat not-sat
; [012|345789]
; ^
; result
(bisect-integers-right (lambda (x) (<= x 7)) 0 9) ; => 8
; sat not-sat
; [0123457|89]
; ^
; result
(bisect-integers-right (lambda (x) (< x -1)) 0 9) ; => 0
; sat not-sat
; [|012345789]
; ^
; result)
(bisect-integers-right (lambda (x) (<= x 100)) 0 9) ; => nil
; sat not-sat
; [012345789|]
; no result
"
(assert (<= low high))
(when (not (funcall predicate high))
(recursively ((low low)
(high high))
(if (= low high)
low
(let ((mid (+ low (floor (- high low) 2))))
(if (funcall predicate mid)
(recur (1+ mid) high)
(recur low mid)))))))
(defun print-hash-table-map (table &key
flip-x
flip-y
swap-axes
extra
(pad 0)
(default #\space)
(key #'identity))
"Print `table` to standard out.
`table` must be a hash table with complex keys. `default` will be used as the
default value for the hash table. `key` will be called on the values before
printing (including `default`), and must return a character.
If `get` is provided, it must be a function of one argument that will be
called on the keys instead of `(gethash ... table default)` to produce the
values. `key` will still be called on the result.
The y-axis will be printed with higher values at the top, unless `flip-y` is
true.
"
(multiple-value-bind (left right bottom top)
(bounds (alexandria:hash-table-keys table))
(incf left (- pad))
(incf right pad)
(incf bottom (- pad))
(incf top pad)
(when flip-x (rotatef left right))
(when flip-y (rotatef bottom top))
(do-irange ((y top bottom))
(do-irange ((x left right))
(let ((pos (if swap-axes
(complex y x)
(complex x y))))
(princ (funcall key (or (when extra
(funcall extra pos))
(gethash pos table default))))))
(terpri))))
(defun esc (string)
(format t "~C~A" #\esc string)
(force-output))
(defun clear ()
(esc "[2J")
(esc "[;H"))
(defun green () (esc "[32m"))
(defun bold () (esc "[1m"))
(defun underline () (esc "[4m"))
(defun reset () (esc "[0m"))
(defun print-2d-array (array &key (printer #'princ) (key #'identity))
(destructuring-bind (rows cols) (array-dimensions array)
(dotimes (r rows)
(dotimes (c cols)
(funcall printer (funcall key (aref array r c))))
(terpri))))
;;;; A* Search ----------------------------------------------------------------
(defstruct path
state
(estimate 0)
(cost 0)
(previous nil))
(defun path-to-list (path &aux result)
(recursively ((path path))
(unless (null path)
(push (path-state path) result)
(recur (path-previous path))))
result)
(defun-inlineable astar (&key start neighbors goalp cost heuristic test limit
get-seen set-seen)
"Search for a path from `start` to a goal using A★.
The following parameters are all required:
* `start`: the starting state.
* `neighbors`: a function that takes a state and returns all states reachable
from it.
* `goalp`: a predicate that takes a state and returns whether it is a goal.
* `cost`: a function that takes two states `a` and `b` and returns the cost
to move from `a` to `b`.
* `heuristic`: a function that takes a state and estimates the distance
remaining to the goal.
* `test`: an equality predicate for comparing nodes. It must be suitable for
passing to `make-hash-table`.
If the heuristic function is admissable (i.e. it never overestimates the
remaining distance) the algorithm will find the shortest path. If you don't
have a decent heuristic, just use `(constantly 0)` to degrade to Dijkstra.
Note that `test` is required. The only sensible default would be `eql`, but
if you were using states that need a different predicate and forgot to pass it
the algorithm would end up blowing the heap, which is unpleasant.
The following parameters are optional:
* `limit`: a maximum cost. Any paths that exceed this cost will not be
considered.
* `set-seen`: a function that takes a state and a cost, and records it.
If not provided a hash table will be used, but sometimes (depending on what
your states are) it can be faster to store visited nodes more efficiently.
* `get-seen`: a function that takes a state and retrieves the stored cost, or
`nil` if the state has not been seen.
"
(let ((seen (unless get-seen (make-hash-table :test test)))
(frontier (pileup:make-heap #'< :key #'path-estimate)))
(labels ((set-seen% (path)
(if set-seen
(funcall set-seen (path-state path) (path-cost path))
(setf (gethash (path-state path) seen) (path-cost path))))
(get-seen% (state)
(if get-seen
(funcall get-seen state)
(gethash state seen)))
(push-path (path)
(set-seen% path)
(pileup:heap-insert path frontier)))
(iterate
(initially (push-path (make-path :state start)))
(for (values current found) = (pileup:heap-pop frontier))
(unless found
(return (values nil nil)))
(for current-state = (path-state current))
(when (funcall goalp current-state)
(return (values (path-to-list current) t)))
(for current-cost = (path-cost current))
(iterate
(for next-state :in (funcall neighbors current-state))
(for next-cost = (+ current-cost (funcall cost current-state next-state)))
(for seen-cost = (get-seen% next-state))
(unless (and limit (> next-cost limit))
(when (or (null seen-cost) (< next-cost seen-cost))
(for next-estimate = (+ next-cost (funcall heuristic next-state)))
(push-path (make-path :state next-state
:cost next-cost
:estimate next-estimate
:previous current)))))))))