A test harness program for testing sorting methods is provided with the rest of the textbook program files. It is the file Sorts.java in the ch11 package. The program includes a swap method that is used by all the sorting methods to swap array elements. Describe an approach to modifying the program so that after calling a sorting method the program prints out the number of swaps needed by the sorting method. Implement your approach. Test your new program by running the selectionSort method. Your program should report 49 swaps.

Determine the Big-O complexity for the selectionSort based on the number of elements moved rather than on the number of comparisons

For the best case.

For the worst case.

Create a data set with 100 integer values. Create a program that uses the division method of hashing to store the data values into hash tables with table sizes of 7, 51, and 151. Use the linear probing method of collision resolution. Print out the tables after the data values have been stored. Search for 10 different values in each of the three hash tables, counting the number of comparisons necessary. Print out the number of comparisons necessary in each case in tabular form. Share a listing of your program and output. Review other program from your classmates and discuss differences.

//---------------------------------------------------------------------------- // Sorts.java by Dale/Joyce/Weems Chapter 10 // // Test harness used to run sorting algorithms. //---------------------------------------------------------------------------- import java.util.*; import java.text.DecimalFormat; public class Sorts { static final int SIZE = 50; // size of array to be sorted static int[] values = new int[SIZE]; // values to be sorted static void initValues() // Initializes the values array with random integers from 0 to 99. { Random rand = new Random(); for (int index = 0; index < SIZE; index++) values[index] = Math.abs(rand.nextInt()) % 100; } static public boolean isSorted() // Returns true if the array values are sorted and false otherwise. { boolean sorted = true; for (int index = 0; index < (SIZE - 1); index++) if (values[index] > values[index + 1]) sorted = false; return sorted; } static public void swap(int index1, int index2) // Precondition: index1 and index2 are >= 0 and < SIZE. // // Swaps the integers at locations index1 and index2 of the values array. { int temp = values[index1]; values[index1] = values[index2]; values[index2] = temp; } static public void printValues() // Prints all the values integers. { int value; DecimalFormat fmt = new DecimalFormat("00"); System.out.println("The values array is:"); for (int index = 0; index < SIZE; index++) { value = values[index]; if (((index + 1) % 10) == 0) System.out.println(fmt.format(value)); else System.out.print(fmt.format(value) + " "); } System.out.println(); } ///////////////////////////////////////////////////////////////// // // Selection Sort static int minIndex(int startIndex, int endIndex) // Returns the index of the smallest value in // values[startIndex]..values[endIndex]. { int indexOfMin = startIndex; for (int index = startIndex + 1; index <= endIndex; index++) if (values[index] < values[indexOfMin]) indexOfMin = index; return indexOfMin; } static void selectionSort() // Sorts the values array using the selection sort algorithm. { int endIndex = SIZE - 1; for (int current = 0; current < endIndex; current++) swap(current, minIndex(current, endIndex)); } ///////////////////////////////////////////////////////////////// // // Bubble Sort static void bubbleUp(int startIndex, int endIndex) // Switches adjacent pairs that are out of order // between values[startIndex]..values[endIndex] // beginning at values[endIndex]. { for (int index = endIndex; index > startIndex; index--) if (values[index] < values[index - 1]) swap(index, index - 1); } static void bubbleSort() // Sorts the values array using the bubble sort algorithm. { int current = 0; while (current < (SIZE - 1)) { bubbleUp(current, SIZE - 1); current++; } } ///////////////////////////////////////////////////////////////// // // Short Bubble Sort static boolean bubbleUp2(int startIndex, int endIndex) // Switches adjacent pairs that are out of order // between values[startIndex]..values[endIndex] // beginning at values[endIndex]. // // Returns false if a swap was made; otherwise, returns true. { boolean sorted = true; for (int index = endIndex; index > startIndex; index--) if (values[index] < values[index - 1]) { swap(index, index - 1); sorted = false; } return sorted; } static void shortBubble() // Sorts the values array using the bubble sort algorithm. // The process stops as soon as values is sorted. { int current = 0; boolean sorted = false; while ((current < (SIZE - 1)) && !sorted) { sorted = bubbleUp2(current, SIZE - 1); current++; } } ///////////////////////////////////////////////////////////////// // // Insertion Sort static void insertItem(int startIndex, int endIndex) // Upon completion, values[0]..values[endIndex] are sorted. { boolean