二次幂乘法-yiteyi-C++库

给定两个数x和n，我们需要x乘以2 ^N 例如：

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Input  : x = 25, n = 3Output : 20025 multiplied by 2 raised to power 3is 200.Input : x = 70, n = 2Output : 280

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

A. 简单解决方案 就是计算2的n次方，然后乘以x。

C++

                         // Simple C/C++ program                       
                         // to compute x * (2^n)                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
                         typedef                                     long                                     long                                     int                                     ll;                       
           
                         // Returns 2 raised to power n                       
                         ll power2(ll n)                       
                         {                       
                                                 if                                     (n == 0)                       
                                                 return                                     1;                       
                                   
                                                 if                                     (n == 1)                       
                                                 return                                     2;                       
                                   
                                                 return                                     power2(n / 2) *                       
                                                 power2(n / 2);                       
                         }                       
           
                         ll multiply(ll x, ll n)                       
                         {                       
                                                 return                                     x * power2(n);                       
                         }                       
           
                         // Driven program                       
                         int                                     main()                       
                         {                       
                                                 ll x = 70, n = 2;                       
                                                 cout<<multiply(x, n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Simple Java program                       
                         // to compute x * (2^n)                       
                         import                                     java.util.*;                       
           
                         class                                     GFG {                       
                                   
                                                 // Returns 2 raised to power n                       
                                                 static                                     long                                     power2(                                     long                                     n)                       
                                                 {                       
                                                 if                                     (n ==                                     0                                     )                       
                                                 return                                     1                                     ;                       
                                   
                                                 if                                     (n ==                                     1                                     )                       
                                                 return                                     2                                     ;                       
                                   
                                                 return                                     power2(n /                                     2                                     )                       
                                                 * power2(n /                                     2                                     );                       
                                                 }                       
                                   
                                                 static                                     long                                     multiply(                                     long                                     x,                                     long                                     n)                       
                                                 {                       
                                                 return                                     x * power2(n);                       
                                                 }                       
                                   
                                                 /* Driver program */                       
                                                 public                                     static                                     void                                     main(String[] args)                       
                                                 {                       
                                                 long                                     x =                                     70                                     , n =                                     2                                     ;                       
                                   
                                                 System.out.println(multiply(x, n));                       
                                                 }                       
                         }                       
                                   
                         // This code is contributed by Arnav Kr. Mandal.                       

Python3

                         # Simple Python program                       
                         # to compute x * (2^n)                       
           
                         # Returns 2 raised to power n                       
                         def                                     power2(n):                       
           
                                                 if                                     (n                                     =                                     =                                     0                                     ):                       
                                                 return                                     1                       
                                                 if                                     (n                                     =                                     =                                     1                                     ):                       
                                                 return                                     2                       
                                                 return                                     power2(n                                     /                                     2                                     )                                     *                       
                                                 power2(n                                     /                                     2                                     );                       
           
           
                         def                                     multiply(x, n):                       
                                                 return                                     x                                     *                                     power2(n);                       
           
           
                         # Driven program                       
                         x                                     =                                     70                       
                         n                                     =                                     2                       
                         print                                     (multiply(x, n))                       
           
                         # This code is contributed by Smitha Dinesh Semwal                       

C#

                         // Simple C# program                       
                         // to compute x * (2^n)                       
                         using                                     System;                       
           
                         class                                     GFG {                       
                                   
                                                 // Returns 2 raised to power n                       
                                                 static                                     long                                     power2(                                     long                                     n)                       
                                                 {                       
                                                 if                                     (n == 0)                       
                                                 return                                     1;                       
                                   
                                                 if                                     (n == 1)                       
                                                 return                                     2;                       
                                   
                                                 return                                     power2(n / 2)                       
                                                 * power2(n / 2);                       
                                                 }                       
                                   
                                                 static                                     long                                     multiply(                                     long                                     x,                                     long                                     n)                       
                                                 {                       
                                                 return                                     x * power2(n);                       
                                                 }                       
                                   
                                                 /* Driver program */                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 long                                     x = 70, n = 2;                       
                                   
                                                 Console.WriteLine(multiply(x, n));                       
                                                 }                       
                         }                       
                                   
                         // This code is contributed by Vt_m.                       

