程序检查N是否为同心六边形

给定整数N ，任务是检查N是否为同心六边形。如果数字N是同心六边形，则打印“是”，否则打印“否” 。

Concentric Hexagonal Numbers are the number sequence forms a pattern with concentric hexagons, and the numbers denote the number of points required after the N-th stage of the pattern. The first few concentric hexagonal numbers are 0, 1, 6, 13, 24, 37, 54, 73, 96, 121 …

例子：

Input: N = 6
Output: Yes
Explanation:
Third Concentrichexagonal number is 6.

Input: N = 20
Output: No

方法：

1. 同心六角形数的第K^个项为：

   Kth Term = (3 * K * K) / 2

2. 因为我们必须检查给定的数字是否可以表示为同心六角形数字。可以检查为：

   Here, Kth Term = N
   => (3 * K * K) / 2 = N
   => 3 * K * K – 2 * N = 0
   The positive root of this equation is:
   K = sqrt((2 * N )/3)

3. 如果使用上述公式计算出的K值为整数，则N为同心六边形数。
4. 否则，数字N不是同心六边形。

   下面是上述方法的实现：

   C++

   // C++ program to check if N is a
   // Concentric Hexagonal Number
     
   #include 
   using namespace std;
     
   // Function to check if the
   // number is a Concentric hexagonal number
   bool isConcentrichexagonal(int N)
   {
       float n = sqrt((2 * N) / 3);
     
       // Condition to check if the
       // number is a Concentric 
       // hexagonal number
       return (n - (int)n) == 0;
   }
     
   // Driver Code
   int main()
   {
       int N = 6;
     
       // Function call
       if (isConcentrichexagonal(N)) {
           cout << "Yes";
       }
       else {
           cout << "No";
       }
       return 0;
   }

   Java

   // Java program to check if N is a
   // Concentric Hexagonal Number
   class GFG{
     
   // Function to check if the
   // number is a Concentric hexagonal number
   static boolean isConcentrichexagonal(int N)
   {
       float n = (float) Math.sqrt((2 * N) / 3);
     
       // Condition to check if the
       // number is a Concentric 
       // hexagonal number
       return (n - (int)n) == 0;
   }
     
   // Driver Code
   public static void main(String[] args)
   {
       int N = 6;
     
       // Function call
       if (isConcentrichexagonal(N)) 
       {
           System.out.print("Yes");
       }
       else 
       {
           System.out.print("No");
       }
   }
   }
     
   // This code is contributed by PrinciRaj1992

   Python3

   # Python3 program to check if N is a 
   # concentric hexagonal number 
   import math
     
   # Function to check if the number
   # is a concentric hexagonal number 
   def isConcentrichexagonal(N):
         
       n = math.sqrt((2 * N) / 3)
         
       # Condition to check if the 
       # number is a concentric 
       # hexagonal number
       return (n - int(n)) == 0
     
   # Driver code
   N = 6
     
   if isConcentrichexagonal(N):
       print("Yes")
   else:
       print("No")
     
   # This code is contributed by divyeshrabadiya07

   C#

   // C# program to check if N is a
   // concentric hexagonal number
   using System;
     
   class GFG{
     
   // Function to check if the number 
   // is a concentric hexagonal number
   static bool isConcentrichexagonal(int N)
   {
       float n = (float) Math.Sqrt((2 * N) / 3);
     
       // Condition to check if the
       // number is a concentric 
       // hexagonal number
       return (n - (int)n) == 0;
   }
     
   // Driver Code
   public static void Main()
   {
       int N = 6;
     
       // Function call
       if (isConcentrichexagonal(N)) 
       {
           Console.Write("Yes");
       }
       else
       {
           Console.Write("No");
       }
   }
   }
     
   // This code is contributed by Code_Mech

   输出：

   Yes