程序检查N是否是居中的七边形数字

给定一个整数N ，任务是检查它是否是一个中心的七边形数字。

Centered heptagonal number is centered figure number that represents a heptagon with dot in center and all other dot surrounding in heptagonal form..The first few Centered heptagonal number are 1, 8, 22, 43, 71, 106, 148, …

例子：

Input: N = 8 
Output: Yes 
Explanation: 
8 is the Second Centered heptagonal number.
Input: 20 
Output: No 
Explanation: 
20 is not a Centered heptagonal number. 
 

方法：
为了解决上述问题，我们必须知道中心七边形数的K^个项为： $K^{th} Term = \frac {7*N^{2} - 7*N + 2}{2}$
因为我们必须检查给定的数字是否可以表示为中心的七边形数字。可以通过将方程式概括为以下内容进行检查：

=> $N = \frac {7*k^{2} - 7*k + 2}{2}$
=> $K = \frac{7 + \sqrt{56*N + 7}}{14}$
 

最后，使用此公式检查计算值是否为整数，如果为整数，则表示N为中心七边形数。
下面是上述方法的实现：

C++

// C++ implementation to check that
// a number is a Centered
// heptagonal number or not
 
#include 
using namespace std;
 
// Function to check that the
// number is a Centered
// heptagonal number
bool isCenteredheptagonal(int N)
{
    float n = (7 + sqrt(56 * N - 7)) / 14;
 
    // Condition to check if the
    // number is a Centered heptagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    int n = 8;
 
    // Function call
    if (isCenteredheptagonal(n)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java

// Java implementation to check that
// a number is a Centered
// heptagonal number or not
import java.lang.Math;
 
class GFG
{
     
// Function to check that the
// number is a Centered
// heptagonal number
public static boolean isCenteredheptagonal(int N)
{
    double n = (7 + Math.sqrt(56 * N - 7)) / 14;
 
    // Condition to check if the
    // number is a Centered heptagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
public static void main(String[] args)
{
    int n = 8;
 
    // Function call
    if (isCenteredheptagonal(n))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
}
}
 
// This code is contributed by divyeshrabadiya07

Python3

# Python3 implementation to check
# that a number is a centered
# heptagonal number or not
import math
 
# Function to check that the
# number is a centered
# heptagonal number
def isCenteredheptagonal(N):
     
    n = (7 + math.sqrt(56 * N - 7)) / 14
     
    # Condition to check if the number
    # is a centered heptagonal number
    return (n - int(n)) == 0
     
# Driver Code
n = 8
 
# Function call
if (isCenteredheptagonal(n)):
    print("Yes")
else:
    print("No")
     
# This code is contributed by ShubhamCoder

C#

// C# implementation to check that
// a number is a centered
// heptagonal number or not
using System;
 
class GFG{
 
// Function to check that the
// number is a centered
// heptagonal number
static bool isCenteredheptagonal(int N)
{
    double n = (7 + Math.Sqrt(56 * N - 7)) / 14;
     
    // Condition to check if the number
    // is a centered heptagonal number
    return (n - (int)n) == 0;
}
     
// Driver Code
static public void Main ()
{
    int n = 8;
     
    // Function call
    if (isCenteredheptagonal(n))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
 
// This code is contributed by ShubhamCoder

Javascript

// Javascript implementation to check that
// a number is a Centered
// heptagonal number or not
 
// Function to check that the
// number is a Centered
// heptagonal number
function isCenteredheptagonal(N)
{
    let n = (7 + Math.sqrt(56 * N - 7)) / 14;
 
    // Condition to check if the
    // number is a Centered heptagonal number
    return (n - parseInt(n)) == 0;
}
 
// Driver Code
let n = 8;
 
// Function call
if (isCenteredheptagonal(n)) {
    document.write("Yes");
}
else {
    document.write("No");
}
 
// This code is contributed by rishavmahato348.

输出：

Yes