finished = false; int current = endIndex; boolean moreToSearch = true; while (moreToSearch && !finished) { if (values[current] < values[current - 1]) { swap(current, current - 1); current--; moreToSearch = (current != startIndex); } else finished = true; } } static void insertionSort() // Sorts the values array using the insertion sort algorithm. { for (int count = 1; count < SIZE; count++) insertItem(0, count); } ///////////////////////////////////////////////////////////////// // // Merge Sort static void merge (int leftFirst, int leftLast, int rightFirst, int rightLast) // Preconditions: values[leftFirst]..values[leftLast] are sorted. // values[rightFirst]..values[rightLast] are sorted. // // Sorts values[leftFirst]..values[rightLast] by merging the two subarrays. { int[] tempArray = new int [SIZE]; int index = leftFirst; int saveFirst = leftFirst; // to remember where to copy back while ((leftFirst <= leftLast) && (rightFirst <= rightLast)) { if (values[leftFirst] < values[rightFirst]) { tempArray[index] = values[leftFirst]; leftFirst++; } else { tempArray[index] = values[rightFirst]; rightFirst++; } index++; } while (leftFirst <= leftLast) // Copy remaining items from left half. { tempArray[index] = values[leftFirst]; leftFirst++; index++; } while (rightFirst <= rightLast) // Copy remaining items from right half. { tempArray[index] = values[rightFirst]; rightFirst++; index++; } for (index = saveFirst; index <= rightLast; index++) values[index] = tempArray[index]; } static void mergeSort(int first, int last) // Sorts the values array using the merge sort algorithm. { if (first < last) { int middle = (first + last) / 2; mergeSort(first, middle); mergeSort(middle + 1, last); merge(first, middle, middle + 1, last); } } ///////////////////////////////////////////////////////////////// // // Quick Sort static int split(int first, int last) { int splitVal = values[first]; int saveF = first; boolean onCorrectSide; first++; do { onCorrectSide = true; while (onCorrectSide) // move first toward last if (values[first] > splitVal) onCorrectSide = false; else { first++; onCorrectSide = (first <= last); } onCorrectSide = (first <= last); while (onCorrectSide) // move last toward first if (values[last] <= splitVal) onCorrectSide = false; else { last--; onCorrectSide = (first <= last); } if (first < last) { swap(first, last); first++; last--; } } while (first <= last); swap(saveF, last); return last; } static void quickSort(int first, int last) { if (first < last) { int splitPoint; splitPoint = split(first, last); // values[first]..values[splitPoint - 1] <= splitVal // values[splitPoint] = splitVal // values[splitPoint+1]..values[last] > splitVal quickSort(first, splitPoint - 1); quickSort(splitPoint + 1, last); } } ///////////////////////////////////////////////////////////////// // // Heap Sort static int newHole(int hole, int lastIndex, int item) // If either child of hole is larger than item this returns the index // of the larger child; otherwise it returns the index of hole. { int left = (hole * 2) + 1; int right = (hole * 2) + 2; if (left > lastIndex) // hole has no children return hole; else if (left == lastIndex) // hole has left child only if (item < values[left]) // item < left child return left; else // item >= left child return hole; else // hole has two children if (values[left] < values[right]) // left child < right child if (values[right] <= item) // right child <= item return hole; else // item < right child return right; else // left child >= right child if (values[left] <= item) // left child <= item return hole; else // item < left child return left; } static void reheapDown(int item, int root, int lastIndex) // Precondition: Current root position is "empty". // // Inserts item into the tree and ensures shape and order properties. { int hole = root; // current index of hole int newhole; // index where hole should move to newhole = newHole(hole, lastIndex, item); // find next hole while (newhole != hole) { values[hole] = values[newhole]; // move value up hole = newhole; // move hole down newhole = newHole(hole, lastIndex, item); // find next hole } values[hole] = item; // fill in the final hole } static void heapSort() // Sorts the values array using the heap sort algorithm. { int index; // Convert the array of values into a heap. for (index = SIZE/2 - 1; index >= 0; index--) reheapDown(values[index], index, SIZE - 1); // Sort the array. for (index = SIZE - 1; index >=1; index--) { swap(0, index); reheapDown(values[0], 0, index - 1); } } ///////////////////////////////////////////////////////////////// // // Main public static void main(String[] args) { initValues(); printValues(); System.out.println("values is sorted: " + isSorted()); System.out.println(); // make call to sorting method here (just remove //) // selectionSort(); // bubbleSort(); // shortBubble(); // insertionSort(); // mergeSort(0, SIZE - 1); // quickSort(0, SIZE - 1); // heapSort(); printValues(); System.out.println("values is sorted: " + isSorted()); System.out.println(); } }