Program to check if N is a Centered Octagonal Number
Last Updated :
18 Sep, 2022
Given an integer N, the task is to check if it is a Centered Octagonal number or not. If the number N is an Centered Octagonal Number then print “Yes” else print “No”.
Centered Octagonal number represents an octagon with a dot in the centre and others dots surrounding the centre dot in the successive octagonal layer.The first few Centered Octagonal numbers are 1, 9, 25, 49, 81, 121, 169, 225, 289, 361 …
Examples:
Input: N = 9
Output: Yes
Explanation:
Second Centered Octagonal number is 9.
Input: 16
Output: No
Approach:
1. The Kth term of the Centered Octagonal number is given as
2. As we have to check that the given number can be expressed as a Centered Octagonal Number or not. This can be checked as follows –
=>
=>
3. If the value of K calculated using the above formula is an integer, then N is a Centered Octagonal Number.
4. Else N is not a Centered Octagonal Number.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
bool isCenteredOctagonal( int N)
{
float n
= (1 + sqrt (N))
/ 2;
return (n - ( int )n) == 0;
}
int main()
{
int N = 9;
if (isCenteredOctagonal(N)) {
cout << "Yes" ;
}
else {
cout << "No" ;
}
return 0;
}
|
Java
import java.util.*;
class GFG{
static boolean isCenteredOctagonal( int N)
{
float n = ( float ) (( 1 + Math.sqrt(N)) / 2 );
return (n - ( int )n) == 0 ;
}
public static void main(String[] args)
{
int N = 9 ;
if (isCenteredOctagonal(N))
{
System.out.print( "Yes" );
}
else
{
System.out.print( "No" );
}
}
}
|
Python3
import numpy as np
def isCenteredOctagonal(N):
n = ( 1 + np.sqrt(N)) / 2
return (n - int (n)) = = 0
N = 9
if (isCenteredOctagonal(N)):
print ( "Yes" )
else :
print ( "No" )
|
C#
using System;
class GFG{
static bool isCenteredOctagonal( int N)
{
float n = ( float ) ((1 + Math.Sqrt(N)) / 2);
return (n - ( int )n) == 0;
}
public static void Main( string [] args)
{
int N = 9;
if (isCenteredOctagonal(N))
{
Console.Write( "Yes" );
}
else
{
Console.Write( "No" );
}
}
}
|
Javascript
<script>
function isCenteredOctagonal( N)
{
let n
= (1 + Math.sqrt(N))
/ 2;
return (n - parseInt(n)) == 0;
}
let N = 9;
if (isCenteredOctagonal(N)) {
document.write( "Yes" );
}
else {
document.write( "No" );
}
</script>
|
Time Complexity: O(logN) because it is using inbuilt sqrt function
Auxiliary Space: O(1)
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