检查除数的计数是偶数还是奇数-yiteyi-C++库

给定一个数“n”，求其除数的总数为偶数或奇数。 例如：

null

Input  : n = 10      Output : EvenInput:  n = 100Output: OddInput:  n = 125Output: Even

我们强烈建议您在继续解决方案之前单击此处并进行练习。

A. 幼稚的方法 那就是找到所有的除数然后看看除数的总数是偶数还是奇数。这种解决方案的时间复杂度为O（sqrt（n））

C++

                         // Naive Solution to find                       
                         // if count of divisors                       
                         // is even or odd                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to count                       
                         // the divisors                       
                         void                                     countDivisors(                                     int                                     n)                       
                         {                       
                                                 // Initialize count                       
                                                 // of divisors                       
                                                 int                                     count = 0;                       
           
                                                 // Note that this                       
                                                 // loop runs till                       
                                                 // square root                       
                                                 for                                     (                                     int                                     i = 1; i <=                                     sqrt                                     (n) + 1; i++)                       
                                                 {                       
                                                 if                                     (n % i == 0)                       
           
                                                 // If divisors are                       
                                                 // equal increment                       
                                                 // count by one                       
                                                 // Otherwise increment                       
                                                 // count by 2                       
                                                 count += (n / i == i) ? 1 : 2;                       
                                                 }                       
           
                                                 if                                     (count % 2 == 0)                       
                                                 cout <<                                     "Even"                                     << endl;                       
                                                 else                       
                                                 cout <<                                     "Odd"                                     << endl;                       
                         }                       
           
                         // Driver Code                       
                         int                                     main()                       
                         {                       
                                                 cout <<                                     "The count of divisor: "                                     ;                       
                                                 countDivisors(10);                       
                                                 return                                     0;                       
                         }                       
           
                         // This code is Contributed by SHUBHAMSINGH10                       

C

                         // Naive Solution to find                       
                         // if count of divisors                       
                         // is even or odd                       
           
                         #include <math.h>                       
                         #include <stdio.h>                       
           
                         // Function to count                       
                         // the divisors                       
                         void                                     countDivisors(                                     int                                     n)                       
                         {                       
                                                 // Initialize count                       
                                                 // of divisors                       
                                                 int                                     count = 0;                       
           
                                                 // Note that this                       
                                                 // loop runs till                       
                                                 // square root                       
                                                 for                                     (                                     int                                     i = 1; i <=                                     sqrt                                     (n) + 1; i++)                       
                                                 {                       
                                                 if                                     (n % i == 0)                       
           
                                                 // If divisors are                       
                                                 // equal increment                       
                                                 // count by one                       
                                                 // Otherwise increment                       
                                                 // count by 2                       
                                                 count += (n / i == i) ? 1 : 2;                       
                                                 }                       
           
                                                 if                                     (count % 2 == 0)                       
                                                 printf                                     (                                     "Even"                                     );                       
           
                                                 else                       
                                                 printf                                     (                                     "Odd"                                     );                       
                         }                       
           
                         // Driver Code                       
                         int                                     main()                       
                         {                       
                                                 printf                                     (                                     "The count of divisor: "                                     );                       
                                                 countDivisors(10);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Naive Solution to find if count                       
                         // of divisors is even or odd                       
           
                         import                                     java.io.*;                       
                         import                                     java.math.*;                       
           
                         class                                     GFG                       
                         {                       
           
                                                 // Function to count                       
                                                 // the divisors                       
                                                 static                                     void                                     countDivisors(                                     int                                     n)                       
                                                 {                       
                                                 // Initialize count                       
                                                 // of divisors                       
                                                 int                                     count =                                     0                                     ;                       
           
                                                 // Note that this                       
                                                 // loop runs till                       
                                                 // square root                       
                                                 for                                     (                                     int                                     i =                                     1                                     ; i <= Math.sqrt(n) +                                     1                                     ; i++)                       
                                                 {                       
                                                 if                                     (n % i ==                                     0                                     )                       
           
                                                 // If divisors are                       
                                                 // equal increment                       
                                                 // count by one                       
                                                 // Otherwise increment                       
                                                 // count by 2                       
                                                 count += (n / i == i) ?                                     1                                     :                                     2                                     ;                       
                                                 }                       
           
