Dado un número n, encuentre el n-ésimo número octogonal centrado.
Un número octogonal centrado representa un octógono con un punto en el centro y otros puntos rodeando el punto central en la sucesiva capa octogonal.
Ejemplos:
Input : 2 Output : 9 Input : 5 Output : 81
El número n-ésimo octogonal centrado viene dado por:
Implementación básica del enfoque anterior:
C++
// Program to find nth
// centered octagonal
// number
#include <bits/stdc++.h>
using namespace std;
// Centered octagonal number function
int cen_octagonalnum(long int n)
{
// Formula to calculate nth
// centered octagonal number &
// return it into main function.
return (4 * n * n - 4 * n + 1);
}
// Driver Code
int main()
{
long int n = 6;
cout << n << "th centered"
<< " octagonal number : ";
cout << cen_octagonalnum(n);
cout << endl;
n = 11;
cout << n << "th centered"
<< " octagonal number : ";
cout << cen_octagonalnum(n);
return 0;
}
C
// C Program to find nth
// centered octagonal
// number
#include <stdio.h>
// Centered octagonal number function
int cen_octagonalnum(long int n)
{
// Formula to calculate nth
// centered octagonal number &
// return it into main function.
return (4 * n * n - 4 * n + 1);
}
// Driver Code
int main()
{
long int n = 6;
printf("%ldth centered octagonal number : ",n);
printf("%d\n",cen_octagonalnum(n));
n = 11;
printf("%ldth centered octagonal number : ",n);
printf("%d\n",cen_octagonalnum(n));
return 0;
}
// This code is contributed by kothavvsaakash.
Java
// Java Program to find nth
// centered octagonal number
import java.io.*;
class GFG
{
// Function to find centered
// octagonal number
static int centeredoctagonalNumber(int n)
{
// Formula to calculate nth
// centered octagonal number
// and return it into main function
return 4 * n * (n - 1) + 1;
}
// Driver Code
public static void main(String args[])
{
int n = 6;
System.out.print(n + "th centered " +
"octagonal number: ");
System.out.println(
centeredoctagonalNumber(n));
n = 11;
System.out.print(n + "th centered " +
"octagonal number: ");
System.out.println(
centeredoctagonalNumber(n));
}
}
// This code has been contributed by Prasad_Kshirsagar.
Python3
# Program to find nth # centered octagonal number def cen_octagonalnum(n) : # Formula to calculate nth # centered octagonal number return (4 * n * n - 4 * n + 1) # Driver Code if __name__ == '__main__' : n = 6 print(n,"th Centered", "octagonal number: ", cen_octagonalnum(n)) n = 11 print(n,"th Centered" , "octagonal number: ", cen_octagonalnum(n)) # This code is contributed # by akt_mit
C#
// Program to find nth centered octagonal
// number
using System;
public class GFG{
// Centered octagonal number function
static long cen_octagonalnum(long n)
{
// Formula to calculate nth
// centered octagonal number &
// return it into main function.
return (4 * n * n - 4 * n + 1);
}
// Driver code
static public void Main ()
{
long n = 6;
Console.WriteLine(n + "th centered"
+ " octagonal number : "
+ cen_octagonalnum(n));
n = 11;
Console.WriteLine(n + "th centered"
+ " octagonal number : "
+ cen_octagonalnum(n));
}
}
// This code is contributed by anuj_67.
PHP
<?php
// Program to find nth
// centered octagonal
// number
// Centered octagonal
// number function
function cen_octagonalnum($n)
{
// Formula to calculate nth
// centered octagonal number &
// return it into main function.
return (4 * $n * $n -
4 * $n + 1);
}
// Driver Code
$n = 6;
echo $n ,"th centered",
" octagonal number : ";
echo cen_octagonalnum($n);
echo "\n";
$n = 11;
echo $n , "th centered",
" octagonal number : ";
echo cen_octagonalnum($n);
// This code is contributed by ajit
?>
Javascript
<script>
// Javascript Program to find nth
// centered octagonal number
// Function to find centered
// octagonal number
function centeredoctagonalNumber(n)
{
// Formula to calculate nth
// centered octagonal number
// and return it into main function
return 4 * n * (n - 1) + 1;
}
// Driver Code
var n = 6;
document.write(n + "th centered " +
"octagonal number: ");
document.write(centeredoctagonalNumber(n) + "<br>");
n = 11;
document.write(n + "th centered " +
"octagonal number: ");
document.write(centeredoctagonalNumber(n));
// This code is contributed by Kirti
</script>
Producción
6th centered octagonal number : 121 11th centered octagonal number : 441
Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)