requisitos previos:
Dado un valor n, la tarea es imprimir series de números pentatópicos hasta el término n .
Ejemplos:
Input: 5 Output: 1 5 15 35 70 Input: 10 Output: 1 5 15 35 70 126 210 330 495 715
Método 1: Uso de series de números tetraédricos:
este problema se puede resolver fácilmente con el hecho de que el N número del pentátopo es igual a la suma de los primeros N números tetraédricos.
Echemos un vistazo a la serie de números pentatópicos y tetraédricos.
Para n = 5
Números tetraédricos = 1, 4, 10, 20, 35
Prefijo Suma de números tetraédricos para cada término: (1), (1 + 4), (1 + 4 + 10), (1 + 4 + 10 + 20), (1 + 4 + 10 + 20 + 35)
Entonces, los números del pentátopo son 1, 5, 15, 35, 70
Calcule el N número tetraédrico usando la fórmula: 
Por lo tanto, imprima la serie de Números pentatópicos generando números tetraédricos y sumándolos con la suma de todos los Números tetraédricos generados previamente.
A continuación se muestra la implementación del enfoque anterior:
CPP
// C++ program to generate Pentatope
// Number series
#include <bits/stdc++.h>
using namespace std;
// Function to generate nth tetrahedral number
int findTetrahedralNumber(int n)
{
return ((n * (n + 1) * (n + 2)) / 6);
}
// Function to print pentatope number
// series upto nth term.
void printSeries(int n)
{
// Initialize prev as 0. It store the
// sum of all previously generated
// pentatope numbers
int prev = 0;
int curr;
// Loop to print pentatope series
for (int i = 1; i <= n; i++)
{
// Find ith tetrahedral number
curr = findTetrahedralNumber(i);
// Add ith tetrahedral number to
// sum of all previously generated
// tetrahedral number to get ith
// pentatope number
curr = curr + prev;
cout << curr << " ";
// Update sum of all previously
// generated tetrahedral number
prev = curr;
}
}
// Driver code
int main()
{
int n = 10;
// Function call to print pentatope
// number series
printSeries(n);
return 0;
}
Java
// Java program to generate Pentatope
// Number series
import java.io.*;
class GFG {
// Function to generate nth tetrahedral number
static int findTetrahedralNumber(int n)
{
return ((n * (n + 1) * (n + 2)) / 6);
}
// Function to print pentatope number
// series upto nth term.
static void printSeries(int n)
{
// Initialize prev as 0. It store the
// sum of all previously generated
// pentatope numbers
int prev = 0;
int curr;
// Loop to print pentatope series
for (int i = 1; i <= n; i++)
{
// Find ith tetrahedral number
curr = findTetrahedralNumber(i);
// Add ith tetrahedral number to
// sum of all previously generated
// tetrahedral number to get ith
// pentatope number
curr = curr + prev;
System.out.print(curr + " ");
// Update sum of all previously
// generated tetrahedral number
prev = curr;
}
}
// Driver code
public static void main (String[] args)
{
int n = 10;
// Function call to print pentatope
// number series
printSeries(n);
}
}
python3
# Python program to generate Pentatope # Number series # Function to generate nth tetrahedral number def findTetrahedralNumber(n) : return (int((n * (n + 1) * (n + 2)) / 6)) # Function to print pentatope number # series upto nth term. def printSeries(n) : # Initialize prev as 0. It store the # sum of all previously generated # pentatope numbers prev = 0 # Loop to print pentatope series for i in range(1, n + 1) : # Find ith tetrahedral number curr = findTetrahedralNumber(i) # Add ith tetrahedral number to # sum of all previously generated # tetrahedral number to get ith # pentatope number curr = curr + prev; print(curr, end=' ') # Update sum of all previously # generated tetrahedral number prev = curr # Driver code n = 10 # Function call to print pentatope # number series printSeries(n)
C#
// C# program to generate Pentatope
// Number series
using System;
public class GFG {
// Function to generate nth tetrahedral number
static int findTetrahedralNumber(int n)
{
return ((n * (n + 1) * (n + 2)) / 6);
}
// Function to print pentatope number
// series upto nth term.
static void printSeries(int n)
{
// Initialize prev as 0. It store the
// sum of all previously generated
// pentatope numbers
int prev = 0;
int curr;
// Loop to print pentatope series
for (int i = 1; i <= n; i++)
{
// Find ith tetrahedral number
curr = findTetrahedralNumber(i);
// Add ith tetrahedral number to
// sum of all previously generated
// tetrahedral number to get ith
// pentatope number
curr = curr + prev;
Console.Write(curr + " ");
// Update sum of all previously
// generated tetrahedral number
prev = curr;
}
}
// Driver code
static public void Main ()
{
int n = 10;
// Function call to print pentatope
// number series
printSeries(n);
}
}
PHP
<?php
// PHP program to generate Pentatope
// Number series
// Function to generate nth tetrahedral number
function findTetrahedralNumber($n)
{
return (($n * ($n + 1) * ($n + 2)) / 6);
}
// Function to print pentatope number
// series upto nth term.
