乘方算法

一般的乘方算法，时间复杂度是O(n)

非递归方式

int Power(int num, int exponent)
{
    int result = 1;
    while (exponent) {
        if (exponent & 1) {
            result *= num;
        }
        num *= num;
        exponent = exponent >> 1;
    }
    return result;
}

通过下面的方式，能达到O(logn)

递归方式

递归的普通操作方式

long power(long num, long exponent)
{
    if (exponent == 0)
        return 1;
    if (exponent == 1)
        return num;
    if (exponent % 2 == 1)
        return num*power(num*num, exponent / 2);

    else
        return power(num*num, exponent / 2);

递归的位操作方式

int Power(int num, int exponent)
{
    if (1 == exponent) {
        return num;
    }

    if (0 == exponent) {
        return 1;
    }

    int result = 0;
    if (exponent & 1) {//if exponent is odd
        result = num * Power(num * num, exponent >> 1);
    } else {//if exponent is even
        result = Power(num * num, exponent >> 1);
    }
    return result;
 }

完整的程序代码：

#include <iostream>

using namespace std;

long power(long num, long exponent)
{
    if (exponent == 0)
        return 1;
    if (exponent == 1)
        return num;
    if (exponent % 2 == 1)
        return num*power(num*num, exponent / 2);

    else
        return power(num*num, exponent / 2);

    //或者采用下边位操作方式
    //if (exponent & 1) //if exponent is odd 
    //{ 
    //  result = num * Power(num * num, exponent >> 1);
    //}
    //else //if exponent is even  
    //{
    //  result = Power(num * num, exponent >> 1);
    //}


}

int main()
{
    long x, n;
    cout << "请输入x和n的值：";
    cin >> x >> n;
    cout << "power(x,n)的值：" << power(x, n) << endl;

    system("pause");
    return 0;
}

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