程序检查N是否是中心五角形数

给定数字N ，任务是检查N是否为中心五角形数。如果数字N是中心五角数字，则打印“是”，否则打印“否” 。

Centered Pentagonal Number is a centered figurate number that represents a pentagon with a dot in the centre and other dots surrounding it in pentagonal layers successively. The first few Centered Pentagonal Number are 1, 6, 16, 31, 51, 76, 106 … 

例子：

Input: N = 6 
Output: Yes 
Explanation: 
Second Centered pentagonal number is 6.

Input: N = 20 
Output: No 

方法：

1.中心五角数的第K^个项为
$K^{th} Term = \frac{5*K^{2} - 5*K + 2}{2}$

2.由于我们必须检查给定的数字是否可以表示为中心五角形数。可以检查为：

=> $N = \frac{5*K^{2} - 5*K + 2}{2}$
=> $K = \frac{5 + \sqrt{40*N - 15}}{10}$

3.如果使用上述公式计算出的K的值为整数，则N为中心五角数。

4.否则，数字N不是中心五角形数字。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to check if number N
// is a Centered pentagonal number
bool isCenteredpentagonal(int N)
{
    float n
        = (5 + sqrt(40 * N - 15))
          / 10;
 
    // Condition to check if N is a
    // Centered pentagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    // Given Number
    int N = 6;
 
    // Function call
    if (isCenteredpentagonal(N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
 
class GFG{
 
// Function to check if number N
// is a centered pentagonal number
static boolean isCenteredpentagonal(int N)
{
    float n = (float) ((5 + Math.sqrt(40 * N -
                                      15)) / 10);
 
    // Condition to check if N is a
    // centered pentagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
public static void main(String[] args)
{
     
    // Given Number
    int N = 6;
 
    // Function call
    if (isCenteredpentagonal(N))
    {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}
 
// This code is contributed by sapnasingh4991

Python3

# Python3 program for the above approach
import numpy as np
 
# Function to check if number N
# is a centered pentagonal number
def isCenteredpentagonal(N):
 
    n = (5 + np.sqrt(40 * N - 15)) / 10
 
    # Condition to check if N is a
    # centered pentagonal number
    return (n - int(n)) == 0
 
# Driver Code
N = 6
 
# Function call
if (isCenteredpentagonal(N)):
    print ("Yes")
else:
    print ("No")
 
# This code is contributed by PratikBasu

C#

// C# program for the above approach
using System;
 
class GFG{
 
// Function to check if number N
// is a centered pentagonal number
static bool isCenteredpentagonal(int N)
{
    float n = (float) ((5 + Math.Sqrt(40 * N -
                                      15)) / 10);
 
    // Condition to check if N is a
    // centered pentagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
public static void Main(string[] args)
{
     
    // Given number
    int N = 6;
 
    // Function call
    if (isCenteredpentagonal(N))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
 
// This code is contributed by rutvik_56

Javascript

// javascript program for the above approach
 
// Function to check if number N
// is a centered pentagonal number
function isCenteredpentagonal(N)
{
    var n =  ((5 + Math.sqrt(40 * N -
                                      15)) / 10);
 
    // Condition to check if N is a
    // centered pentagonal number
    return (n - parseInt(n) == 0);
}
 
// Driver Code
//Given Number
var N = 6;
 
// Function call
if (isCenteredpentagonal(N))
{
    document.write("Yes");
}
else
{
    document.write("No");
}
 
// This code is contributed by Amit Katiyar

输出：

Yes

时间复杂度： O(1)

辅助空间： O(1)