Java Program to Print 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.

Example:

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

Approach #1: 

nCr formula:

 n ! / ( n – r ) ! r ! 

After using nCr formula, the pictorial representation becomes:

           0C0
        1C0   1C1
     2C0   2C1   2C2
  3C0   3C1   3C2   3C3

Algorithm:

• Take a number of rows to be printed, assume it to be n
• Make outer iteration i from 0 to n times to print the rows.
• Make inner iteration for j from 0 to (N – 1).
• Print single blank space ” “
• Close inner loop (j loop) //it’s needed for left spacing
• Make inner iteration for j from 0 to i.
• Print nCr of i and j.
• Close inner loop.
• Print newline character (\n) after each inner iteration.

Below is the implementation of the above approach:

Java

// Print Pascal's Triangle in Java
import java.io.*;

class GFG {
    public int factorial(int i)
    {
        if (i == 0)
            return 1;
        return i * factorial(i - 1);
    }
    public static void main(String[] args)
    {
        int n = 4, i, j;
        GFG g = new GFG();
        for (i = 0; i <= n; i++) {
            for (j = 0; j <= n - i; j++) {

                // for left spacing
                System.out.print(" ");
            }
            for (j = 0; j <= i; j++) {

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

            // for newline
            System.out.println();
        }
    }
}

Output

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

Time Complexity: O(N²)

Approach #2:

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

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

Below is the Implementation of given approach:

Java

// Print Pascal's Triangle in Java
import java.io.*;
class GFG {

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

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

            // used to represent C(line, i)
            int C = 1;
            for (int i = 1; i <= line; i++) {

                // The first value in a line is always 1
                System.out.print(C + " ");
                C = C * (line - i) / i;
            }
            System.out.println();
        }
    }

    // Driver code
    public static void main(String[] args)
    {
        int n = 4;
        printPascal(n);
    }
}

Output

    1 
   1 1 
  1 2 1 
 1 3 3 1 

Time Complexity: O(N²)

Auxiliary space: O(1) as it is using constant space for variables