二分指数

2025年2月6日 | 阅读3分钟

顾名思义，它是对一个数字或一个二进制分量进行计算，其结果可以小至零，也可以复杂至十的十八次方。二元指数的概念利用了指数的两个基本概念。我们在低年级的时候学过，任何数字都可以用求和或求幂的幂次表示法来表示。

这两种方法使我们能够超越传统的三次穷举法来表示二进制数字的计算。在本文中，我们将深入探讨 C++ 编程语言中的二元指数概念。

算法

// In this tutorial, we are going to learn about the concept of binary 
// exponentiation in C++ programming language with its relevant code and 
// output supported by comments and syntax, the below algorithm depicts
// the binary exponentiation in simpler terms 
POWER(a,b) :
    if b==0 :{
        return 1
    }
// function to calculate and return the answer to the main driver code
    else if b is odd :{
// if the initial condition fails, we compute for the next best edge case
        return a*POWER(a,(b-1)/2)*POWER(a,(b-1)/2)
    }
    else :{
// if the initial condition fails, we compute for the next best edge case
        return POWER(a,b/2)*POWER(a,b/2)
    }   

C++ 代码

// In this tutorial, we are going to learn about the concept of binary 
// exponentiation in C++ programming language with its relevant code and 
// output supported by comments and syntax 
#include <iostream>
using namespace std;
// function to calculate and return the answer to the main driver code
int exponent(int a, int b){
    
// this is our recursive base case when the variable b turns to 0
    if(b==0){
// universal fact a numerical which is raised to 0 is always one for sure
        return 1;
    }
    
// if the initial condition fails, we compute for the next best edge case
// b-1 operating b-1, which returns a and the answer to the main driver
// code functionality 
    
 // Here, we have created variables a and b which will store 'a' raised 
// to the power of 'b.'
    int answer = a * exponent(a,b-1);
    
    return answer;
}
// The main driver code functionality starts from here
int main() {
	
// Here, we have created variables a and b, which will compute a raised 
// to the power of b
	int a = 44, b = 8;
	
// Here, we are calling the  variables a and b, which will compute a raised 
// to the power of b
	cout<<"44 raised to the power 8 is : "<<exponent(a,b)<<endl;
// the main driver code functionality ends from here	
	return 0;
}

输出

44 raised to the power eight is: -614400000

C++ 代码

// In this article, we are going to learn about the concept of binary 
// exponentiation in C++ programming language with its relevant code and 
// output supported by comments and syntax 
#include <iostream>
using namespace std;

// function to calculate and return the answer to the main driver code
// operating a raised to the power of b
int power (int a, int b){
// this is our recursive base case when the variable b turns to 0
    if(b==0){
        return 1;
    }
    //edge case cementing if the variable b turns out to be odd
    else if(b%2==1){
        return a*power(a,(b-1)/2)*power(a,(b-1)/2);
    }
//edge case cementing if the variable b turns out to be even
    else{
        return power(a,b/2)*power(a,b/2);
    }
}
// The main driver code functionality starts from here
int main() {
	
// Here, we have created variables a and b, which will compute a raised 
// to the power of b

	int a = 15 , b = 23;
	
	// here, we are trying to output the answer
	cout<<"15 raised to the power 23 is: "<<power(a,b)<<endl;
	
	return 0;
// The main driver code functionality starts from here
 }

输出

15 raised to the power 23 is: 300332143

C++ 代码

#include <iostream>
using namespace std;

int main() {
	int a = 35 , b = 28;
	int answer = 1;
	while(b>0){
	    if(b%2==1){
	        answer = answer*a;
	        a = a*a;
	    }
	    else{
	        a = a*a;
	    }
	    b = b/2;
	    
	}
	cout<<"35 raised to the power 28 is: "<<answer<<endl;
	return 0;
}

输出

35 raised to the power 28 is: -1049643599

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