python尾递归

def fact(n):    if n==1:        return 1    return n * fact(n - 1)

使用递归函数需要注意防止栈溢出。在计算机中，函数调用是通过栈（stack）这种数据结构实现的，每当进入一个函数调用，栈就会加一层栈帧，每当函数返回，栈就会减一层栈帧。由于栈的大小不是无限的，所以，递归调用的次数过多，会导致栈溢出。

>>> fact(1000)Traceback (most recent call last):  File "<stdin>", line 1, in <module>  File "<stdin>", line 4, in fact  ...  File "<stdin>", line 4, in factRuntimeError: maximum recursion depth exceeded

解决递归调用栈溢出的方法是通过尾递归优化，事实上尾递归和循环的效果是一样的，所以，把循环看成是一种特殊的尾递归函数也是可以的。

尾递归是指，在函数返回的时候，调用自身本身，并且，return语句不能包含表达式。这样，编译器或者解释器就可以把尾递归做优化，使递归本身无论调用多少次，都只占用一个栈帧，不会出现栈溢出的情况。

def fact(n):    return fact_iter(1, 1, n)def fact_iter(product, count, max):    if count > max:        return product    return fact_iter(product * count, count + 1, max)

有一个针对尾递归优化的decorator，可以参考源码：

http://code.activestate.com/recipes/474088-tail-call-optimization-decorator/

#!/usr/bin/env python2.4# This program shows off a python decorator(# which implements tail call optimization. It# does this by throwing an exception if it is # it's own grandparent, and catching such # exceptions to recall the stack.import sysclass TailRecurseException:  def __init__(self, args, kwargs):    self.args = args    self.kwargs = kwargsdef tail_call_optimized(g):  """  This function decorates a function with tail call  optimization. It does this by throwing an exception  if it is it's own grandparent, and catching such  exceptions to fake the tail call optimization.    This function fails if the decorated  function recurses in a non-tail context.  """  def func(*args, **kwargs):    f = sys._getframe()    if f.f_back and f.f_back.f_back \        and f.f_back.f_back.f_code == f.f_code:      raise TailRecurseException(args, kwargs)    else:      while 1:        try:          return g(*args, **kwargs)        except TailRecurseException, e:          args = e.args          kwargs = e.kwargs  func.__doc__ = g.__doc__  return func@tail_call_optimizeddef factorial(n, acc=1):  "calculate a factorial"  if n == 0:    return acc  return factorial(n-1, n*acc)print factorial(10000)# prints a big, big number,# but doesn't hit the recursion limit.@tail_call_optimizeddef fib(i, current = 0, next = 1):  if i == 0:    return current  else:    return fib(i - 1, next, current + next)print fib(10000)# also prints a big number,# but doesn't hit the recursion limit.

解决递归调用栈溢出的方法是通过尾递归优化，事实上尾递归和循环的效果是一样的，所以，把循环看成是一种特殊的尾递归函数也是可以的。

尾递归是指，在函数返回的时候，调用自身本身，并且，return语句不能包含表达式。这样，编译器或者解释器就可以把尾递归做优化，使递归本身无论调用多少次，都只占用一个栈帧，不会出现栈溢出的情况。

def fact(n):    return fact_iter(1, 1, n)def fact_iter(product, count, max):    if count > max:        return product    return fact_iter(product * count, count + 1, max)