                                                 if                                     (count %                                     2                                     ==                                     0                                     )                       
                                                 System.out.println(                                     "Even"                                     );                       
           
                                                 else                       
                                                 System.out.println(                                     "Odd"                                     );                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main(String args[])                       
                                                 {                       
                                                 System.out.print(                                     "The count of divisor: "                                     );                       
                                                 countDivisors(                                     10                                     );                       
                                                 }                       
                         }                       
                         // This code is contributed by Nikita Tiwari                       

Python3

                         # Naive Solution to find if count                       
                         # of divisors is even or odd                       
                         import                                     math                       
           
                         # Function to count                       
                         # the divisors                       
                         def                                     countDivisors(n) :                       
                                   
                                                 # Initialize count                       
                                                 # of divisors                       
                                                 count                                     =                                     0                       
           
                                                 # Note that this loop                       
                                                 # runs till square                       
                                                 # root                       
                                                 for                                     i                                     in                                     range                                     (                                     1                                     , (                                     int                                     )(math.sqrt(n))                                     +                                     2                                     ) :                       
                                                 if                                     (n                                     %                                     i                                     =                                     =                                     0                                     ) :                       
                                   
                                                 # If divisors are                       
                                                 # equal, increment                       
                                                 # count by one                       
                                                 # Otherwise increment                       
                                                 # count by 2                       
                                                 if                                     ( n                                     /                                     /                                     i                                     =                                     =                                     i) :                       
                                                 count                                     =                                     count                                     +                                     1                       
                                                 else                                     :                       
                                                 count                                     =                                     count                                     +                                     2                       
           
                                                 if                                     (count                                     %                                     2                                     =                                     =                                     0                                     ) :                       
                                                 print                                     (                                     "Even"                                     )                       
                                                 else                                     :                       
                                                 print                                     (                                     "Odd"                                     )                       
           
           
                         # Driver Code                       
                         print                                     (                                     "The count of divisor: "                                     )                       
                         countDivisors(                                     10                                     )                       
           
                         # This code is contributed by Nikita Tiwari                       

C#

                         // C# program using Naive                       
                         // Solution to find if                       
                         // count of divisors                       
                         // is even or odd                       
                         using                                     System;                       
           
                         class                                     GFG {                       
           
                                                 // Function to count                       
                                                 // the divisors                       
                                                 static                                     void                                     countDivisors(                                     int                                     n)                       
                                                 {                       
                                                 // Initialize count                       
                                                 // of divisors                       
                                                 int                                     count = 0;                       
           
                                                 // Note that this                       
                                                 // loop runs till                       
                                                 // square root                       
                                                 for                                     (                                     int                                     i = 1; i <= Math.Sqrt(n)                       
                                                 + 1;                       
                                                 i++) {                       
                                                 if                                     (n % i == 0)                       
           
                                                 // If divisors are                       
                                                 // equal increment                       
                                                 // count by one                       
                                                 // Otherwise increment                       
                                                 // count by 2                       
                                                 count += (n / i == i) ? 1 : 2;                       
                                                 }                       
           
                                                 if                                     (count % 2 == 0)                       
                                                 Console.Write(                                     "Even"                                     );                       
           
                                                 else                       
                                                 Console.Write(                                     "Odd"                                     );                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 Console.Write(                                     "The count of divisor: "                                     );                       
                                                 countDivisors(10);                       
                                                 }                       
                         }                       
           
                         // This code is contributed by Sam007.                       

PHP

                         <?php                       
                         // Naive Solution to                       
                         // find if count of                       
                         // divisors is even                       
                         // or odd                       
           
                         // Function to count                       
                         // the divisors                       
                         function                                     countDivisors(                                     $n                                     )                       
                         {                       
                                   
                                                 // Initialize count                       
                                                 // of divisors                       
                                                 $count                                     = 0;                       
           
                                                 // Note that this                       
                                                 // loop runs till                       
                                                 // square root                       
                                                 for                                     (                                     $i                                     = 1;                                     $i                                     <= sqrt(                                     $n                                     ) + 1;                                     $i                                     ++)                       
                                                 {                       
                                                 if                                     (                                     $n                                     %                                     $i                                     == 0)                       
           
