程序检查N是否为中心六边形

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

Centered hexagonal number are figurate numbers and are in the form of the Hexagon. The Centered Hexagonal number is different from Hexagonal Number because it contains one element at the center..The first few Centered hexagonal numbers are 1, 7, 19, 37, 61, 91, 127 …

例子：

Input: N = 7 
Output: Yes 
Explanation: 
Second Centered hexagonal number is 7.

Input: N = 20 
Output: No 
 

方法：

• 中心六边形数的第K^个项为
  $K^{th} Term = {3*K^{2} - 3*K + 2}$
• 因为我们必须检查给定的数字是否可以表示为中心六边形数字。可以检查为：

=> $N = {3*K^{2} - 3*K + 2}$
=> $K = \frac{3 + \sqrt{12*N - 3}}{6}$
 

• 如果使用上述公式计算的K值为整数，则N为中心六边形数。
• 否则，数字N不是中心六边形数字。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to check that the
// number is a Centered hexagonal number
bool isCenteredhexagonal(int N)
{
    float n
        = (3 + sqrt(12 * N - 3))
          / 6;
 
    // Condition to check if the
    // number is a Centered hexagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    int N = 7;
 
    // Function call
    if (isCenteredhexagonal(N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java

// Java program for the above approach
class GFG{
 
// Function to check that the
// number is a Centered hexagonal number
static boolean isCenteredhexagonal(int N)
{
    float n = (float)((3 + Math.sqrt(12 * N - 3)) / 6);
 
    // Condition to check if the
    // number is a Centered hexagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
public static void main(String[] args)
{
    int N = 7;
 
    // Function call
    if (isCenteredhexagonal(N))
    {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}
 
// This code is contributed by sapnasingh4991

Python3

# Python3 program for the above approach
import math
 
# Function to check that the number
# is a centered hexagonal number
def isCenteredhexagonal(N):
     
    n = (3 + math.sqrt(12 * N - 3)) / 6
     
    # Condition to check if the number
    # is a centered hexagonal number
    return (n - int(n)) == 0
 
# Driver Code
N = 7
 
if isCenteredhexagonal(N):
    print("Yes")
else :
    print("No")
 
# This code is contributed by ishayadav181

C#

// C# program for the above approach
using System;
 
class GFG{
 
// Function to check that the number
// is a centered hexagonal number
static bool isCenteredhexagonal(int N)
{
    float n = (float)((3 + Math.Sqrt(12 * N -
                                     3)) / 6);
 
    // Condition to check if the number
    // is a centered hexagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
public static void Main(String[] args)
{
    int N = 7;
 
    // Function call
    if (isCenteredhexagonal(N))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
 
// This code is contributed by amal kumar choubey

Javascript

 
// Javascript program for the above approach
 
// Function to check that the
// number is a Centered hexagonal number
function isCenteredhexagonal(N)
{
    let n = parseInt((3 + Math.sqrt(12 * N - 3)) / 6);
 
    // Condition to check if the
    // number is a Centered hexagonal number
    return (n - parseInt(n)) == 0;
}
 
// Driver Code
let N = 7;
 
// Function call
if (isCenteredhexagonal(N))
{
    document.write("Yes");
}
else
{
    document.write("No");
}
 
// This code is contributed by souravmahato348
 

输出：

Yes