Dado un número N y la tarea es encontrar el N número hexagonal centrado. Además, encuentre la serie hexagonal centrada.
Ejemplos:
Entrada: N = 2
Salida: 7
Entrada: N = 10
Salida: 271
Números hexagonales centrados: los números hexagonales centrados son números figurados y tienen la forma del hexágono. El número hexagonal centrado es diferente del número hexagonal porque contiene un elemento en el centro.
Algunos de los números hexagonales centrales son:
1, 7, 19, 37, 61, 91, 127, 169 ...
Por ejemplo:
The First N numbers are - 1, 7, 19, 37, 61, 91, 127 ... The cumulative sum of these numbers are - 1, 1+7, 1+7+19, 1+7+19+37... which is nothing but the sequence - 1, 8, 27, 64, 125, 216 ... That is in the form of - 13, 23, 33, 43, 53, 63 ....
Como los números del Hexágono Central suman el N ésimo término será el N 3 . Eso es –
1 3 + 2 3 + 3 3 + 4 3 + 5 3 + 6 3 …. hasta N términos = N 3
Entonces, N ésimo término será –
=> N 3 – (N – 1) 3
=> 3*N*(N – 1) + 1
Enfoque: Para encontrar el N -ésimo término del Número Hexagonal Centrado use las fórmulas – 3*N*(N – 1) + 1 .
A continuación se muestra la implementación del enfoque anterior:
C++
// Program to find nth
// centered hexadecimal number.
#include <bits/stdc++.h>
using namespace std;
// Function to find centered
// hexadecimal number.
int centeredHexagonalNumber(int n)
{
// Formula to calculate nth
// centered hexadecimal number
// and return it into main function.
return 3 * n * (n - 1) + 1;
}
// Driver Code
int main()
{
int n = 10;
cout << n << "th centered hexagonal number: ";
cout << centeredHexagonalNumber(n);
return 0;
}
Java
// Java Program to find nth
// centered hexadecimal number
import java.io.*;
class GFG
{
// Function to find centered
// hexadecimal number
static int centeredHexagonalNumber(int n)
{
// Formula to calculate nth
// centered hexadecimal number
// and return it into main function
return 3 * n * (n - 1) + 1;
}
// Driver Code
public static void main(String args[])
{
int n = 10;
System.out.print(n + "th centered " +
"hexagonal number: ");
System.out.println(centeredHexagonalNumber(n));
}
}
// This code is contributed by Nikita Tiwari.
Python3
# Python 3 program to find nth # centered hexagonal number # Function to find # centered hexagonal number def centeredHexagonalNumber(n) : # Formula to calculate # nth centered hexagonal return 3 * n * (n - 1) + 1 # Driver Code if __name__ == '__main__' : n = 10 print(n, "th centered hexagonal number: " , centeredHexagonalNumber(n)) # This code is contributed # by 'Akanshgupta'
C#
// C# Program to find nth
// centered hexadecimal number
using System;
class GFG
{
// Function to find centered
// hexadecimal number
static int centeredHexagonalNumber(int n)
{
// Formula to calculate nth
// centered hexadecimal number
// and return it into main function
return 3 * n * (n - 1) + 1;
}
// Driver Code
public static void Main()
{
int n = 10;
Console.Write(n + "th centered "+
"hexagonal number: ");
Console.Write(centeredHexagonalNumber(n));
}
}
// This code is contributed by vt_m.
PHP
<?php
// PHP Program to find nth
// centered hexadecimal number.
// Function to find centered
// hexadecimal number.
function centeredHexagonalNumber( $n)
{
// Formula to calculate nth
// centered hexadecimal
// number and return it
// into main function.
return 3 * $n * ($n - 1) + 1;
}
// Driver Code
$n = 10;
echo $n , "th centered hexagonal number: ";
echo centeredHexagonalNumber($n);
// This code is contributed by anuj_67.
?>
Javascript
<script>
// Program to find nth
// centered hexadecimal number.
// Function to find centered
// hexadecimal number.
function centeredHexagonalNumber(n)
{
// Formula to calculate nth
// centered hexadecimal number
// and return it into main function.
return 3 * n * (n - 1) + 1;
}
// Driver Code
let n = 10;
document.write(n + "th centered hexagonal number: ");
document.write(centeredHexagonalNumber(n));
// This code is contributed by rishavmahato348.
