Un número triangular o número triangular cuenta objetos dispuestos en un triángulo equilátero, como en el diagrama de la derecha. El n-ésimo número triangular es el número de puntos que componen un triángulo con n puntos en un lado, y es igual a la suma de los n números naturales de 1 a n.
Ejemplos:
Input : 5 Output : 1 3 6 10 15 Input : 10 Output : 1 3 6 10 15 21 28 36 45 55 Explanation : For k = 1 and j = 1 -> print k ( i.e. 1); increase j by 1 and add into k then print k ( i.e 3 ) update k increase j by 1 and add into k then print k ( i.e 6 ) update k increase j by 1 and add into k then print k ( i.e 10 ) update k increase j by 1 and add into k then print k ( i.e 15 ) update k increase j by 1 and add into k then print k ( i.e 21 ) update k . . and so on.
El enfoque utilizado es muy simple. Iterar el ciclo for hasta el valor dado n y para cada iteración aumentar j en 1 y agregarlo a k, lo que simplemente imprimirá la serie de números triangulares hasta n.
A continuación se muestra el programa que implementa el enfoque anterior:
C
// C Program to find Triangular Number Series
#include <stdio.h>
// Function to find triangular number
void triangular_series(int n)
{
int i, j = 1, k = 1;
// For each iteration increase j by 1
// and add it into k
for (i = 1; i <= n; i++) {
printf(" %d ", k);
j = j + 1; // Increasing j by 1
k = k + j; // Add value of j into k and update k
}
}
// Driven Function
int main()
{
int n = 5;
triangular_series(n);
return 0;
}
Java
// Java Program to print triangular number series till n
import java.util.*;
class GFG {
// Function to find triangular number
static void triangular_series(int n)
{
int i, j = 1, k = 1;
// For each iteration increase j by 1
// and add it into k
for (i = 1; i <= n; i++) {
System.out.printf("%d ", k);
j = j + 1; // Increasing j by 1
k = k + j; // Add value of j into k and update k
}
}
// Driver function
public static void main(String[] args)
{
int n = 5;
triangular_series(n);
}
}
// This code is contributed by Arnav Kr. Mandal.
Python3
# Python3 code to find Triangular # Number Series # Function to find triangular number def triangular_series( n ): j = 1 k = 1 # For each iteration increase j # by 1 and add it into k for i in range(1, n + 1): print(k, end = ' ') j = j + 1 # Increasing j by 1 # Add value of j into k and update k k = k + j # Driven Code n = 5 triangular_series(n) # This code is contributed by "Sharad_Bhardwaj"
C#
// C# Program to print triangular
// number series till n
using System;
class GFG {
// Function to find triangular number
static void triangular_series(int n)
{
int i, j = 1, k = 1;
// For each iteration increase j by 1
// and add it into k
for (i = 1; i <= n; i++) {
Console.Write(k +" ");
j += 1; // Increasing j by 1
k += j; // Add value of j into k and update k
}
}
// Driver Code
public static void Main()
{
int n = 5;
triangular_series(n);
}
}
// This code is contributed by vt_m.
PHP
<?php
// PHP Program to find
// Triangular Number Series
// Function to find
// triangular number
function triangular_series($n)
{
$i; $j = 1; $k = 1;
// For each iteration increase j
// by 1 and add it into k
for ($i = 1; $i <= $n; $i++)
{
echo(" " . $k . " ");
// Increasing j by 1
$j = $j + 1;
// Add value of j into k and update k
$k = $k + $j;
}
}
// Driver Code
$n = 5;
triangular_series($n);
// This code is contributed by Ajit.
?>
Javascript
<script>
// javascript Program to find Triangular Number Series
// Function to find triangular number
function triangular_series( n)
{
let i, j = 1, k = 1;
// For each iteration increase j by 1
// and add it into k
for (i = 1; i <= n; i++)
{
document.write(k+" ");
j = j + 1; // Increasing j by 1
k = k + j; // Add value of j into k and update k
}
}
// Driven Function
let n = 5;
triangular_series(n);
// This code is contributed by Rajput-Ji
</script>
Producción :
1 3 6 10 15
Complejidad del tiempo : O(n)
Espacio auxiliar : O(1)
Solución alternativa:
La solución se basa en el hecho de que el i-ésimo número triangular es la suma de los primeros i números naturales, es decir, i * (i + 1)/2
C
// C Program to find Triangular Number Series
#include <stdio.h>
// Function to find triangular number
void triangular_series(int n)
{
for (int i = 1; i <= n; i++)
printf(" %d ", i*(i+1)/2);
}
// Driven Function
int main()
{
int n = 5;
triangular_series(n);
return 0;
}
Java
//Java program to print triangular number series till n
import java.util.*;
class GFG {
// Function to find triangular number
static void triangular_series(int n)
{
for (int i = 1; i <= n; i++)
System.out.printf("%d ";, i*(i+1)/2);
}
// Driver function
public static void main(String[] args)
{
int n = 5;
triangular_series(n);
}
}
//This code is contributed by Arnav Kr. Mandal.
Python3
# Python3 code to find Triangular # Number Series def triangular_series(n): for i in range(1, n + 1): print( i*(i+1)//2,end=' ') # Driver code n = 5 triangular_series(n) # This code is contributed by ihritik
C#
// C# program to print triangular
// number series till n
using System;
class GFG {
// Function to find triangular number
static void triangular_series(int n)
{
for (int i = 1; i <= n; i++)
Console.Write(i * (i + 1) / 2 + " ");
}
// Driver Code
public static void Main()
{
int n = 5;
triangular_series(n);
}
}
// This code is contributed by vt_m.
PHP
<?php
// PHP Program to find
// Triangular Number Series
// Function to find
// triangular number
function triangular_series($n)
{
for ($i = 1; $i <= $n; $i++)
echo(" " . $i * ($i + 1) /
2 . " ");
}
// Driver Code
$n = 5;
triangular_series($n);
// This code is contributed by Ajit.
?>
Javascript
<script>
// javascript Program to find Triangular Number Series
// Function to find triangular number
function triangular_series( n)
{
for (let i = 1; i <= n; i++)
document.write(" "+ i * (i + 1)/2);
}
// Driven Function
let n = 5;
triangular_series(n);
// This code is contributed by gauravrajput1
</script>
Producción :
1 3 6 10 15
Complejidad de tiempo: O(n)
Espacio auxiliar: O(1) , ya que no se ha tomado ningún espacio adicional.
Publicación traducida automáticamente
Artículo escrito por Shahnawaz_Ali y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA