比较pow(x,y)的实现算法

概述

用python，比较pow的实现算法

思路

主要对比递归和while循环。PowCircle2函数和PowCircle类似，PowCircle2更容易理解一些。

源码

from time import ctime
from math import *


def PowRecursion(x,y):
    if(y==0):
        return 1
    if(y==1):
        return x

    t = PowRecursion(x, (int)(y / 2))
    if y&1 == 1:
        return x * t * t
    else:
        return t * t

def PowCircle(x,y):
    r=1
    if(y&1 == 1):
        r=x
        y=y-1
    y = y>>1
    while y>0:
        x = x*x
        y = y >> 1
    return r*x

def PowCircle2(x,y):
    r=1
    if(y&1 == 1):
        r=x
        y=y-1

    i=2
    while i<y:
        x = x*x
        i = i*2
    return r*x


def PowInternet(a, b):
    r = 1
    while b > 1:
        if b & 1 == 1:  #与运算一般可以用于取某位数，这里就是取最后一位。
            r *= a
        a *= a
        b = b >> 1 #这里等价于b//=2
    return r * a


X = 9
Y = 9
COUNT= 5000000


def main_recursion():
    print('%s main_recursion start' % ctime())
    for i in range(COUNT):
        PowRecursion(X, Y)
    print('%s main_recursion end\n' % ctime())


def main_pow():
    print('%s main_pow start' % ctime())
    for i in range(COUNT):
        pow(X, Y)
    print('%s main_pow end\n' % ctime())

def main_circle():
    print('%s main_circle start' % ctime())
    for i in range(COUNT):
        PowCircle(X, Y)
    print('%s main_circle end\n' % ctime())

def main_circle2():
    print('%s main_circle2 start' % ctime())
    for i in range(COUNT):
        PowCircle2(X, Y)
    print('%s main_circle2 end\n' % ctime())

def main_internet():
    print('%s main_internet start' % ctime())
    for i in range(COUNT):
        PowInternet(X, Y)
    print('%s main_internet end\n' % ctime())


if __name__=='__main__':
    print('PowRecursion(X, Y)',PowRecursion(X, Y))
    print('pow(X, Y)', pow(X, Y))
    print('PowCircle(X, Y)', PowCircle(X, Y))
    print('PowCircle2(X, Y)', PowCircle2(X, Y))
    print('PowInternet(X, Y)', PowInternet(X, Y))
    main_recursion()
    main_pow()
    main_circle()
    main_circle2()
    main_internet()

运行结果

PowRecursion(X, Y) 387420489
pow(X, Y) 387420489.0
PowCircle(X, Y) 387420489
PowCircle2(X, Y) 59049
PowInternet(X, Y) 387420489
Fri Sep 11 17:31:39 2020 main_recursion start
Fri Sep 11 17:31:46 2020 main_recursion end

Fri Sep 11 17:31:46 2020 main_pow start
Fri Sep 11 17:31:47 2020 main_pow end

Fri Sep 11 17:31:47 2020 main_circle start
Fri Sep 11 17:31:50 2020 main_circle end

Fri Sep 11 17:31:50 2020 main_circle2 start
Fri Sep 11 17:31:52 2020 main_circle2 end

Fri Sep 11 17:31:52 2020 main_internet start
Fri Sep 11 17:31:56 2020 main_internet end

后记

1、递归的函数调用要消耗时间，比while要慢
2、python内部的pow接口最快，待进一步研究？！