Pascal’s Triangle in Java – Print Binomial Coefficients Using Nested Loops

In this blog post, we’ll learn how to print Pascal’s Triangle using Java. It’s a famous triangle of numbers that represents binomial coefficients, and it's also asked frequently in interviews.

📐 What is Pascal’s Triangle?

Pascal’s Triangle is a triangle where each number is the sum of the two numbers directly above it. The triangle starts with a 1 at the top, and the edges are always 1.

Example for n = 5 rows:

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

✅ Java Program to Print Pascal’s Triangle

public class PascalsTriangle {
    public static void main(String[] args) {
        int rows = 5;

        for (int i = 0; i < rows; i++) {
            // Print leading spaces
            for (int space = 1; space < rows - i; space++) {
                System.out.print(" ");
            }

            int number = 1;
            for (int j = 0; j <= i; j++) {
                System.out.print(number + " ");
                number = number * (i - j) / (j + 1);
            }

            System.out.println();
        }
    }
}

🧠 Interview Tip

Pascal’s Triangle tests your understanding of loops, math (combinations), and printing with proper formatting. The formula used is based on: nCr = n! / (r!(n - r)!) but is optimized using iteration.

🎯 Output

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

📌 Conclusion

We have seen how to print Pascal’s Triangle in Java. This is not only a popular pattern program but also builds your understanding of nested loops and combinatorial math.