Depth-First search in Python

Question

I'm trying to do a Depth-First search in Python but it's not working.

Basically we have a peg-solitaire board:

[1,1,1,1,1,0,1,1,1,1]

1's represent a peg, and 0 is an open spot. You must move a peg one at a time TWO SLOTS backwards or forward ONLY to an empty spot. If you jump over another peg in the process it becomes an empty slot. You do this until one peg remains. So basically, a game goes like:

[1, 1, 1, 1, 1, 0, 1, 1, 1, 1]
[1, 1, 1, 0, 0, 1, 1, 1, 1, 1]
[1, 0, 0, 1, 0, 1, 1, 1, 1, 1]
[1, 0, 0, 1, 1, 0, 0, 1, 1, 1]
[1, 0, 0, 0, 0, 1, 0, 1, 1, 1]
[1, 0, 0, 0, 0, 1, 1, 0, 0, 1]
[1, 0, 0, 0, 0, 0, 0, 1, 0, 1] #etc until only 1 peg left

Here's what I have:

class MiniPeg():
    def start(self):
        ''' returns the starting board '''
        board = [1,1,1,1,1,0,1,1,1,1]
        return board

    def goal(self, node):
        pegs = 0

        for pos in node:
            if pos == 1:
                pegs += 1

        return (pegs == 1) # returns True if there is only 1 peg

    def succ(self, node):
        pos = 0
        for peg in node:
            if peg == 1:                
                if pos < (len(node) - 2):  # try to go forward
                    if node[pos+2] == 0 and node[pos+1] == 1:
                        return create_new_node(node, pos, pos+2)

                if pos > 2: # try to go backwards 
                    if node[pos-2] == 0 and node[pos-1] == 1:
                        return create_new_node(node, pos, pos-2)
        pos += 1

def create_new_node(node, fr, to):
    node[fr] = 0
    node[to] = 1
    if fr > to:
        node[fr-1] = 0
    else:
        node[fr+1] = 0
    return node

if __name__ == "__main__":
    s = MiniPeg()
    b = s.start()

    while not s.goal(b):
        print b
        b = s.succ(b)

So, now my questions:

1. Is this the right way to do a Depth-First search for this?
2. My algorithm doesn't work!!! It gets stuck. I've been struggling on this for days before asking here so please help.
3. Looks like I'm not following DRY, any suggestions?
4. omg help me?

Answer 1

The normal way to implement DFS in a situation where each step is a "move" from a "board position" to some possible next one, until a goal is reached, is as follows (pseudocode)

seenpositions = set()
currentpositions = set([startingposition])
while currentpositions:
  nextpositions = set()
  for p in currentpositions:
    seenpositions.add(p)
    succ = possiblesuccessors(p)
    for np in succ:
      if np in seenpositions: continue
      if isending(np): raise FoundSolution(np)
      nextpositions.add(np)
  currentpositions = nextpositions
raise NoSolutionExists()

You probably also want to keep backward links to be able to emit, at the end, the series of moves leading to the found solution (if any), but that's an ancillary problem.

I don't recognize a trace of this general structure (or reasonable variant thereof) in your code. Why not try to record it this way? You only need to code possiblesuccessors and isending (if you insist on keeping a position as a list you'll have to turn it into a tuple to check membership in set and add to set, but, that's pretty minor;-).

Answer 2

It doesn't appear that you're creating new nodes, just re-using existing ones. DFS requires some kind of stack (either the call stack, or your own stack). Where is that?