程序检查N是否为十六进制数

给定整数N ，任务是检查N是否为十六进制数。如果数字N是十六进制数字，则打印“是”，否则打印“否” 。

Hexadecagonal Number is class of figurate number and a perfect squares. It has 16-sided polygon called Hexadecagon or Hexakaidecagon. The nth Hexadecagonal Number counts the sixteen number of dots and all others dots are surrounding to its successive layer.The first few Hexadecagonal Numbers are 1, 16, 45, 88, 145, 216… 

例子：

Input: N = 16 
Output: Yes 
Explanation: 
Second hexadecagonal number is 16.

Input: N = 30 
Output: No 

方法：

1.十六进制数的第K^个项为
$K^{th} Term = \frac{14*K^{2} - 12*K}{2}$

2.由于我们必须检查给定的数字是否可以表示为十六进制数字。可以检查为：

=> $N = \frac{14*K^{2} - 12*K}{2}$
=> $K = \frac{12 + \sqrt{112*N + 144}}{28}$
 

3.如果使用上述公式计算的K值为整数，则N为十六进制数。

4.其他N不是十六进制数。

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 N is a
// hexadecagonal number
bool ishexadecagonal(int N)
{
    float n
        = (12 + sqrt(112 * N + 144))
          / 28;
 
    // Condition to check if the
    // number is a hexadecagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    // Given Number
    int N = 16;
 
    // Function call
    if (ishexadecagonal(N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java

// Java program for the above approach
import java.lang.Math;
 
class GFG{
     
// Function to check if N is a
// hexadecagonal number
public static boolean ishexadecagonal(int N)
{
    double n = (12 + Math.sqrt(112 * N +
                               144)) / 28;
     
    // Condition to check if the
    // number is a hexadecagonal number
    return (n - (int)n) == 0;
}
     
// Driver code   
public static void main(String[] args)
{
         
    // Given number
    int N = 16;
     
    // Function call
    if (ishexadecagonal(N))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
}
}
 
// This code is contributed by divyeshrabadiya07

Python3

# Python3 program for the above approach
from math import sqrt
 
# Function to check if N is
# a hexadecagonal number
def ishexadecagonal(N):
 
    n = (12 + sqrt(112 * N + 144)) / 28;
 
    # Condition to check if the number
    # is a hexadecagonal number
    return (n - int(n)) == 0;
 
# Driver code
if __name__ == "__main__":
 
    # Given number
    N = 16;
 
    # Function call
    if (ishexadecagonal(N)):
        print("Yes");
    else:
        print("No");
     
# This code is contributed by AnkitRai01

C#

// C# program for the above approach
using System;
 
class GFG{
     
// Function to check if N is a
// hexadecagonal number
public static bool ishexadecagonal(int N)
{
    double n = (12 + Math.Sqrt(112 * N +
                             144)) / 28;
     
    // Condition to check if the
    // number is a hexadecagonal number
    return (n - (int)n) == 0;
}
     
// Driver code
public static void Main(string[] args)
{
         
    // Given number
    int N = 16;
     
    // Function call
    if (ishexadecagonal(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 N is a
// hexadecagonal number
function ishexadecagonal( N)
{
    let n
        = (12 + Math.sqrt(112 * N + 144))
          / 28;
 
    // Condition to check if the
    // number is a hexadecagonal number
    return (n - parseInt(n)) == 0;
}
 
// Driver Code
 
    // Given Number
    let N = 16;
 
    // Function Call
    if (ishexadecagonal(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)