En matemáticas, particularmente en teoría de arrays y combinatoria, la array de Pascal es una array infinita que contiene los coeficientes binomiales como sus elementos. Hay tres formas de lograr esto: ya sea como una array triangular superior, una array triangular inferior o una array simétrica.
Los truncamientos de 5 x 5 de estos se muestran a continuación:
Los elementos de la Array Pascal simétrica son el coeficiente binomial, es decir
Dado un entero positivo n . La tarea es imprimir la Array Pascal Simétrica de tamaño nx n.
Ejemplos:
Input : n = 5 Output : 1 1 1 1 1 1 2 3 4 5 1 3 6 10 15 1 4 10 20 35 1 5 15 35 70
A continuación se muestra el código para implementar la array pascal simétrica nxn:
C++
// CPP Program to print symmetric pascal matrix.
#include <bits/stdc++.h>
using namespace std;
// Print Pascal Matrix
void printpascalmatrix(int n)
{
int C[2 * n + 1][2 * n + 1] = { 0 };
// Calculate value of Binomial Coefficient in
// bottom up manner
for (int i = 0; i <= 2 * n; i++) {
for (int j = 0; j <= min(i, 2 * n); j++) {
// Base Cases
if (j == 0 || j == i)
C[i][j] = 1;
// Calculate value using previously
// stored values
else
C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
}
}
// Printing the pascal matrix
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++)
cout << C[i + j][i] << " ";
cout << endl;
}
}
// Driven Program
int main()
{
int n = 5;
printpascalmatrix(n);
return 0;
}
Java
// java Program to print
// symmetric pascal matrix.
import java.io.*;
class GFG
{
// Print Pascal Matrix
static void printpascalmatrix(int n)
{
int C[][] = new int[2 * n + 1][2 * n + 1];
// Calculate value of Binomial Coefficient in
// bottom up manner
for (int i = 0; i <= 2 * n; i++)
{
for (int j = 0; j <= Math.min(i, 2 * n); j++)
{
// Base Cases
if (j == 0 || j == i)
C[i][j] = 1;
// Calculate value using previously
// stored values
else
C[i][j] = C[i - 1][j - 1]
+ C[i - 1][j];
}
}
// Printing the pascal matrix
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
System.out.print ( C[i + j][i] +" ");
System.out.println();
}
}
// Driven Program
public static void main (String[] args)
{
int n = 5;
printpascalmatrix(n);
}
}
// This code is contributed by vt_m.
Python3
# Python3 Program to print # symmetric pascal matrix. # Print Pascal Matrix def printpascalmatrix(n): C = [[0 for x in range(2 * n + 1)] for y in range(2 * n + 1)] # Calculate value of # Binomial Coefficient # in bottom up manner for i in range(2 * n + 1): for j in range(min(i, 2 * n) + 1): # Base Cases if (j == 0 or j == i): C[i][j] = 1; # Calculate value # using previously # stored values else: C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]); # Printing the # pascal matrix for i in range(n): for j in range(n): print(C[i + j][i], end = " "); print(); # Driver Code n = 5; printpascalmatrix(n); # This code is contributed by mits
C#
// C# program to print
// symmetric pascal matrix.
using System;
class GFG {
// Print Pascal Matrix
static void printpascalmatrix(int n)
{
int[, ] C = new int[2 * n + 1, 2 * n + 1];
// Calculate value of Binomial Coefficient
// in bottom up manner
for (int i = 0; i <= 2 * n; i++) {
for (int j = 0; j <= Math.Min(i, 2 * n); j++) {
// Base Cases
if (j == 0 || j == i)
C[i, j] = 1;
// Calculate value using previously
// stored values
else
C[i, j] = C[i - 1, j - 1]
+ C[i - 1, j];
}
}
// Printing the pascal matrix
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++)
Console.Write(C[i + j, i] + " ");
Console.WriteLine();
}
}
// Driven Program
public static void Main()
{
int n = 5;
printpascalmatrix(n);
}
}
// This code is contributed by vt_m.
PHP
<?php
// PHP Program to print symmetric
// pascal matrix.
// Print Pascal Matrix
function printpascalmatrix($n)
{
$C[2 * $n + 1][2 * $n + 1] = (0);
// Calculate value of Binomial
// Coefficient in bottom up manner
for ($i = 0; $i <= 2 * $n; $i++)
{
for ($j = 0; $j <= min($i, 2 * $n); $j++)
{
// Base Cases
if ($j == 0 || $j == $i)
$C[$i][$j] = 1;
// Calculate value
// using previously
// stored values
else
$C[$i][$j] = $C[$i - 1][$j - 1] +
$C[$i - 1][$j];
}
}
// Printing the pascal matrix
for ($i = 0; $i < $n; $i++) {
for ( $j = 0; $j < $n; $j++)
echo $C[$i + $j][$i], " ";
echo "\n";
}
}
// Driver Code
$n = 5;
printpascalmatrix($n);
// This code is contributed by aj_36
?>
Javascript
<script>
// JavaScript Program to print
// symmetric pascal matrix.
// Print Pascal Matrix
function printpascalmatrix(n)
{
let C = new Array(2 * n + 1);
// Loop to create 2D array using 1D array
for (var i = 0; i < C.length; i++) {
C[i] = new Array(2);
}
// Calculate value of Binomial Coefficient in
// bottom up manner
for (let i = 0; i <= 2 * n; i++)
{
for (let j = 0; j <= Math.min(i, 2 * n); j++)
{
// Base Cases
if (j == 0 || j == i)
C[i][j] = 1;
// Calculate value using previously
// stored values
else
C[i][j] = C[i - 1][j - 1]
+ C[i - 1][j];
}
}
// Printing the pascal matrix
for (let i = 0; i < n; i++)
{
for (let j = 0; j < n; j++)
document.write( C[i + j][i] +" ");
document.write("<br/>");
}
}
// Driver code
let n = 5;
printpascalmatrix(n);
</script>
Producción
1 1 1 1 1 1 2 3 4 5 1 3 6 10 15 1 4 10 20 35 1 5 15 35 70