Program to check if N is a Icositrigonal number

Given an integer N, the task is to check if it is an Icositrigonal number or not.

Icositrigonal number is a class of figurate number. It has 23 – sided polygon called Icositrigon. The N-th Icositrigonal number count’s the 23 number of dots and all others dots are surrounding with a common sharing corner and make a pattern. The first few Icositrigonol numbers are 1, 23, 66, 130, 215, 321, 448 …

Examples: 

Input: N = 23 
Output: Yes 
Explanation: 
Second icositrigonal number is 23.

Input: N = 30 
Output: No 

Approach: 

1. The K^th term of the icositrigonal number is given as
K^{th} Term = \frac{21*K^{2} - 19*K}{2}     

2. As we have to check whether the given number can be expressed as an icositrigonal number or not. This can be checked as follows - 

=> N = \frac{21*K^{2} - 19*K}{2}     
=> K = \frac{19 + \sqrt{168*N + 361}}{42}     
 

3. Finally, check the value computed using this formula is an integer, which means that N is an icositrigonal number.

Below is the implementation of the above approach:

// C++ implementation to check that
// a number is a icositrigonal number or not

#include <bits/stdc++.h>

using namespace std;

// Function to check that the
// number is a icositrigonal number
bool isicositrigonal(int N)
{
    float n
        = (19 + sqrt(168 * N + 361))
          / 42;

    // Condition to check if the
    // number is a icositrigonal number
    return (n - (int)n) == 0;
}

// Driver Code
int main()
{
    int i = 23;

    // Function call
    if (isicositrigonal(i)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

// Java implementation to check that
// a number is a icositrigonal number or not
import java.util.*;
class GFG{

// Function to check that the
// number is a icositrigonal number
static boolean isicositrigonal(int N)
{
    float n = (float)(19 + Math.sqrt(168 * N + 361)) / 42;

    // Condition to check if the
    // number is a icositrigonal number
    return (n - (int)n) == 0;
}

// Driver Code
public static void main(String args[])
{
    int i = 23;

    // Function call
    if (isicositrigonal(i)) 
    {
        System.out.print("Yes");
    }
    else
    {
        System.out.print("No");
    }
}
}

// This code is contributed by Akanksha_Rai

# Python3 implementation to check that a  
# number is a icositrigonal number or not 
import math

# Function to check that the number 
# is a icositrigonal number 
def isicositrigonal(N): 

    n = (19 + math.sqrt(168 * N + 361)) / 42

    # Condition to check if the number  
    # is a icositrigonal number 
    return (n - int(n)) == 0

# Driver Code 
i = 23

# Function call 
if (isicositrigonal(i)): 
    print("Yes") 
else: 
    print("No") 

# This code is contributed by divyamohan123

// C# implementation to check that
// a number is a icositrigonal number or not
using System;
class GFG{

// Function to check that the
// number is a icositrigonal number
static bool isicositrigonal(int N)
{
    float n = (float)(19 + Math.Sqrt(168 * N + 361)) / 42;

    // Condition to check if the
    // number is a icositrigonal number
    return (n - (int)n) == 0;
}

// Driver Code
public static void Main()
{
    int i = 23;

    // Function call
    if (isicositrigonal(i)) 
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}

// This code is contributed by Nidhi_Biet

<script>

// JavaScript implementation to check that
// a number is a icositrigonal number or not

// Function to check that the
// number is a icositrigonal number
function isicositrigonal(N)
{
    var n
        = (19 + Math.sqrt(168 * N + 361))
          / 42;

    // Condition to check if the
    // number is a icositrigonal number
    return (n - parseInt(n)) == 0;
}

// Driver Code
var i = 23;
// Function call
if (isicositrigonal(i)) {
    document.write("Yes");
}
else {
    document.write("No");
}
   
</script>

Yes

Time Complexity: O(log N) because sqrt() function is being used
Auxiliary Space: O(1)

spp____

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Article Tags :

• Mathematical
• Geometric
• DSA

Practice Tags :

• Geometric
• Mathematical