Python递归深度超出限制，超出限制，并且不知道如何删除递归

Question

Maybe the problem can be solved by deleting all those functions, can't it? However, i really don't know what to do to get the source work. By the way, it just simulates a horse in a chesstable, going around and around, randomly, trying to visit each square once; and I get a recursion depth exceeded error.

import random

def main():
    global tries,moves
    tries,moves=0,0
    restart()

def restart():
    global a,indexes,x,y
    a=[[0 for y in range(8)] for x in range(8)] #Costrutto chic
    indexes=[x for x in range(8)]
    #Random part
    x=random.randint(0,7)
    y=random.randint(0,7)
    a[x][y]=1
    start()

def start():
    global i,indexes,moves,tries
    i=0
    random.shuffle(indexes) #List filled with random numbers that i'll use as indexes
    while i<=7:
        if indexes[i]==0:
            move(-2,-1)
        elif indexes[i]==1:
            move(-2,1)
        elif indexes[i]==2:
            move(-1,-2)
        elif indexes[i]==3:
            move(-1,2)
        elif indexes[i]==4:
            move(1,-2)
        elif indexes[i]==5:
            move(1,2)
        elif indexes[i]==6:
            move(2,-1)
        elif indexes[i]==7:
            move(2,1)
        i+=1
    for _ in a:
        if 0 in _:
            print "Wasted moves: %d"%(moves)
            tries+=1
            moves=0
            restart()
    print "Success obtained in %d tries"%(tries)

def move(column,row):
    global x,y,a,moves
    try: b=a[x+row][y+column]
    except IndexError: return 0
    if b==0 and 0<=x+row<=7 and 0<=y+column<=7:
        x=x+row
        y=y+column
        a[x][y]=1
        moves+=1
        start()
    else: return 0

try :main()
#except: print "I couldn't handle it" <-Row added to prevent python from returning a huge amount of errors

EDIT: This is the modified version, which still does not works, but at least it's an improvement:

import random

def move((column,row),x,y):
    try: cell=squares_visited[x+row][y+column]
    except IndexError: return x,y ## NONE TYPE OBJECT
    if cell==0 and 0<=x+row<=7 and 0<=y+column<=7:
        x+=row
        y+=column
        squares_visited[x][y]=1
        return x,y ## NONE TYPE OBJECT

squares_visited=[[0] * 8 for _ in range(8)]
x=random.randint(0,7)
y=random.randint(0,7)
squares_visited[x][y]=1
moves=[(-2,-1),(-2,1),(-1,-2),(-1,2),(1,-2),(1,2),(2,-1),(2,1)]
indexes=list(range(8))
tries=0
print "The horse starts in position %d,%d"%(x,y)

while True:
    random.shuffle(indexes)
    for _ in indexes:
        cells=move(moves[indexes[_]],x,y) ##Passing as arguments x and y looks weird
        x=cells[0]
        y=cells[1]
    #If you out this for cicle, there are no legal moves anymore(due to full completion with 1, or to lack of legit moves)
    for _ in squares_visited:
        if 0 in _:
            squares_visited=[[0] * 8 for _ in range(8)]
            tries+=1
    else:
        print "You managed to do it in %d tries."%(tries)

Answer 1

This code has a lot of problems -- enough that it's worth going over in full:

import random

def main():
    global tries,moves

The first of many examples of over-use of global variables. When possible, pass parameters; or create a class. This is a general strategy that will help you construct more comprehensible (and thus more debuggable) algorithms; and in a general sense, this is part of why your code fails -- not because of any particular bug, but because the complexity of your code makes it hard to find bugs.

    tries,moves=0,0
    restart()

def restart():
    global a,indexes,x,y

Why do you name your board a ? That's a terrible name! Use something descriptive like squares_visited .

    a=[[0 for y in range(8)] for x in range(8)] #Costrutto chic
    indexes=[x for x in range(8)]

Minor: in python 2, [x for x in range(8)] == range(8) -- they do exactly the same thing, so the list comprehension is unnecessary. In 3, it works a little differently, but if you want a list (rather than a range object) just pass it to list as in ( list(range(8)) ).