PHP

                         <?php                       
                         // Simple PHP program                       
                         // to compute x * (2^n)                       
           
                         // Returns 2 raised to power n                       
                         function                                     power2(                                     $n                                     )                       
                         {                       
                                                 if                                     (                                     $n                                     == 0)                       
                                                 return                                     1;                       
                                   
                                                 if                                     (                                     $n                                     == 1)                       
                                                 return                                     2;                       
                                   
                                                 return                                     power2(                                     $n                                     / 2) *                       
                                                 power2(                                     $n                                     / 2);                       
                         }                       
           
                         function                                     multiply(                                     $x                                     ,                                     $n                                     )                       
                         {                       
                                                 return                                     $x                                     * power2(                                     $n                                     );                       
                         }                       
           
                         // Driver Code                       
                         $x                                     = 70;                                     $n                                     = 2;                       
                         echo                                     multiply(                                     $x                                     ,                                     $n                                     );                       
           
                         // This code is contributed by ajit                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Simple JavaScript program                       
                         // to compute x * (2^n)                       
           
                         // Returns 2 raised to power n                       
                         function                                     power2(n)                       
                         {                       
                                                 if                                     (n == 0)                       
                                                 return                                     1;                       
                                   
                                                 if                                     (n == 1)                       
                                                 return                                     2;                       
                                   
                                                 return                                     power2(n / 2) *                       
                                                 power2(n / 2);                       
                         }                       
           
                         function                                     multiply( x, n)                       
                         {                       
                                                 return                                     x * power2(n);                       
                         }                       
           
                         // Driver Code                       
                         let x = 70                       
                         let n = 2;                       
                         document.write( multiply(x, n));                       
           
                         // This code is contributed by mohan                       
           
                         </script>                       

输出：

时间复杂性： O（对数n）一 有效解决方案 就是使用按位左移位运算符我们知道1意味着2被提升为幂。

C++

                         // Efficient C/C++ program to compute x * (2^n)                       
                         #include <stdio.h>                       
                         typedef                                     long                                     long                                     int                                     ll;                       
           
                         ll multiply(ll x, ll n)                       
                         {                       
                                                 return                                     x << n;                       
                         }                       
           
                         // Driven program to check above function                       
                         int                                     main()                       
                         {                       
                                                 ll x = 70, n = 2;                       
                                                 printf                                     (                                     "%lld"                                     , multiply(x, n));                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // JAVA Code for Multiplication with a                       
                         // power of 2                       
                         import                                     java.util.*;                       
           
                         class                                     GFG {                       
                                   
                                                 static                                     long                                     multiply(                                     long                                     x,                                     long                                     n)                       
                                                 {                       
                                                 return                                     x << n;                       
                                                 }                       
                                   
                                                 /* Driver program to test above function */                       
                                                 public                                     static                                     void                                     main(String[] args)                       
                                                 {                       
                                                 long                                     x =                                     70                                     , n =                                     2                                     ;                       
                                                 System.out.println(multiply(x, n));                       
                                                 }                       
                         }                       
           
                         //This code is contributed by Arnav Kr. Mandal.                       

Python3

                         # Efficient Python3 code to compute x * (2^n)                       
           
                         def                                     multiply( x , n ):                       
                                                 return                                     x << n                       
                                   
                         # Driven code to check above function                       
                         x                                     =                                     70                       
                         n                                     =                                     2                       
                         print                                     ( multiply(x, n))                       
           
                         # This code is contributed by "Sharad_Bhardwaj".                       

C#

                         // C# Code for Multiplication with a                       
                         // power of 2                       
                         using                                     System;                       
           
                         class                                     GFG {                       
                                   
                                                 static                                     int                                     multiply(                                     int                                     x,                                     int                                     n)                       
                                                 {                       
                                                 return                                     x << n;                       
                                                 }                       
                                   
                                                 /* Driver program to test above function */                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     x = 70, n = 2;                       
                                   
                                                 Console.WriteLine(multiply(x, n));                       
                                                 }                       
                         }                       
           
                         //This code is contributed by vt_m.                       

PHP

                         <?php                       
                         // Efficient PHP program to compute x * (2^n)                       
           
                         function                                     multiply(                                     $x                                     ,                                     $n                                     )                       
                         {                       
                                                 return                                     $x                                     <<                                     $n                                     ;                       
                         }                       
           
                                                 // Driver Code                       
                                                 $x                                     = 70;                       
                                                 $n                                     = 2;                       
                                                 echo                                     multiply(                                     $x                                     ,                                     $n                                     );                       
                                   
                         // This code is contributed by ajit                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Efficient JavaScript program to compute x * (2^n)                       
           
                         function                                     multiply(x, n)                       
                         {                       
                                                 return                                     x << n;                       
                         }                       
           
                                                 // Driver Code                       
                                                 let x = 70;                       
                                                 let n = 2;                       
                                                 document.write(multiply(x, n));                       
           
                         // This code is contributed by mohan                       
           
                         </script>                       

输出：

时间复杂度：O（1）

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