Task 1 (40 pts). Implement the Quick Sort algorithm as discussed in Lecture 4. (Hint: use the function checked_sorted to check if your output is indeed sorted.) Task 2 (40 pts). Implement the Counting Sort algorithm as discussed in Lecture 4. (Hint: use the function checked_sorted to check if your output is indeed sorted.) Task 3 (20 pts). Generate a report to discuss the time performance of the two algorithms. Compare it with their theoretical time complexity as discussed in the lecture. Plots and figures are encouraged to help draw the conclusion. import java.util.*; 1 public class Sort3 { public static int[] quick_sort.lintilaccasamintheminta) { } public static int partition.LintIdmancavamintvkenint.cd. { } public static int[] counting sort.Cintilaccan mint..k) { } public static int[] generate_random_array (int n, int k) { List list; int[] array; Random rnd; rnd = new Random(System.currentTimeMillis(); list = new ArrayList (); for (int i = 1; i list; int[] array; list = new ArrayList (); for (int i = 1; i array[i]) return false; } return true; } public static void print_array (int[] array) { for (int i = 0; i