Dado un número n, encuentra el n-ésimo número piramidal pentagonal.
Un número piramidal pentagonal pertenece a la clase de números figurados. Es el número de objetos en una pirámide de base pentagonal. El enésimo número piramidal pentagonal es igual a la suma de los primeros n números pentagonales .
Ejemplos:
Input : n = 3 Output : 18 Input : n = 7 Output : 196
Método 1: (Enfoque ingenuo):
este enfoque es simple. Dice que hay que sumar todos los números pentagonales hasta n (ejecutando un bucle) para obtener el número piramidal pentagonal n-ésimo.
A continuación se muestra la implementación de este enfoque:
C++
// CPP Program to get nth Pentagonal
// pyramidal number.
#include <bits/stdc++.h>
using namespace std;
// function to get nth Pentagonal
// pyramidal number.
int pentagon_pyramidal(int n)
{
int sum = 0;
// Running loop from 1 to n
for (int i = 1; i <= n; i++) {
// get nth pentagonal number
int p = (3 * i * i - i) / 2;
// add to sum
sum = sum + p;
}
return sum;
}
// Driver Program
int main()
{
int n = 4;
cout << pentagon_pyramidal(n) << endl;
return 0;
}
Java
// Java Program to get nth
// Pentagonal pyramidal number.
import java.io.*;
class GFG
{
// function to get nth
// Pentagonal pyramidal number.
static int pentagon_pyramidal(int n)
{
int sum = 0;
// Running loop from 1 to n
for (int i = 1; i <= n; i++)
{
// get nth pentagonal number
int p = (3 * i * i - i) / 2;
// add to sum
sum = sum + p;
}
return sum;
}
// Driver Code
public static void main (String[] args)
{
int n = 4;
System.out.println(pentagon_pyramidal(n));
}
}
// This code is contributed by anuj_67.
Python3
# Python3 Program to get nth Pentagonal # pyramidal number. # function to get nth Pentagonal # pyramidal number. def pentagon_pyramidal(n): sum = 0 # Running loop from 1 to n for i in range(1, n + 1): # get nth pentagonal number p = ( 3 * i * i - i ) / 2 # add to sum sum = sum + p return sum # Driver Program n = 4 print(int(pentagon_pyramidal(n)))
C#
// C# Program to get nth
// Pentagonal pyramidal number.
using System;
class GFG
{
// function to get nth
// Pentagonal pyramidal number.
static int pentagon_pyramidal(int n)
{
int sum = 0;
// Running loop from 1 to n
for (int i = 1; i <= n; i++)
{
// get nth pentagonal number
int p = (3 * i *
i - i) / 2;
// add to sum
sum = sum + p;
}
return sum;
}
// Driver Code
static public void Main ()
{
int n = 4;
Console.WriteLine(pentagon_pyramidal(n));
}
}
// This code is contributed by ajit.
PHP
<?php
// PHP Program to get nth
// Pentagonal pyramidal number.
// function to get nth
// Pentagonal pyramidal number.
function pentagon_pyramidal($n)
{
$sum = 0;
// Running loop from 1 to n
for ($i = 1; $i <= $n; $i++)
{
// get nth pentagonal number
$p = (3 * $i *
$i - $i) / 2;
// add to sum
$sum = $sum + $p;
}
return $sum;
}
// Driver Code
$n = 4;
echo pentagon_pyramidal($n);
// This code is contributed by m_kit
?>
Javascript
<script>
// javascript Program to get nth
// Pentagonal pyramidal number.
// function to get nth
// Pentagonal pyramidal number.
function pentagon_pyramidal(n)
{
var sum = 0;
// Running loop from 1 to n
for (i = 1; i <= n; i++)
{
// get nth pentagonal number
var p = (3 * i * i - i) / 2;
// add to sum
sum = sum + p;
}
return sum;
}
// Driver Code
var n = 4;
document.write(pentagon_pyramidal(n));
// This code is contributed by Amit Katiyar
</script>
Producción :
40
Complejidad de tiempo : O(n)
Método 2: (Enfoque eficiente):
en este enfoque, usamos la fórmula para obtener el enésimo número piramidal pentagonal en tiempo O(1).
Enésimo número piramidal pentagonal = n 2 (n + 1) / 2
A continuación se muestra la implementación de este enfoque:
C++
// CPP Program to get nth Pentagonal
// pyramidal number.
#include <bits/stdc++.h>
using namespace std;
// function to get nth Pentagonal
// pyramidal number.
int pentagon_pyramidal(int n)
{
return n * n * (n + 1) / 2;
}
// Driver Program
int main()
{
int n = 4;
cout << pentagon_pyramidal(n) << endl;
return 0;
}
Java
// Java Program to get nth
// Pentagonal pyramidal number.
import java.io.*;
class GFG
{
// function to get nth
// Pentagonal pyramidal number.
static int pentagon_pyramidal(int n)
{
return n * n *
(n + 1) / 2;
}
// Driver Code
public static void main (String[] args)
{
int n = 4;
System.out.println(pentagon_pyramidal(n));
}
}
// This code is contributed by ajit
Python3
# Python3 Program to get nth Pentagonal # pyramidal number. # function to get nth Pentagonal # pyramidal number. def pentagon_pyramidal(n): return n * n * (n + 1) / 2 # Driver Program n = 4 print(int(pentagon_pyramidal(n)))
C#
// C# Program to get nth
// Pentagonal pyramidal number.
using System;
class GFG
{
// function to get nth
// Pentagonal pyramidal number.
static int pentagon_pyramidal(int n)
{
return n * n *
(n + 1) / 2;
}
// Driver Code
static public void Main ()
{
int n = 4;
Console.WriteLine(
pentagon_pyramidal(n));
}
}
// This code is contributed
// by ajit
PHP
<?php
// PHP Program to get
// nth Pentagonal
// pyramidal number.
// function to get
// nth Pentagonal
// pyramidal number.
function pentagon_pyramidal($n)
{
return $n * $n *
($n + 1) / 2;
}
// Driver Code
$n = 4;
echo pentagon_pyramidal($n);
// This code is contributed
// by akt_mit
?>
Javascript
<script>
// javascript Program to get nth
// Pentagonal pyramidal number.
// function to get nth
// Pentagonal pyramidal number.
function pentagon_pyramidal(n)
{
return n * n *
(n + 1) / 2;
}
// Driver Code
var n = 4;
document.write(pentagon_pyramidal(n));
// This code is contributed by Princi Singh
</script>
Producción :
40
Complejidad de tiempo : O(1)
Publicación traducida automáticamente
Artículo escrito por Prasad_Kshirsagar y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA