Example: Pascal's Triangle using Dynamic Programming in Java

// Pascal's Triangle using Dynamic Programming
import java.util.ArrayList;
import java.util.List;
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: Initialize a list to store all rows of the triangle
        List<List<Integer>> triangle = new ArrayList<>();

        // Step 2: Iterate to generate each row
        for (int i = 0; i < numRows; i++) {
            // Step 3: Create a new list for the current row
            List<Integer> currentRow = new ArrayList<>();

            // Step 4: Iterate to generate elements of the current row
            for (int j = 0; j <= i; j++) {
                if (j == 0 || j == i) {
                    // First and last elements of each row are always 1
                    currentRow.add(1);
                } else {
                    // Sum the two elements from the previous row
                    List<Integer> prevRow = triangle.get(i - 1);
                    int sum = prevRow.get(j - 1) + prevRow.get(j);
                    currentRow.add(sum);
                }
            }
            // Step 5: Add the completed current row to the triangle
            triangle.add(currentRow);
        }

        // Step 6: Print the generated triangle
        for (int i = 0; i < numRows; i++) {
            // Print leading spaces for alignment
            for (int k = 0; k < numRows - i - 1; k++) {
                System.out.print(" ");
            }
            for (int num : triangle.get(i)) {
                System.out.print(num + " ");
            }
            System.out.println();
        }
        scanner.close();
    }
}