requisitos previos:
Dado un valor n, la tarea es imprimir series de números tetraédricos hasta el término n.
Ejemplos:
Input: 5 Output: 1 4 10 20 35 Input: 10 Output: 1 4 10 20 35 56 84 120 165 220
Método 1: Uso de series de números triangulares:
este problema se puede resolver fácilmente con el hecho de que el N número tetraédrico es igual a la suma de los primeros N números triangulares.
Echemos un vistazo a las series de números triangulares y tetraédricos.
To print series upto 5th term: Triangular Numbers = 1 3 6 10 15 Tetrahedral numbers = 1 4 10 20 35 i.e (1) (1 + 3) (1 + 3 + 6) (1 + 3 + 6 + 10) (1 + 3 + 6 + 10 + 35)
Calcule el N número triangular usando la fórmula
Entonces, imprima la serie de números tetraédricos generando números triangulares y sumándolos con la suma de todos los números triangulares generados previamente.
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ program to generate tetrahedral // number series #include <bits/stdc++.h> using namespace std; // function to generate nth triangular // number long findTriangularNumber(int n) { return (n * (n + 1)) / 2; } // function to print tetrahedral number // series up to n void printSeries(int n) { // Initialize prev as 0. It stores // the sum of all previously generated // triangular number int prev = 0; int curr; // Loop to print series for (int i = 1; i <= n; i++) { // Find ith triangular number curr = findTriangularNumber(i); // Add ith triangular number to // sum of all previously generated // triangular number to get ith // tetrahedral number curr = curr + prev; cout << curr << " "; // Update sum of all previously // generated triangular number prev = curr; } } // Driver code int main() { int n = 10; // function call to print series printSeries(n); return 0; }
Java
// Java program to generate tetrahedral // number series import java.io.*; class GFG { // function to generate nth triangular // number static long findTriangularNumber(int n) { return (n * (n + 1)) / 2; } // function to print tetrahedral number // series up to n static void printSeries(int n) { // Initialize prev as 0. It store // the sum of all previously generated // triangular number long prev = 0; long curr; // Loop to print series for (int i = 1; i <= n; i++) { // Find ithh triangular number curr = findTriangularNumber(i); // Add ith triangular number to // sum of all previously generated // triangular number to get ith // tetrahedral number curr = curr + prev; System.out.print(curr + " "); // Update sum of all previously // generated triangular number prev = curr; } } // Driver code public static void main (String[] args) { int n = 10; // function call to print series printSeries(n); } }
Python3
# Python3 program to generate # tetrahedral number series # function to generate nth # triangular number def findTriangularNumber(n): return (n * (n + 1)) / 2 # function to print tetrahedral # number series up to n def printSeries(n): # Initialize prev as 0. # It stores the sum of all # previously generated # triangular number prev = 0 # Loop to print series for i in range(1, n+1): # Find ith triangular number curr = findTriangularNumber(i) # Add ith triangular number # to sum of all previously # generated triangular number # to get ith tetrahedral number curr = int(curr + prev) print(curr, end = ' ') # Update sum of all previously # generated triangular number prev = curr # Driver code n = 10 # function call to # print series printSeries(n) # This code is contributed by Mahadev.