function printSeries($n)
{
// Initialize prev as 0. It store the
// sum of all previously generated
// pentatope numbers
$prev = 0;
$curr;
// Loop to print pentatope series
for ($i = 1; $i <= $n; $i++)
{
// Find ith tetrahedral number
$curr = findTetrahedralNumber($i);
// Add ith tetrahedral number to
// sum of all previously generated
// tetrahedral number to get ith
// pentatope number
$curr = $curr + $prev;
echo($curr . " ");
// Update sum of all previously
// generated tetrahedral number
$prev = $curr;
}
}
// Driver code
$n = 10;
// Function call to print pentatope
// number series
printSeries($n);
?>
Javascript
<script>
// JavaScript program to generate Pentatope
// Number series
// Function to generate nth tetrahedral number
function findTetrahedralNumber(n)
{
return ((n * (n + 1) * (n + 2)) / 6);
}
// Function to print pentatope number
// series upto nth term.
function printSeries(n)
{
// Initialize prev as 0. It store the
// sum of all previously generated
// pentatope numbers
let prev = 0;
let curr;
// Loop to print pentatope series
for (let i = 1; i <= n; i++)
{
// Find ith tetrahedral number
curr = findTetrahedralNumber(i);
// Add ith tetrahedral number to
// sum of all previously generated
// tetrahedral number to get ith
// pentatope number
curr = curr + prev;
document.write(curr+" ");
// Update sum of all previously
// generated tetrahedral number
prev = curr;
}
}
// Driver code
let n = 10;
// Function call to print pentatope
// number series
printSeries(n);
// This code is contributed by sravan kumar
</script>
Producción:
1 5 15 35 70 126 210 330 495 715
Complejidad de tiempo: O(n), donde n representa el entero dado.
Espacio auxiliar: O(1), no se requiere espacio adicional, por lo que es una constante.
Método 2: Uso de la fórmula del número de pentátopo:
La fórmula para encontrar el número N de pentátopo A
continuación se muestra la implementación requerida:
CPP
// C++ program to print Pentatope number series.
#include <bits/stdc++.h>
using namespace std;
// Function to print pentatope series up to nth term
void printSeries(int n)
{
// Loop to print pentatope number series
for (int i = 1; i <= n; i++)
{
// calculate and print ith pentatope number
int num = (i * (i + 1) * (i + 2) * (i + 3) / 24);
cout << num << " ";
}
}
// Driver code
int main()
{
int n = 10;
// Function call to print pentatope number series
printSeries(n);
return 0;
}
Java
// Java program to print Pentatope number series.
import java.io.*;
class GFG {
// Function to print pentatope series up to nth term
static void printSeries(int n)
{
// Loop to print pentatope number series
for (int i = 1; i <= n; i++)
{
// calculate and print ith pentatope number
int num = (i * (i + 1) * (i + 2) * (i + 3) / 24);
System.out.print(num + " ");
}
}
// Driver code
public static void main (String[] args)
{
int n = 10;
// Function call to print pentatope number series
printSeries(n);
}
}
python3
# Python program to print Pentatope number series. # Function to print pentatope series up to nth term def printSeries(n) : # Loop to print pentatope number series for i in range(1, n + 1) : # calculate and print ith pentatope number num = int(i * (i + 1) * (i + 2) * (i + 3) // 24) print(num, end=' '); # Driver code n = 10 # Function call to print pentatope number series printSeries(n)
C#
// C# program to print Pentatope number series.
using System;
public class GFG {
// Function to print pentatope series up to nth term
static void printSeries(int n)
{
// Loop to print pentatope number series
for (int i = 1; i <= n; i++)
{
// calculate and print ith pentatope number
int num = (i * (i + 1) * (i + 2) * (i + 3) / 24);
Console.Write(num + " ");
}
}
// Driver code
static public void Main ()
{
int n = 10;
// Function call to print pentatope number series
printSeries(n);
}
}
PHP
<?php
// PHP program to print Pentatope number series.
// Function to print pentatope series up to nth term
function printSeries($n)
{
// Loop to print pentatope number series
for ($i = 1; $i <= $n; $i++)
{
// calculate and print ith pentatope number
$num = ($i * ($i + 1) * ($i + 2) * ($i + 3) / 24);
echo($num . " ");
}
}
// Driver code
$n = 10;
// Function call to print pentatope number series
printSeries($n);
?>
Javascript
<script>
// Javascript program to print Pentatope number series.
// Function to print pentatope series up to nth term
function printSeries(n)
{
// Loop to print pentatope number series
for (let i = 1; i <= n; i++)
{
// calculate and print ith pentatope number
num = (i * (i + 1) * (i + 2) * (i + 3) / 24);
document.write(num+" ");
}
}
// Driver code
let n = 10;
// Function call to print pentatope number series
printSeries(n);
// This code is contributed by sravan kumar
</script>
Producción:
1 5 15 35 70 126 210 330 495 715
Complejidad de tiempo: O(n), donde n representa el entero dado.
Espacio auxiliar: O(1), no se requiere espacio adicional, por lo que es una constante.