    #Random part
    x=random.randint(0,7)
    y=random.randint(0,7)
    a[x][y]=1
    start()

So my understanding of the code so far is that a is the board, x and y are the starting coordinates, and you've marked the first spot visited with a 1 . So far so good. But then things start to get hairy, because you call start at the end of restart instead of calling it from a top-level control function. That's theoretically OK, but it makes the recursion more complicated than necessary; this is another part of your problem.

def start():
    global i,indexes,moves,tries

Argh more globals...

    i=0
    random.shuffle(indexes) #List filled with random numbers that i'll use as indexes
    while i<=7:
        if indexes[i]==0:
            move(-2,-1)
        elif indexes[i]==1:
            move(-2,1)
        elif indexes[i]==2:
            move(-1,-2)
        elif indexes[i]==3:
            move(-1,2)
        elif indexes[i]==4:
            move(1,-2)
        elif indexes[i]==5:
            move(1,2)
        elif indexes[i]==6:
            move(2,-1)
        elif indexes[i]==7:
            move(2,1)
        i+=1

Ok, so what you're trying to do is go through each index in indexes in sequence. Why are you using while though? And why is i global?? I don't see it being used anywhere else. This is way overcomplicated. Just use a for loop to iterate over indexes directly, as in

    for index in indexes: 
        if index==0:
            ...

Ok, now for the specific problems...

    for _ in a:
        if 0 in _:
            print "Wasted moves: %d"%(moves)
            tries+=1
            moves=0
            restart()
    print "Success obtained in %d tries"%(tries)

I don't understand what you're trying to do here. It seems like you're calling restart every time you find a 0 (ie an unvisited spot) on your board. But restart resets all board values to 0 , so unless there's some other way to fill the board with 1 s before hitting this point, this will result in an infinite recursion. In fact, the mutual recursion between move and start might be able to achieve that in principle, but as it is, it's way too complex! The problem is that there's no clear recursion termination condition.

def move(column,row):
    global x,y,a,moves
    try: b=a[x+row][y+column]
    except IndexError: return 0
    if b==0 and 0<=x+row<=7 and 0<=y+column<=7:
        x=x+row
        y=y+column
        a[x][y]=1
        moves+=1
        start()
    else: return 0

Here, in principle, the idea seems to be that if your move hits a 1 or goes off the board, then the current branch of the recursion terminates. But because i and indexes are global above in start , when start is re-called, it re-shuffles indexes and resets i to 0! The result is sheer chaos! I can't even begin to comprehend how that will effect the recursion; it seems likely that because i gets reset at the beginning of start every time, and because every successful call of move results in a call of start , the while loop in start will never terminate!

I suppose it's possible that eventually this process will manage to visit every square, at which point things might work as expected, but as it is, this is too complex even to predict.

try :main()
#except: print "I couldn't handle it" <-Row added to prevent python from returning a huge amount of errors

Not sure what you mean by that last line, but it doesn't sound like a good sign -- you're papering over an error instead of finding the root cause.

I'm going to play with this code a bit and see if I can get it to behave marginally better by de-globalizing some of its state... will report back soon.

Update :

Ok I de-globalized indexes as described above. I then replaced the start / restart recursion with an infinite loop in restart , a return statement in start where the call to restart used to be, and a sys.exit() at the end of start (to break out of the infinite loop on success). The result behaves more as expected. This is still poor design but it works now, in the sense that it recursively tries a bunch of random paths until every local position has been visited.

Of course it still doesn't ever succeed; it just keeps looping. Actually finding a solution will probably require a lot more rethinking of this algorithm! But following my above suggestions should help some, at least.

Answer 2

start() and move() call each other, making it an indirect recursive call BUT the move() return startment get out of move() and notout of the recursion.

You see, when you are calling a function, that calls a function that calls a functions, it all goes in a stack that reference each calls. When you get a your final result, you are supposed to go backward, and unstack these function calls.

Here, you don't, you call move() , that calls start() , and it it returns something then you just keep going deeper in the stack.

Try to make an iterative version of your code. Recursion is hard, start with something easier.

If you do want to persist in the recursive version, make move() call itself, and then go backward in the stack from it self once it reach the out condition. It will be clearer than dealing with recursive calls from two functions.

BTW:

• Avoid using global variables. Either pass the data as arguments, or use a class. I would use argument passing, it will force you to come up with a better algo that this one.
• the while loop is not necessary. Replace it with a for loop on indexes
• the huge if/elif statement is not necessary, replace it with a dictionary

You should end up with somthing like this:

for i in indexes:
    move(*MOVES[i])

MOVES , being a dict of values of i associated with params for move() .

• you may want to use generators instead of your list comprehensions, but that would require some algo changes. It could be better for your memory footprint. At the very least, make this shorter:

[x for x in range(8)] can be written range(8) [[0 for y in range(8)] for x in range(8)] can be written [[0] * 8 for x in range(8)]

range() can be replaced by xrange()