Instructions. You are provided the skeleton code namedSort3.java. Please modify the skeleton code to solve the following tasks. 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.

package sorting;

import java.util.*;

public class Sort3 { public static int[] quick_sort (int[] array, int p, int r) { } public static int partition (int[] array, int p, int r) { } public static int[] counting_sort (int[] array, int 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 <= n; i++) list.add(new Integer(rnd.nextInt(k+1))); Collections.shuffle(list, rnd); array = new int[n]; for (int i = 0; i < n; i++) array[i] = list.get(i).intValue(); return array; } public static int[] generate_random_array (int n) { List list; int[] array; list = new ArrayList (); for (int i = 1; i <= n; i++) list.add(new Integer(i)); Collections.shuffle(list, new Random(System.currentTimeMillis())); array = new int[n]; for (int i = 0; i < n; i++) array[i] = list.get(i).intValue(); return array; } /* * Input: an integer array * Output: true if the array is acsendingly sorted, otherwise return false */ public static boolean check_sorted (int[] array) { for (int i = 1; i < array.length; i++) { if (array[i-1] > array[i]) return false; } return true; } public static void print_array (int[] array) { for (int i = 0; i < array.length; i++) System.out.print(array[i] + ", "); System.out.println(); } public static void main(String[] args) { // TODO Auto-generated method stub int k = 10000; System.out.println("Quick sort starts ------------------"); for (int n = 100000; n <= 1000000; n=n+100000) { int[] array = Sort3.generate_random_array(n); long t1 = System.currentTimeMillis(); array = Sort3.quick_sort(array, 0, n-1); long t2 = System.currentTimeMillis(); long t = t2 - t1; boolean flag = Sort3.check_sorted(array); System.out.println(n + "," + t + "," + flag); } System.out.println("Quick sort ends ------------------"); System.out.println("Counting sort starts ------------------"); for (int n = 100000; n <= 1000000; n=n+100000) { int[] array = Sort3.generate_random_array(n, k); long t1 = System.currentTimeMillis(); array = Sort3.counting_sort(array, k); long t2 = System.currentTimeMillis(); long t = t2 - t1; boolean flag = Sort3.check_sorted(array); System.out.println(n + "," + t + "," + flag); } System.out.println("Counting sort ends ------------------"); } }