Example: Pascal's Triangle Space-Efficient DP in Java

// Pascal's Triangle Space-Efficient DP
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);
        System.out.print("Enter the number of rows for Pascal's Triangle: ");
        int numRows = scanner.nextInt();

        // Step 1: Iterate through each row
        for (int i = 0; i < numRows; i++) {
            // Step 2: Print leading spaces for triangular alignment
            for (int k = 0; k < numRows - i - 1; k++) {
                System.out.print(" ");
            }

            long currentVal = 1; // First element of each row is always 1

            // Step 3: Iterate through each element in the current row
            for (int j = 0; j <= i; j++) {
                System.out.print(currentVal + " "); // Print the current element
                
                // Step 4: Calculate the next element using the nCr pattern: C(n,r) = C(n,r-1) * (n-r+1)/r
                // For Pascal's triangle, currentVal is C(i, j), nextVal is C(i, j+1)
                // C(i, j+1) = C(i, j) * (i - j) / (j + 1)
                currentVal = currentVal * (i - j) / (j + 1); 
            }
            System.out.println(); // Move to the next line after each row
        }
        scanner.close();
    }
}