📜  程序检查N是否是居中的七边形数字

📅  最后修改于: 2021-04-24 18:45:06             🧑  作者: Mango

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。

例子:

方法:
为了解决上述问题,我们必须知道中心七边形数的K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:

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


输出:
Yes