Example: Pascal's Triangle with Space Optimization (1D Array) in Java

// Pascal's Triangle with Space Optimization (1D Array)
import java.util.Scanner;

// Main class containing the entry point of the program
public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        // Step 1: Get the number of rows from the user
        System.out.print("Enter the number of rows for Pascal's Triangle: ");
        int numRows = scanner.nextInt();

        // Step 2: Declare and initialize a 1D array to store the current row
        // The maximum length of a row will be numRows
        int[] currentRow = new int[numRows];

        System.out.println("\nPascal's Triangle (" + numRows + " rows):");

        // Step 3: Iterate through each row to calculate and print
        for (int i = 0; i < numRows; i++) {
            // Add leading spaces for proper alignment
            for (int k = 0; k < numRows - i - 1; k++) {
                System.out.print(" ");
            }

            // Step 4: Calculate elements for the current row, iterating backward
            // This is crucial to use the values from the *previous* iteration (previous row)
            // before they are overwritten for the current row's calculation.
            for (int j = i; j >= 0; j--) {
                if (j == 0 || j == i) {
                    currentRow[j] = 1; // First and last element are always 1
                } else {
                    currentRow[j] = currentRow[j - 1] + currentRow[j];
                }
            }

            // Step 5: Print the current row
            for (int j = 0; j <= i; j++) {
                System.out.print(currentRow[j] + " ");
            }
            System.out.println();
        }

        scanner.close();
    }
}