分別用迭代方法和遞歸方法實現求冪
迭代方法的時間復雜度為O(n),空間復雜度為O（1）
遞歸方法1的時間復雜度為O(logn),空間復雜度為O（logn）
遞歸方法2的時間復雜度為O（n），空間復雜度為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
#偶數情況
if(even(counter)): return pow_1_rec(x*x, counter//2) #奇數情況
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)
'''
#判斷counter是否為偶數
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))