                                                 // If divisors are                       
                                                 // equal increment                       
                                                 // count by one                       
                                                 // Otherwise increment                       
                                                 // count by 2                       
                                                 $count                                     += (                                     $n                                     /                                     $i                                     ==                                     $i                                     )? 1 : 2;                       
                                                 }                       
           
                                                 if                                     (                                     $count                                     % 2 == 0)                       
                                                 echo                                     "Even"                                     ;                       
                                   
                                                 else                       
                                                 echo                                     "Odd"                                     ;                       
                         }                       
           
                                                 // Driver Code                       
                                                 echo                                     "The count of divisor: "                                     ;                       
                                                 countDivisors(10);                       
                                   
                         // This code is contributed by ajit.                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Naive Solution to find                       
                         // if count of divisors                       
                         // is even or odd                       
           
                         // Function to count                       
                         // the divisors                       
                         function                                     countDivisors(n)                       
                         {                       
                                                 // Initialize count                       
                                                 // of divisors                       
                                                 let count = 0;                       
           
                                                 // Note that this                       
                                                 // loop runs till                       
                                                 // square root                       
                                                 for                                     (let i = 1; i <= Math.sqrt(n) + 1; i++)                       
                                                 {                       
                                                 if                                     (n % i == 0)                       
           
                                                 // If divisors are                       
                                                 // equal increment                       
                                                 // count by one                       
                                                 // Otherwise increment                       
                                                 // count by 2                       
                                                 count += (Math.floor(n / i) == i) ? 1 : 2;                       
                                                 }                       
           
                                                 if                                     (count % 2 == 0)                       
                                                 document.write(                                     "Even"                                     +                                     "<br>"                                     );                       
                                                 else                       
                                                 document.write(                                     "Odd"                                     +                                     "<br>"                                     );                       
                         }                       
           
                         // Driver Code                       
                                                 document.write(                                     "The count of divisor: "                                     );                       
                                                 countDivisors(10);                       
           
                         // This code is contributed by Surbhi Tyagi.                       
           
                         </script>                       

输出：

The count of divisor: Even

高效的解决方案： 我们可以观察到，只有在完全平方的情况下，除数的数目才是奇数。因此，最好的解决方案是检查给定的数字是否为完全平方。如果它是一个完美的正方形，那么除数的数量将是奇数，否则它将是偶数。以下是上述理念的实施：

C++

                         // C++ program for                       
                         // Efficient Solution to find                       
                         // if count of divisors is                       
                         // even or odd                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find if count                       
                         // of divisors is even or                       
                         // odd                       
                         void                                     countDivisors(                                     int                                     n)                       
                         {                       
                                                 int                                     root_n =                                     sqrt                                     (n);                       
           
                                                 // If n is a perfect square,                       
                                                 // then it has odd divisors                       
                                                 if                                     (root_n * root_n == n)                       
                                                 printf                                     (                                     "Odd"                                     );                       
                                                 else                       
                                                 printf                                     (                                     "Even"                                     );                       
                         }                       
           
                         // Driver Code                       
                         int                                     main()                       
                         {                       
                                                 cout <<                                     "The count of divisors"                       
                                                 <<                                     " of 10 is: "                                     ;                       
           
                                                 countDivisors(14);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program for Efficient                       
                         // Solution to find if count of                       
                         // divisors is even or odd                       
                         import                                     java.io.*;                       
                         import                                     java.math.*;                       
           
                         class                                     GFG                       
                         {                       
           
                                                 // Function to find if count                       
                                                 // of divisors is even or                       
                                                 // odd                       
                                                 static                                     void                                     countDivisors(                                     int                                     n)                       
                                                 {                       
                                                 int                                     root_n = (                                     int                                     )(Math.sqrt(n));                       
           
                                                 // If n is a perfect square,                       
                                                 // then, it has odd divisors                       
                                                 if                                     (root_n * root_n == n)                       
                                                 System.out.println(                                     "Odd"                                     );                       
           
                                                 else                       
                                                 System.out.println(                                     "Even"                                     );                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     main(String args[])                       
                                                 throws                                     IOException                       
                                                 {                       
                                                 System.out.print(                                     "The count of"                                     +                       
                                                 "divisors of 10 is: "                                     );                       
           
