算法：求幂，python版

分别用迭代方法和递归方法实现求幂
迭代方法的时间复杂度为O(n),空间复杂度为O（1）
递归方法1的时间复杂度为O(logn),空间复杂度为O（logn）
递归方法2的时间复杂度为O（n），空间复杂度为O（n）
#!/usr/bin/env python
#coding -*- utf:8 -*-

def pow_1(x, n, choice):
    if choice==0:
        return pow_1_iter(x, n, 1)
    if choice==1:
        return pow_1_rec(x, n)

#iteration
def pow_1_iter(x, counter, product):
    if counter==0:
        return product
    else:
        return pow_1_iter(x, counter-1, x*product)

#recursion1
def pow_1_rec(x, counter):
    if counter==0:
        return 1
    #偶数情况
    if(even(counter)):
        return pow_1_rec(x*x, counter//2)
    #奇数情况
    else:
        return x * pow_1_rec(x, counter-1)
        #return x * pow_1_rec(x*x, counter//2)
'''

#recursion2

def pow_2_rec(x, counter):
if n==0:
return 1
    else:
return x*pow_2_rec(x,counter-1)
'''
#判断counter是否为偶数
def even(i):
    if i%2==0:
        return True
    else:
        return False


if __name__=='__main__':
    a = int(input("Please enter the x:"))
    b = int(input("Please enter the m:"))
    c = int(input("Which method do you want?(0:iteration, 1:recursion) "))
    print("result: ",pow_1(a, b, c))