程序检查N是否为居中十六进制数字

给定数字N ，任务是检查N是否为中心十六进制数。如果数字N是中心十六进制数字，则打印“是”，否则打印“否” 。

Centered Hexadecagonal Number represents a dot in the centre and other dots around it in successive Hexadecagonal(16 sided polygon) layers… The first few Centered Hexadecagonal Numbers are 1, 17, 49, 97, 161, 241 … 
 

例子：

Input: N = 17 
Output: Yes 
Explanation: 
Second Centered hexadecagonal number is 17.
Input: N = 20 
Output: No 

方法：

1.中心六边形数的第K^个项为
$K^{th} Term = 8*K^{2} - 8*K + 1$

2.由于我们必须检查给定的数字是否可以表示为中心十六进制数。可以检查为：

=> $N = 8*K^{2} - 8*K + 1$
=> $K = \frac{8 + \sqrt{32*N + 32}}{16}$

3.如果使用上述公式计算的K值为整数，则N为中心十六进制数。

4.否则，数字N不是中心十六进制数。

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 the number N
// is a Centered hexadecagonal number
bool isCenteredhexadecagonal(int N)
{
    float n
        = (8 + sqrt(32 * N + 32))
          / 16;
 
    // Condition to check if the N is a
    // Centered hexadecagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    // Given Number
    int N = 17;
 
    // Function call
    if (isCenteredhexadecagonal(N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java

// Java program for the above approach
import java.io.*;
import java.util.*;
 
class GFG {
     
// Function to check if the number N
// is a centered hexadecagonal number
static boolean isCenteredhexadecagonal(int N)
{
    double n = (8 + Math.sqrt(32 * N + 32)) / 16;
 
    // Condition to check if the N is a
    // centered hexadecagonal number
    return (n - (int)n) == 0;
}
     
// Driver code
public static void main(String[] args)
{
     
    // Given Number
    int N = 17;
 
    // Function call
    if (isCenteredhexadecagonal(N))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
}
}
 
// This code is contributed by coder001

Python3

# Python3 program for the above approach
import numpy as np
 
# Function to check if the number N
# is a Centered hexadecagonal number
def isCenteredhexadecagonal(N):
 
    n = (8 + np.sqrt(32 * N + 32)) / 16
 
    # Condition to check if the N is a
    # Centered hexadecagonal number
    return (n - int(n)) == 0
 
# Driver Code
N = 17
 
# Function call
if (isCenteredhexadecagonal(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 the number N
// is a centered hexadecagonal number
static bool isCenteredhexadecagonal(int N)
{
    double n = (8 + Math.Sqrt(32 * N + 32)) / 16;
 
    // Condition to check if the N is a
    // centered hexadecagonal number
    return (n - (int)n) == 0;
}
     
// Driver code
public static void Main(string[] args)
{
     
    // Given Number
    int N = 17;
 
    // Function call
    if (isCenteredhexadecagonal(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 the number N
// is a Centered hexadecagonal number
function isCenteredhexadecagonal( N)
{
    let n
        = (8 + Math.sqrt(32 * N + 32))
          / 16;
 
    // Condition to check if the N is a
    // Centered hexadecagonal number
    return (n - parseInt(n)) == 0;
}
 
// Driver Code
 
    // Given Number
    let N = 17;
 
    // Function Call
    if (isCenteredhexadecagonal(N)) {
        document.write( "Yes");
    }
    else {
        document.write( "No");
    }
 
// This code contributed by Rajput-Ji
 

输出：

Yes

时间复杂度： O(1)

辅助空间： O(1)