I'm working on a knight's tour implementation using DFS.
My problem is, when I run it, it works fine up to step 20, but after that the algorithm freaks out and outputs this on a 5x5 board (there is a solution for a 5x5 board starting at (0,0)):
(1 10 5 16 24)
(4 15 2 11 20)
(9 6 17 23 22)
(14 3 8 19 12)
(7 18 13 21 25)
*Legal successors must be 0 <= row < n and 0 <= column < n and not be a previous step.
My implementation involves generating *legal successors using the genSuccessors function, throwing them onto a stack and recursively running the algorithm with the item at the top of the stack as the new current position. I only increment the step_count (in charge of tracking the order of squares the knight visits) if the next position is a step not taken before. When I cannot generate any more children, the algorithm explores other alternatives in the frontier until frontier empty (fail condition) or the step_count = # squares on the board (win).
I think the algorithm in general is sound.
edit: I think the problem is that when I can't generate more children, and I go to explore the rest of the frontier I need to scrap some of the current tour. My question is, how do I know how far back I need to go?
Graphically, in a tree I think I would need to go back up to the closest node that had a branch to an unvisited child and restart from there scrapping all the nodes visited when going down the previous (wrong) branch. Is this correct? How would I keep track of that in my code?
Thanks for reading such a long post; and thanks for any help you guys can give me.
Yikes! Your code is really scary. In particular:
1) It uses mutation everywhere. 2) It tries to model "return". 3) It doesn't have any test cases.
I'm going to be a snooty-poo, here, and simply remark that this combination of features makes for SUPER-hard-to-debug programs.
Also... for DFS, there's really no need to keep track of your own stack; you can just use recursion, right?
Sorry not to be more helpful.
Here's how I'd write it:
#lang racket
;; a position is (make-posn x y)
(struct posn (x y) #:transparent)
(define XDIM 5)
(define YDIM 5)
(define empty-board
(for*/set ([x XDIM]
[y YDIM])
(posn x y)))
(define (add-posn a b)
(posn (+ (posn-x a) (posn-x b))
(+ (posn-y a) (posn-y b))))
;; the legal moves, represented as posns:
(define moves
(list->set
(list (posn 1 2) (posn 2 1)
(posn -1 2) (posn 2 -1)
(posn -1 -2) (posn -2 -1)
(posn 1 -2) (posn -2 1))))
;; reachable knights moves from a given posn
(define (possible-moves from-posn)
(for/set ([m moves])
(add-posn from-posn m)))
;; search loop. invariant: elements of path-taken are not
;; in the remaining set. The path taken is given in reverse order.
(define (search-loop remaining path-taken)
(cond [(set-empty? remaining) path-taken]
[else (define possibilities (set-intersect (possible-moves
(first path-taken))
remaining))
(for/or ([p possibilities])
(search-loop (set-remove remaining p)
(cons p path-taken)))]))
(search-loop (set-remove empty-board (posn 0 0)) (list (posn 0 0)))
;; start at every possible posn:
#;(for/or ([p empty-board])
(search-loop (set-remove empty-board p) (list p)))