C#
// C# program to generate tetrahedral // number series using System; public class GFG{ // function to generate nth triangular // number static long findTriangularNumber(int n) { return (n * (n + 1)) / 2; } // function to print tetrahedral number // series up to n static void printSeries(int n) { // Initialize prev as 0. It store // the sum of all previously generated // triangular number long prev = 0; long curr; // Loop to print series for (int i = 1; i <= n; i++) { // Find ithh triangular number curr = findTriangularNumber(i); // Add ith triangular number to // sum of all previously generated // triangular number to get ith // tetrahedral number curr = curr + prev; Console.Write(curr + " "); // Update sum of all previously // generated triangular number prev = curr; } } // Driver code static public void Main () { int n = 10; // function call to print series printSeries(n); } }
PHP
<?php // PHP program to generate tetrahedral // number series // function to generate nth triangular // number function findTriangularNumber($n) { return ($n * ($n + 1)) / 2; } // function to print tetrahedral number // series up to n function printSeries($n) { // Initialize prev as 0. It store // the sum of all previously generated // triangular number $prev = 0; $curr; // Loop to print series for ($i = 1; $i <= $n; $i++) { // Find ithh triangular number $curr = findTriangularNumber($i); // Add ith triangular number to // sum of all previously generated // triangular number to get ith // tetrahedral number $curr = $curr + $prev; echo($curr . " "); // Update sum of all previously // generated triangular number $prev = $curr; } } // Driver code $n = 10; // function call to print series printSeries($n); ?>
Javascript
<script> // Javascript program to generate tetrahedral // number series // function to generate nth triangular // number function findTriangularNumber(n) { return (n * (n + 1)) / 2; } // function to print tetrahedral number // series up to n function printSeries(n) { // Initialize prev as 0. It stores // the sum of all previously generated // triangular number var prev = 0; var curr; // Loop to print series for (var i = 1; i <= n; i++) { // Find ith triangular number curr = findTriangularNumber(i); // Add ith triangular number to // sum of all previously generated // triangular number to get ith // tetrahedral number curr = curr + prev; document.write( curr + " "); // Update sum of all previously // generated triangular number prev = curr; } } // Driver code var n = 10; // function call to print series printSeries(n); // This code is contributed by itsok. </script>
1 4 10 20 35 56 84 120 165 220
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 tetraédrico:
fórmula para encontrar el número tetraédrico n- ésimo :
a continuación se muestra la implementación requerida:
C++
// C++ program to generate series of // tetrahedral numbers #include <bits/stdc++.h> using namespace std; // function to print tetrahedral // number series up to n void printSeries(int n) { // loop to print series for (int i = 1; i <= n; i++) { // Calculate and print ith // tetrahedral number int num = i * (i + 1) * (i + 2) / 6; cout << num << " "; } } // Driver code int main() { int n = 10; // function call to print series printSeries(n); return 0; }
Java
// Java program to generate series of // tetrahedral numbers import java.io.*; class GFG { // function to print tetrahedral // number series up to n static void printSeries(int n) { // loop to print series for (int i = 1; i <= n; i++) { // Calculate and print ith // tetrahedral number int num = i * (i + 1) * (i + 2) / 6; System.out.print(num + " "); } } // Driver code public static void main (String[] args) { int n = 10; // function call to print series printSeries(n); } }
Python3
# Python3 code to print tetrahedral # numbers series up to n # function to print tetrahedral series up to n def printSeries(n): # loop to print series for i in range(1, n + 1): # Calculate and print ith # Tetrahedral number num = i * (i + 1) * (i + 2) // 6 print(num, end =' ') # Driver code n = 10 # function call to print series printSeries(n)
C#
// C# program to generate series of // tetrahedral numbers using System; public class GFG{ // function to print tetrahedral // number series up to n static void printSeries(int n) { // loop to print series for (int i = 1; i <= n; i++) { // Calculate and print ith // tetrahedral number int num = i * (i + 1) * (i + 2) / 6; Console.Write(num + " "); } } // Driver code static public void Main () { int n = 10; // function call to print series printSeries(n); } }
PHP
<?php // PHP program to generate series of // tetrahedral numbers // function to print tetrahedral // number series up to n function printSeries($n) { // loop to print series for ($i = 1; $i <= $n; $i++) { // Calculate and print ith // tetrahedral number $num = $i * ($i + 1) * ($i + 2) / 6; echo ($num . " "); } } // Driver code $n = 10; // function call to print series printSeries($n); ?>
Javascript
<script> // Javascript program to generate series of // tetrahedral numbers // function to print tetrahedral // number series up to n function printSeries(n) { let i; // loop to print series for (i = 1; i <= n; i++) { // Calculate and print ith // tetrahedral number let num = i * (i + 1) * ((i + 2) / 6); document.write(num + " "); } } // driver program let n = 10; // function call to print series printSeries(n); // This code is contributed by susmitakundugoaldanga. </script>
1 4 10 20 35 56 84 120 165 220
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.