</script>
Producción :
10th centered hexagonal number: 271
Análisis de rendimiento:
- Complejidad del tiempo: en el enfoque dado anteriormente, estamos encontrando el término N del número hexagonal centrado que toma un tiempo constante. Por lo tanto, la complejidad será O(1)
- Complejidad espacial: en el enfoque dado anteriormente, no estamos utilizando ningún otro espacio auxiliar para el cálculo. Por lo tanto, la complejidad del espacio será O(1) .
Serie hexagonal centrada
Dado un número N, la tarea es encontrar series hexagonales centradas hasta N.
Enfoque:
iterar el ciclo usando una variable de ciclo (digamos i ) y encontrar el término i -ésimo del número hexagonal centrado usando las fórmulas – 3*i*( i – 1) + 1
A continuación se muestra la implementación del enfoque anterior:
C++
// Program to find the series
// of centered hexadecimal number
#include <bits/stdc++.h>
using namespace std;
// Function to find the
// series of centered
// hexadecimal number.
void centeredHexagonalSeries(int n)
{
// Formula to calculate
// nth centered hexadecimal
// number.
for (int i = 1; i <= n; i++)
cout << 3 * i * (i - 1) + 1
<< " ";
}
// Driver Code
int main()
{
int n = 10;
centeredHexagonalSeries(n);
return 0;
}
Java
// Program to find the series of
// centered hexadecimal number.
import java.io.*;
class GFG
{
// Function to find the series of
// centered hexadecimal number.
static void centeredHexagonalSeries(int n)
{
// Formula to calculate nth
// centered hexadecimal number.
for (int i = 1; i <= n; i++)
System.out.print( 3 * i *
(i - 1) + 1 + " ");
}
// Driver Code
public static void main(String args[])
{
int n = 10;
centeredHexagonalSeries(n);
}
}
// This code is contributed by Nikita Tiwari.
Python3
# Python3 program to find # nth centered hexagonal number # Function to find centered hexagonal # series till n given numbers. def centeredHexagonalSeries(n) : for i in range(1, n + 1) : # Formula to calculate nth # centered hexagonal series. print(3 * i * (i - 1) + 1, end=" ") # Driver Code if __name__ == '__main__' : n = 10 centeredHexagonalSeries(n) # This code is contributed # by 'Akanshgupta'
C#
// C# Program to find the
// series of centered
// hexadecimal number.
using System;
class GFG
{
// Function to find the
// series of centered
// hexadecimal number.
static void centeredHexagonalSeries(int n)
{
// Formula to calculate nth
// centered hexadecimal number.
for (int i = 1; i <= n; i++)
Console.Write( 3 * i *
(i - 1) + 1 + " ");
}
// Driver Code
public static void Main()
{
int n = 10;
centeredHexagonalSeries(n);
}
}
// This code is contributed by vt_m.
PHP
<?php
// Program to find the
// series of centered
// hexadecimal number.
// Function to find the
// series of centered
// hexadecimal number.
function centeredHexagonalSeries( $n)
{
// Formula to calculate
// nth centered hexadecimal
// number.
for ( $i = 1; $i <= $n; $i++)
echo 3 * $i * ($i - 1) + 1 ," ";
}
// Driver Code
$n = 10;
centeredHexagonalSeries($n);
// This code is contributed by anuj_67.
?>
Javascript
<script>
// JavaScript program to find the series of
// centered hexadecimal number.
// Function to find the series of
// centered hexadecimal number.
function centeredHexagonalSeries(n)
{
// Formula to calculate nth
// centered hexadecimal number.
for (let i = 1; i <= n; i++)
document.write( 3 * i *
(i - 1) + 1 + " ");
}
// Driver code
let n = 10;
centeredHexagonalSeries(n);
</script>
Producción :
1 7 19 37 61 91 127 169 217 271
Complejidad temporal: O(n)
Espacio auxiliar: O(1)
Publicación traducida automáticamente
Artículo escrito por Dharmendra_Kumar y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA