Example: Pascal's Triangle using Recursion in Java

// Pascal's Triangle using Recursion
import java.util.Scanner;

// Main class containing the entry point of the program
public class Main {

    // Recursive helper function to calculate the value at a specific position (row, col)
    public static int pascalValue(int row, int col) {
        // Step 1: Base Cases
        // The first and last elements of each row are always 1.
        // Also handles the top of the triangle (row 0, col 0).
        if (col == 0 || col == row) {
            return 1;
        }
        // Step 2: Recursive Step
        // Any other element is the sum of the two elements directly above it
        // (one from the previous row at the same column, and one from the previous row at the previous column).
        return pascalValue(row - 1, col - 1) + pascalValue(row - 1, col);
    }

    public static void main(String[] args) {
        // Step 1: Prompt user for the number of rows
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter the number of rows for Pascal's Triangle: ");
        int numRows = scanner.nextInt();
        scanner.close();

        System.out.println("Pascal's Triangle (recursive):");

        // Step 2: Iterate through each row to print the triangle
        for (int i = 0; i < numRows; i++) {
            // Step 3: Print leading spaces for formatting
            // This centers the triangle visually.
            for (int k = 0; k < numRows - i; k++) {
                System.out.print(" ");
            }

            // Step 4: Iterate through each column in the current row
            for (int j = 0; j <= i; j++) {
                // Step 5: Calculate and print the value using the recursive helper function
                System.out.print(pascalValue(i, j) + " ");
            }
            System.out.println(); // Move to the next line after printing each row
        }
    }
}