Java Program to Print Star Pascal’s Triangle

Pascal’s triangle is a triangular array of the binomial coefficients. Write a function that takes an integer value n as input and prints the first n lines of Pascal’s triangle. Following are the first 6 rows of Pascal’s Triangle.In this article, we will look into the process of printing Pascal’s triangle. Pascal’s triangle is a pattern of the triangle which is based on nCr.below is the pictorial representation of Pascal’s triangle.

Illustration:

Input : N = 5
Output:
          1
        1   1
      1   2   1
    1   3   3   1
  1   4   6   4   1
1   5   10   10   5   1

Methods: 

There are two approaches for the same. Let’s check them out.

1. Using nCr formula
2. Using Binomial Coefficient

Method 1: Using nCr formula

Implementation: Follow the below algorithm for printing Pascal’s triangle using the nCr formula

• Let n be the number of rows to be printed
• Use outer iteration a from 0 to k times to print the rows
• Make inner iteration for b from 0 to (K – 1).
• Then print space as ” “.
• Close the inner ‘b’ loop.
• Make inner iteration for b from ‘0’ to ‘a’.
• Output nCr of ‘a’ and ‘b’.
• Close inner loop.
• Print newline character (\n) after each inner iteration.

Example

Java

// Java Program to Print Pascal's Triangle

// Importing input output classes
import java.io.*;

// Main Class
public class GFG {

    // Method 1
    // To find factorial of a number
    public int factorial(int a)
    {
        // Edge case
        // Factorial of 0 is unity
        if (a == 0)

            // Hence return 1
            return 1;

        // else recursively call the function over the
        // number whose factorial is to be computed
        return a * factorial(a - 1);
    }

    // Method 2
    // Main driver method
    public static void main(String[] args)
    {
        // Declare and initialize number whose
        // factorial is to be computed
        int k = 4;

        int a, b;

        // Creating an object of GFG class
        // in the main() method
        GFG g = new GFG();

        // iterating using nested for loop to traverse over
        // matrix

        // Outer for loop
        for (a = 0; a <= k; a++) {

            // Inner loop 1
            for (b = 0; b <= k - a; b++) {

                // Print white space for left spacing
                System.out.print(" ");
            }

            // Inner loop 2
            for (b = 0; b <= a; b++) {

                // nCr formula
                System.out.print(
                    " "
                    + g.factorial(a)
                          / (g.factorial(a - b)
                             * g.factorial(b)));
            }

            // By now, we are done with one row so
            // a new line
            System.out.println();
        }
    }
}

Output

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

Time complexity: O(2ⁿ) due to recursive method

Auxiliary Space: O(n) due to recursive stack space

Method 2: Using Binomial Coefficient

The ‘A’th entry in a line number line is Binomial Coefficient C(line, a) and all lines start with value 1. The idea is to calculate C(line, a) using C(line, a-1).  

C(line, i) = C(line, i-1) * (line - i + 1) / i

Implementation:

Example

Java

// Java Program to Print Pascal's Triangle

// Importing input output classes
import java.io.*;

// Main Class
public class GFG {

    // Method 1
    // Pascal function
    public static void printPascal(int k)
    {
        for (int line = 1; line <= k; line++) {
            for (int b = 0; b <= k - line; b++) {

                // Print whitespace for left spacing
                System.out.print(" ");
            }

            // Variable used to represent C(line, i)
            int C = 1;

            for (int a = 1; a <= line; a++) {

                // The first value in a line is always 1
                System.out.print(C + " ");

                C = C * (line - a) / a;
            }

            // By now, we are done with one row so
            // a new line is required
            System.out.println();
        }
    }

    // Method 2
    // Main driver method
    public static void main(String[] args)
    {
        // Declare and initialize variable number
        // upto which Pascal's triangle is  required on
        // console
        int n = 6;

        // Calling the Pascal function(Method 1)
        printPascal(n);
    }
}

Output

      1 
     1 1 
    1 2 1 
   1 3 3 1 
  1 4 6 4 1 
 1 5 10 10 5 1 

Time complexity: O(n^2) where n is given input for no of rows of pascal triangle

Auxiliary Space: O(1)