Program to check if N is a Centered Hexagonal Number

Given an integer N, the task is to check if N is a Centered Hexagonal Number or not. If the number N is a Centered Hexagonal Number then print “Yes” else print “No”.

Centered hexagonal number are figurate numbers and are in the form of the Hexagon. The Centered Hexagonal number is different from Hexagonal Number because it contains one element at the center..The first few Centered hexagonal numbers are 1, 7, 19, 37, 61, 91, 127 …

Examples:

Input: N = 7
Output: Yes
Explanation:
Second Centered hexagonal number is 7.

Input: N = 20
Output: No

Approach:

• The Kth term of the Centered hexagonal number is given as
• As we have to check that the given number can be expressed as a Centered hexagonal number or not. This can be checked as:

=>
=>

• If the value of K calculated using the above formula is an integer, then N is a Centered Hexagonal Number.
• Else the number N is not a Centered Hexagonal Number.

Below is the implementation of the above approach:

C++

 // C++ program for the above approach#include using namespace std; // Function to check that the// number is a Centered hexagonal numberbool isCenteredhexagonal(int N){    float n        = (3 + sqrt(12 * N - 3))          / 6;     // Condition to check if the    // number is a Centered hexagonal number    return (n - (int)n) == 0;} // Driver Codeint main(){    int N = 7;     // Function call    if (isCenteredhexagonal(N)) {        cout << "Yes";    }    else {        cout << "No";    }    return 0;}

Java

 // Java program for the above approachclass GFG{ // Function to check that the// number is a Centered hexagonal numberstatic boolean isCenteredhexagonal(int N){    float n = (float)((3 + Math.sqrt(12 * N - 3)) / 6);     // Condition to check if the    // number is a Centered hexagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void main(String[] args){    int N = 7;     // Function call    if (isCenteredhexagonal(N))     {        System.out.print("Yes");    }    else    {        System.out.print("No");    }}} // This code is contributed by sapnasingh4991

Python3

 # Python3 program for the above approach import math # Function to check that the number# is a centered hexagonal number def isCenteredhexagonal(N):         n = (3 + math.sqrt(12 * N - 3)) / 6         # Condition to check if the number     # is a centered hexagonal number     return (n - int(n)) == 0 # Driver Code N = 7 if isCenteredhexagonal(N):    print("Yes")else :    print("No") # This code is contributed by ishayadav181

C#

 // C# program for the above approachusing System; class GFG{ // Function to check that the number // is a centered hexagonal numberstatic bool isCenteredhexagonal(int N){    float n = (float)((3 + Math.Sqrt(12 * N -                                      3)) / 6);     // Condition to check if the number     // is a centered hexagonal number    return (n - (int)n) == 0;} // Driver Codepublic static void Main(String[] args){    int N = 7;     // Function call    if (isCenteredhexagonal(N))     {        Console.Write("Yes");    }    else    {        Console.Write("No");    }}} // This code is contributed by amal kumar choubey

Javascript

 

Output:
Yes

Time Complexity: O(logN) because it is using inbuilt sqrt function
Auxiliary Space: O(1)

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