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Pascal Triangle

Steilla Mitchel19112-Jun-2024

Given an integer numRows, return the first numRows of Pascal's triangle.

In Pascal's triangle, each number is the sum of the two numbers directly above it as shown:

 

Example 1:

Input: numRows = 5 Output: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]

Example 2:

Input: numRows = 1 Output: [[1]]

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Updated on 13-Jun-2024
Steilla Mitchel

Steilla Mitchel

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Ashutosh Kumar Verma

Ashutosh Kumar Verma

13-Jun-2024

Pascal's Triangle

Pascal’s triangle is a geometric arrangement of binomial factors in a square. Each number in a square is the sum of the two directly above it. It is named after the French mathematician Blaise Pascal, although he was known in various parts of the world long before his time.

Sample of Pascal's triangle with 5 rows

                 1
              1     1
           1     2     1
        1     3     3     1
     1     4     6     4     1

The number at the edge of the triangle is always 1, and each inner number is the sum of the two digits above it. This process is continuous.

Example- 

Here is a basic C# example to demonstrate Pascal's triangle,

using System;
namespace MindStickSoft
{
   class Program
   {
       public static void Main(string[] args)
       {
           Console.WriteLine("Enter the number of rows for Pascal's Triangle");
           int rowNum = int.Parse(Console.ReadLine());
           PrintTriangle(rowNum);
           Console.ReadLine();
       }
       static void PrintTriangle(int rownumber)
       {
           for (int i = 0; i < rownumber; i++)
           {
               int number = 1;
               for (int j = 0; j < rownumber - i; j++)
               {
                   Console.Write("   ");
               }
               for (int k = 0; k <= i; k++)
               {
                   Console.Write("   {0:D}  ", number);
                   number = number * (i - k) / (k + 1);
               }
               Console.WriteLine();
           }
       }
   }
}

Output- 

Enter the number of rows for Pascal's Triangle
5
                 1
              1     1
           1     2     1
        1     3     3     1
     1     4     6     4     1

Also, Read: What is out keyword in C#?

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