使用快速幂运算将A的升高值计算为B的幂

忘是亡心i 2023-03-05 04:29 3阅读 0赞

Now here we are going to learn that **how to compute the value of a^b i.e. "A" raise to the power "B" using an optimized algorithm called as "fast-exponentiation"**?

现在，我们将在这里学习**如何使用称为“快速幂运算”的优化算法来计算a ^ b的值，即“ A”提高到幂“ B”** ？

we could have used a brute force approach to do the required task but then it would have taken **O(b)** i.e a brute force approach can solve the required task in linear time whereas the same task could be done in **O(log b)** using **FAST–EXPONENTIATION**.

我们本可以使用蛮力方法来完成所需的任务，但随后它会采用**O(b)，**即蛮力方法可以在线性时间内解决所需的任务，而相同的任务可以在**O(log b)中**使用**快速赋权** 。

**Fast exponentiation** uses a simple recursive approach whose recurrence relation can be written as :

**快速求幂**使用一种简单的递归方法，其递归关系可以写成：

**F(a,b) = F(a,b/2)\*F(a,b/2)**

**F(a，b)= F(a，b / 2)\* F(a，b / 2)**

From the above recurrence relation, it can be easily seen that the time complexity would be **O(log b)**.

从上面的递归关系可以很容易地看出时间复杂度为**O(log b)** 。

## C ++程序使用快速幂运算来查找A ^ B的值 **(**C++ program to find the value of A^B using fast exponentiation**)** ##

#include <iostream>
    using namespace std;
    
    //function to find a^b
    int fcheck(int a,int b){
        
    	if(b == 0)
    	    return 1;
    	if(b == 1)
    		return a;
    	return fcheck(a,b/2)*fcheck(a,b/2);
    }
    
    //main code
    int main(){
        
    	int a,b;
    
    	cout<<"Enter the first number (value of a): ";
    	cin>>a;
    	cout<<"Enter the second number (Value of b): ";
    	cin>>b;
    
    	int x=fcheck(a,b);
    	if(b%2==0 || b==1)
    		cout<<a<<" raise to the power "<<b<<" is = " <<x<<endl;
    	else
    		cout<<a<<" raise to the power "<<b<<" is = " <<a*x<<endl;
    
    	return 0;
    }

**Output**

**输出量**

First run:
    Enter the first number (value of a): 5
    Enter the second number (Value of b): 3
    5 raise to the power 3 is = 125
    
    Second run:
    Enter the first number (value of a): 5
    Enter the second number (Value of b): 0
    5 raise to the power 0 is = 1
    
    Third run:
    Enter the first number (value of a): 5
    Enter the second number (Value of b): 1
    5 raise to the power 1 is = 5

> 翻译自: [https://www.includehelp.com/algorithms/compute-the-value-of-a-raise-to-the-power-b-using-fast-exponentiation.aspx][https_www.includehelp.com_algorithms_compute-the-value-of-a-raise-to-the-power-b-using-fast-exponentiation.aspx]

[https_www.includehelp.com_algorithms_compute-the-value-of-a-raise-to-the-power-b-using-fast-exponentiation.aspx]: https://www.includehelp.com/algorithms/compute-the-value-of-a-raise-to-the-power-b-using-fast-exponentiation.aspx