帕斯卡矩阵
在数学中，特别是在矩阵理论和组合学中，帕斯卡矩阵是包含二项式系数作为其元素的无限矩阵。有三种方法可以实现:作为上三角矩阵、下三角矩阵或对称矩阵。这些的 5 x 5 截断如下所示:
对称帕斯卡矩阵的元素是二项式系数，即
给定正整数 n 。任务是打印大小为 n×n 的对称帕斯卡矩阵 示例:
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
下面是实现 n×n 对称帕斯卡矩阵的代码:
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 语言(一种计算机语言，尤用于创建网站)
// 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.
Python 3
# 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 ottom 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.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to print symmetric
// pascal matrix.
// Print Pascal Matrix
function printpascalmatrix($n)
{
$C[2 * $n + 1][2 * $n + 1] = (0);
// Calculate value of Binomial
// Coefficient in ottom up manner
for ($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
?>
java 描述语言
<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>
输出:
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
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