(Maximum increasingly ordered subsequence) Write a program that prompts the user to enter a string and displays the maximum increasingly ordered subsequence of characters. Analyze the time complexity of your program. Here is a sample run:

/*********************************************************************************
* (Maximum increasingly ordered subsequence) Write a program that prompts the    *
* user to enter a string and displays the maximum increasingly ordered           *
* subsequence of characters. Analyze the time complexity of your program.        *
*********************************************************************************/
import java.util.*;

public class Exercise_22_02 {
	public static void main(String[] args) {
		// Create a Scanner
		Scanner input = new Scanner(System.in);

		// Prompt the user to enter a string
		System.out.print("Enter a string: ");
		String string = input.nextLine(); 

		LinkedList<Character> max = new LinkedList<>();

		// Find the maximum increasingly ordered subsequence
		for (int i = 0; i < string.length(); i++) { 
			LinkedList<Character> list = new LinkedList<>();
			list.add(string.charAt(i));
			for (int j = i + 1; j < string.length(); j++) {
				if (string.charAt(j) > list.getLast()) {
					list.add(string.charAt(j)); 
				}
			}

			if (list.size() > max.size()) {
				max.clear();
				max.addAll(list);
			}
			list.clear();
		}

		// Display the maximum consecutive 
		// increasingly ordered substring
		for (Character ch: max) { // single loop
			System.out.print(ch); // Simple statement
		}
		System.out.println();
	}

/*********************************************************************************
* 	Analyze the time complexity of your program:                                  *  
* 	1 outerloop = n;                                                              *
* 	1 innerloop = n - 1;                                                          *
*  1 simple statement = 1                                                        *
* 	1 single loop * 1 simple statement = 1;                                       * 
*  T(n) = (n * (n - 1)) + (1 + 1);                                               *  
*  T(n) = O(n^2) + O(n);                                                         *  
* 	T(n) = O(n^2) Quadratic time;                                                 * 
*********************************************************************************/ 
}