我正在尝试对 Lisp 中的拼图“8-puzzle”实施启发式搜索策略 A*。
要运行我的搜索，我使用以下命令： (run-best '(0 1 2 3 4 5 6 B 7) '(0 1 2 3 4 5 6 7 B))
其中第一个状态是开始目标，第二个是最终目标。
但是，我的程序运行了很长时间。最终，我认为它会stack-overflow。*编辑：它并没有耗尽内存，但是它花了 30 分钟，比我的广度优先搜索要长得多。
搜索算法代码：
;;; This is one of the example programs from the textbook:
;;;
;;; Artificial Intelligence:
;;; Structures and strategies for complex problem solving
;;;
;;; by George F. Luger and William A. Stubblefield
;;;
;;; Corrections by Christopher E. Davis (chris2d@cs.unm.edu)
;;; insert-by-weight will add new child states to an ordered list of
;;; states-to-try.
(defun insert-by-weight (children sorted-list)
(cond ((null children) sorted-list)
(t (insert (car children)
(insert-by-weight (cdr children) sorted-list)))))
(defun insert (item sorted-list)
(cond ((null sorted-list) (list item))
((< (get-weight item) (get-weight (car sorted-list)))
(cons item sorted-list))
(t (cons (car sorted-list) (insert item (cdr sorted-list))))))
;;; run-best is a simple top-level "calling" function to run best-first-search
(defun run-best (start goal)
(declare (special *goal*)
(special *open*)
(special *closed*))
(setq *goal* goal)
(setq *open* (list (build-record start nil 0 (heuristic start))))
(setq *closed* nil)
(best-first))
;;; These functions handle the creation and access of (state parent)
;;; pairs.
(defun build-record (state parent depth weight)
(list state parent depth weight))
(defun get-state (state-tuple) (nth 0 state-tuple))
(defun get-parent (state-tuple) (nth 1 state-tuple))
(defun get-depth (state-tuple) (nth 2 state-tuple))
(defun get-weight (state-tuple) (nth 3 state-tuple))
(defun retrieve-by-state (state list)
(cond ((null list) nil)
((equal state (get-state (car list))) (car list))
(t (retrieve-by-state state (cdr list)))))
;; best-first defines the actual best-first search algorithm
;;; it uses "global" open and closed lists.
(defun best-first ()
(declare (special *goal*)
(special *open*)
(special *closed*)
(special *moves*))
(print "open =") (print *open*)
(print "closed =") (print *closed*)
(cond ((null *open*) nil)
(t (let ((state (car *open*)))
(setq *closed* (cons state *closed*))
(cond ((equal (get-state state) *goal*) (reverse (build-solution *goal*)))
(t (setq *open*
(insert-by-weight
(generate-descendants (get-state state)
(1+ (get-depth state))
*moves*)
(cdr *open*)))
(best-first)))))))
;;; generate-descendants produces all the descendants of a state
(defun generate-descendants (state depth moves)
(declare (special *closed*)
(special *open*))
(cond ((null moves) nil)
(t (let ((child (funcall (car moves) state))
(rest (generate-descendants state depth (cdr moves))))
(cond ((null child) rest)
((retrieve-by-state child rest) rest)
((retrieve-by-state child *open*) rest)
((retrieve-by-state child *closed*) rest)
(t (cons (build-record child state depth
(+ depth (heuristic child)))
rest)))))))
(defun build-solution (state)
(declare (special *closed*))
(cond ((null state) nil)
(t (cons state (build-solution
(get-parent
(retrieve-by-state state *closed*)))))))
8puzzle 的启发式函数：
(defun hole (grid)
"Return integer index into GRID at which the 'hole' is located."
(position '0 grid))
(defun col (pair)
(car pair))
(defun row (pair)
(cdr pair))
(defun coords (index1)
"Transform INDEX, an integer index into the list, into an (X . Y)
coordinate pair for a 3x3 grid."
(cons (second (multiple-value-list (floor index1 3)))
(floor index1 3)))
(defun index1 (coords)
"Transform COORDS, an (X . Y) coordinate pair for a 3x3 grid, into
an integer index."
(+ (col coords)
(* 3 (row coords))))
(defun swap (a b list)
"Return a new list equivalent to LIST but with the items at indexes
A and B swapped."
(let ((new (copy-seq list)))
(setf (nth a new)
(nth b list))
(setf (nth b new)
(nth a list))
new))
(defun right1 (grid)
"Move the 'hole' on the 3x3 GRID one space to the right. If there
is no space to the right, return NIL."
(let ((hole (coords (hole grid))))
(if (= 2 (col hole))
nil
(swap (index1 hole)
(index1 (cons (1+ (col hole)) (row hole)))
grid))))
(defun left1 (grid)
"Move the 'hole' on the 3x3 GRID one space to the left. If there
is no space to the left, return NIL."
(let ((hole (coords (hole grid))))
(if (zerop (col hole))
nil
(swap (index1 hole)
(index1 (cons (1- (col hole)) (row hole)))
grid))))
(defun up (grid)
"Move the 'hole' on the 3x3 GRID one space up. If there is no space
up, return NIL."
(let ((hole (coords (hole grid))))
(if (zerop (row hole))
nil
(swap (index1 (cons (col hole) (1- (row hole))))
(index1 hole)
grid))))
(defun down (grid)
"Move the 'hole' on the 3x3 GRID one space down. If there is no
space down, return NIL."
(let ((hole (coords (hole grid))))
(if (= 2 (row hole))
nil
(swap (index1 (cons (col hole) (1+ (row hole))))
(index1 hole)
grid))))
;Moves
(setq *moves*
'(right1 left1 up down))
;heuristics for puzzle8
(defun heuristic (state)
(declare (special *goal*))
(heuristic-eval state *goal*))
(defun heuristic-eval (state goal)
(cond ((null state) 0)
((equal (car state) (car goal))
(heuristic-eval (cdr state) (cdr goal)))
(t (1+ (heuristic-eval (cdr state) (cdr goal))))))