Python 递归函数

# 循环方式 
def sum_cycle(n): 
    sum = 0 
    for i in range(1,n+1) : 
        sum += i print(sum)

# 递归方式 
def sum_recu(n): 
    if n>0: 
       return n +sum_recu(n-1) 
    else: 
       return 0 

sum_cycle(100) 
sum = sum_recu(100) print(sum)

def normal_recursion(n):
    if n == 1:
        return 1
    else:
        return n + normal_recursion(n-1)

normal_recursion(5)
5 + normal_recursion(4)
5 + 4 + normal_recursion(3)
5 + 4 + 3 + normal_recursion(2)
5 + 4 + 3 + 2 + normal_recursion(1)
5 + 4 + 3 + 3
5 + 4 + 6
5 + 10
15

def tail_recursion(n, total=0):
    if n == 0:
        return total
    else:
        return tail_recursion(n-1, total+n)

tail_recursion(5)
tail_recursion(4, 5)
tail_recursion(3, 9)
tail_recursion(2, 12)
tail_recursion(1, 14)
tail_recursion(0, 15)
15

int tail_recursion(int n, int total) {
    if (n == 0) {
        return total;
    }
    else {
        return tail_recursion(n-1, total+n);
    }
}

int main(void) {
    int total = 0, n = 4;
    tail_recursion(n, total);
    return 0;
}

#!/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 sys

class TailRecurseException:
    def __init__(self, args, kwargs):
        self.args = args
        self.kwargs = kwargs

def 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()
        # 为什么是grandparent, 函数默认的第一层递归是父调用,
        # 对于尾递归, 不希望产生新的函数调用(即:祖父调用),
        # 所以这里抛出异常, 拿到参数, 退出被修饰函数的递归调用栈!(后面有动图分析)
        if f.f_back and f.f_back.f_back \
            and f.f_back.f_back.f_code == f.f_code:
            # 抛出异常
            raise TailRecurseException(args, kwargs)
        else:
            while 1:
                try:
                    return g(*args, **kwargs)
                except TailRecurseException, e:
                    # 捕获异常, 拿到参数, 退出被修饰函数的递归调用栈
                    args = e.args
                    kwargs = e.kwargs
    func.__doc__ = g.__doc__
    return func

@tail_call_optimized
def factorial(n, acc=1):
    "calculate a factorial"
    if n == 0:
        return acc
    return factorial(n-1, n*acc)

print factorial(10000)

sys._getframe([depth]):
Return a frame object from the call stack.
If optional integer depth is given, return the frame object that many calls below the top of the stack.
If that is deeper than the call stack, ValueEfror is raised. The default for depth is zero,
returning the frame at the top of the call stack.

即返回depth深度调用的栈帧对象.

import sys

def get_cur_info():
    print sys._getframe().f_code.co_filename  # 当前文件名
    print sys._getframe().f_code.co_name  # 当前函数名
    print sys._getframe().f_lineno # 当前行号
    print sys._getframe().f_back # 调用者的帧

#The binary search function

def  Binary_Search(data_source,find_n):
    #判断列表长度是否大于1，小于1就是一个值
    if len(data_source) >= 1: 
        #获取列表中间索引；奇数长度列表长度除以2会得到小数，通过int将转换整型     
        mid = int(len(data_source)/2) 
        #判断查找值是否超出最大值   
        if find_n > data_source[-1]:                                    
            print('{}查找值不存在！'.format(find_n))
            exit()
        #判断查找值是否超出最小值
        elif find_n < data_source[0]:                                   
            print('{}查找值不存在！'.format(find_n))
            exit()
        #判断列表中间值是否大于查找值
        if data_source[mid]  > find_n:                                  
            print('查找值在 {} 左边'.format(data_source[mid]))
            #调用自己，并将中间值左边所有元素做参数
            Binary_Search(data_source[:mid],find_n)  
        #判断列表中间值是否小于查找值                   
        elif data_source[mid] < find_n:                                 
            #print('查找值在 {} 右边'.format(data_source[mid]))     
            #调用自己，并将中间值右边所有元素做参数      
            Binary_Search(data_source[mid:],find_n)
        else:
            #找到查找值
            print('找到查找值',data_source[mid])                          
    else:
        #特殊情况，返回查找不到
        print('{}查找值不存在！'.format(find_n))                          

Data = [22,12,41,99,101,323,1009,232,887,97]
#列表从小到大排序
Data.sort()       
#查找323                                                      
Binary_Search(Data,323)   
                                              
执行结果：
找到查找值 323