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in AI and Deep Learning by (50.2k points)

I've written an iterative deepening algorithm, it works except when I add cycle checking, the algorithm returns a deeper solution than it should. But when I don't check for cycles it does work correctly, but it takes too long. Can anyone please spot the bug?

(defun rec-depth-limited (problem node cutoff closed)

  (if (= cutoff 0)

    (if (funcall (problem-goalp problem) node)


    (if (visited-p node closed)



          ;; when i remove the next line, it works correctly

          (setf (gethash (node-state node) closed) t)

          (loop for child in (expand node (problem-actions problem)) do

            (let ((result (rec-depth-limited problem child (1- cutoff) closed)))

                (if result

                    (return result))))))))

(defun iterative-deepening (problem)

  "Iterative deepening search"

  (let ((cutoff 0))


      (format t "~%cut-off: ~A" cutoff)

      (let ((solution (rec-depth-limited


                             (make-node :state (problem-state problem)) 


                             (make-hash-table :test #'equalp)))) ;solve problem up to cutoff

        (if (null  solution) 

            (incf cutoff);if solution is not found, increment the depth

            (return solution))))))

(defun visited-p (node table)

  "Checks if the state in the node was visited before by checking

if it exists in the table"

  (nth-value 1 (gethash (node-state node) table)))

Edit: here is the expand function

(defun expand (node actions)

  "Expands a node, returns a list of the new nodes"

  (remove-if #'null (apply-actions node actions)));apply all actions on all nodes

(defun apply-actions (node actions)

  "Applies all actions to a state, returns a list of new states"

  (mapcan #'(lambda (action) 

              (mapcar #'(lambda (tile) (funcall action tile node))

                     (node-state node)))


This is one of the actions, they are all the same except for minor changes

(defun slide-right (tile node)

  "slide the tile one cell to the right. returns nil if not possible, 

  otherwise returns a node with the new state"

  (when (can-slide-right-p tile (node-state node));if can slide right

      (and visualize (format t "~%slide ~A to the right" (tile-label tile)))

      (let*  ((newstate (mapcar #'copy-tile (node-state node)));copy the current state

             (depth (node-depth node))

             (newcol (incf (tile-col (find tile newstate :test #'equalp))));update state

             (cost (1+ (node-cost node))))

        (make-node :state newstate ;create new node with the new state

                   :parent node 

                   :depth (1+ depth) 

                   :action (concatenate 'string

                                        "slide "

                                        (tile-label tile)

                                        " right" )

                   :cost cost))))


 (defun can-slide-right-p (tile state)

  "returns T if the specified tile can be sled one cell to the right"

  (let  ((row (tile-row tile)) 

        (end (+ (tile-col tile) (tile-length tile))) ;col at which tile ends after being sled

        (orient (tile-orientation tile)))

    (and (equal orient 'H)

         (or (tile-is-mouse tile) (< end *board-w*))

         (empty-cell-p row end state))))

(defun spans-cell-p (row col tile)

  "returns T if the specified tile spans the specified cell"

  (if (equal (tile-orientation tile) 'H)

      (horizontally-spans-cell-p row col tile)

      (vertically-spans-cell-p row col tile)))

(defun horizontally-spans-cell-p (row col tile)

  "Tests if the specified horizontal tile spans the specified cell"

  (let ((tile-col (tile-col tile))

        (tile-row (tile-row tile))

        (tile-len (tile-length tile)))

    (and (= tile-row row) (>= col tile-col) (< col (+ tile-col tile-len)))))

(defun vertically-spans-cell-p (row col tile)

  "Tests if the specified vertical tile spans the specified cell"

  (let  ((tile-col (tile-col tile))

        (tile-row (tile-row tile))

        (tile-len (tile-length tile)))

    (and (= tile-col col) (>= row tile-row) (< row (+ tile-row tile-len)))))

1 Answer

0 votes
by (108k points)

A confined depth-first search with cycle detection may return a longer path when the first path that leads to the goal is longer than any other shorter path that includes the same state. Iterative Deepening search (IDS) with a lookup table a brute force approach, where the search tree is rebuilt during each iteration of increasing depth. The search was augmented by a lookup table of all positions 6 moves away from the solution. In the implementation, this was not all that different from the bi-directional search. I ran one search from the goal position for 6 moves to fill in the entries in the "lookup table." The table was implemented as the same binary search tree I used for indexing positions in the bi-directional search.

Let D be a goal state:

 A -- B -- C -- D


  C -- D

With a depth limit of 2, if the top branch is visited first, B and C will be visited and saved in the hash table. When the bottom branch is visited, it won't expand past C, because it was marked as visited.

A feasible solution is to set the hash value to the minimum depth where the state was found. This presents the state known as visited for a certain depth and beyond, but it'll be possible to expand it again if visited with less depth.

 (defun visited-p (node table)

  (let ((visited-depth (gethash (node-state node) table)))

    (and visited-depth

         (>= (node-depth node) visited-depth))))

(defun set-visited (node table)

  (let ((visited-depth (gethash (node-state node) table)))

    (setf (gethash (node-state node) table)

          (if visited-depth

              (min visited-depth (node-depth node))

              (node-depth node)))))

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