                                                 countDivisors(                                     10                                     );                       
                                                 }                       
                         }                       
           
                         // This code is contributed by Nikita Tiwari                       

Python3

                         # Python program for                       
                         # Efficient Solution to find                       
                         # find if count of divisors                       
                         # is even or odd                       
                         import                                     math                       
           
                         def                                     NumOfDivisor(n):                       
                                                 if                                     n <                                     1                                     :                       
                                                 return                       
                                                 root_n                                     =                                     int                                     (math.sqrt(n))                       
                                   
                                                 # If n is a perfect square,                       
                                                 # then it has odd divisors                       
                                                 if                                     root_n                                     *                                     *                                     2                                     =                                     =                                     n:                       
                                                 print                                     (                                     'Odd'                                     )                       
                                                 else                                     :                       
                                                 print                                     (                                     'Even'                                     )                       
                                   
                         # Driver code                       
                         if                                     __name__                                     =                                     =                                     '__main__'                                     :                       
                                                 print                                     (                                     "The count of divisor is:"                                     )                       
                                                 NumOfDivisor(                                     14                                     )                       
                                   
                         # This code is contributed by Yt R                       

C#

                         // C# program for efficient                       
                         // solution to find of                       
                         // count of divisors is                       
                         // even or odd                       
                         using                                     System;                       
           
                         class                                     GFG {                       
           
                                                 // Function to find if                       
                                                 // count of divisors                       
                                                 // is even or odd                       
                                                 static                                     void                                     countDivisors(                                     int                                     n)                       
                                                 {                       
                                                 int                                     root_n = (                                     int                                     )(Math.Sqrt(n));                       
           
                                                 // If n is a perfect square,                       
                                                 // then, it has odd divisors                       
                                                 if                                     (root_n * root_n == n)                       
                                                 Console.WriteLine(                                     "Odd"                                     );                       
           
                                                 else                       
                                                 Console.WriteLine(                                     "Even"                                     );                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 Console.Write(                                     "The count of divisors : "                                     );                       
           
                                                 countDivisors(10);                       
                                                 }                       
                         }                       
           
                         // This code is contributed by Sam007.                       

PHP

                         <?php                       
                         // Php program for Efficient                       
                         // Solution to find if count of                       
                         // divisors is even or odd                       
           
                         // Function to find if count                       
                         // of divisors is even or                       
                         // odd                       
           
                         function                                     countDivisors(                                     $n                                     )                       
                         {                       
                                                 $root_n                                     = sqrt(                                     $n                                     );                       
           
                                                 // If n is a perfect square,                       
                                                 // then it has odd divisors                       
                                                 if                                     (                                     $root_n                                     *                                     $root_n                                     ==                                     $n                                     )                       
                                                 echo                                     "Odd"                                     ;                       
                                                 else                       
                                                 echo                                     "Even"                                     ;                       
                         }                       
           
                         // Driver Code                       
                         echo                                     "The count of divisors of 10 is: "                                     ;                       
           
                         countDivisors(10);                       
           
                         // This code is contributed by ajit                       
                         ?>                       

Javascript

                         <script>                       
           
                         // JavaScript program for                       
                         // Efficient Solution to find                       
                         // if count of divisors                       
                         // is even or odd                       
           
                         // Function to count                       
                         // the divisors                       
                         function                                     countDivisors(n)                       
                         {                       
                                                 // Store square root of n                       
                                                 let root_n = Math.sqrt(n);                       
           
                                                 // If n is a perfect square,                       
                                                 // then it has odd divisors                       
                                                 if                                     (root_n * root_n == n)                       
                                                 document.write(                                     "Odd"                                     +                                     "<br>"                                     );                       
                                                 else                       
                                                 document.write(                                     "Even"                                     +                                     "<br>"                                     );                       
                         }                       
           
                         // Driver Code                       
                                                 document.write(                                     "The count of divisor: "                                     );                       
                                                 countDivisors(10);                       
           
                         // This code is contributed by Surbhi Tyagi.                       
           
                         </script>                       

输出：

The count of divisor: Even

本文由阿什图什·库马尔。如果您发现任何不正确的地方，或者您想分享有关上述主题的更多信息，请发表评论。

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