java/data structures

P3 (20 points)

Write the java code for the method

public static > boolean isSorted(T[ ] a)

which returns true if the array a is in sorted in ascending order. The code must run in O(n) time.

P4 (30 points)

Consider a revised selection sort algorithm so that on each pass it finds both the largest and smallest values in the unsorted portion of the array. The sort then moves each of these values into its correct location by swapping array entries.

Implement the modified selection sort using the method

public static > void modifiedSelectionSort(T[] a, int n)

How many comparisons are necessary to sort n values?

using java file below to add code

ArraySearcher.java

/** A class of static methods for searching an array of Comparable objects. @author Frank M. Carrano @author Timothy M. Henry @version 4.0 */ public class ArraySearcher { // Segment 18.3 /** Searches an unsorted array for anEntry. */ public static boolean inArrayIterativeUnsorted(T[] anArray, T anEntry) { boolean found = false; int index = 0; while (!found && (index < anArray.length)) { if (anEntry.equals(anArray[index])) found = true; index++; } // end while return found; } // end inArrayIterativeUnsorted // ======================================================================================== // Segment 18.6 /** Searches an unsorted array for anEntry. */ public static boolean inArrayRecursiveUnsorted(T[] anArray, T anEntry) { return search(anArray, 0, anArray.length - 1, anEntry); } // end inArrayRecursiveUnsorted // Searches anArray[first] through anArray[last] for desiredItem. // first >= 0 and < anArray.length. // last >= 0 and < anArray.length. private static boolean search(T[] anArray, int first, int last, T desiredItem) { boolean found = false; if (first > last) found = false; // No elements to search else if (desiredItem.equals(anArray[first])) found = true; else found = search(anArray, first + 1, last, desiredItem); return found; } // end search // ========================================================================================

/** Searches a sorted array for anEntry. */ public static > boolean inArrayRecursiveSorted(T[] anArray, T anEntry) { return binarySearch(anArray, 0, anArray.length - 1, anEntry); } // end inArrayRecursiveSorted // Segment 18.13 // Searches anArray[first] through anArray[last] for desiredItem. // first >= 0 and < anArray.length. // last >= 0 and < anArray.length. private static > boolean binarySearch(T[] anArray, int first, int last, T desiredItem) { boolean found; int mid = first + (last - first) / 2; if (first > last) found = false; else if (desiredItem.equals(anArray[mid])) found = true; else if (desiredItem.compareTo(anArray[mid]) < 0) found = binarySearch(anArray, first, mid - 1, desiredItem); else found = binarySearch(anArray, mid + 1, last, desiredItem); return found; } // end binarySearch // ========================================================================================

public static void display(T[] anArray) { System.out.print("The array contains the following entries: "); for (int index = 0; index < anArray.length; index++) { System.out.print(anArray[index] + " "); } // end for System.out.println(); } // end display } // end ArraySearcher

ArraySort.java

import java.util.* ; public class SortArray { public static > void selectionSort(T[] a, int n) { for (int index = 0; index < n - 1; index++) { int indexOfSmallest = indexOfSmallest(a, index, n - 1); T temp = a[index]; a[index] = a[indexOfSmallest]; a[indexOfSmallest] = temp; //Invariant: a[0] <= a[1] <= . . . <= a[index] <= all other a[i] } // end for } // end selectionSort private static > int indexOfSmallest(T[] a, int first, int last) { T min = a[first]; int indexOfMin = first; for (int index = first + 1; index <= last; index++) { if (a[index].compareTo(min) < 0) { min = a[index]; indexOfMin = index; } } return indexOfMin; }

public static > void insertionSort(T[] a, int n) { for(int unsorted = 1; unsorted < n; ++unsorted) { T item = a[unsorted]; int loc = unsorted; while(loc > 0 && a[loc-1].compareTo(item) > 0) { a[loc] = a[loc-1]; --loc; } a[loc] = item; } }

public static > void bubbleSort(T[] a, int n) { for(int pass = 1; pass < n ; ++pass) { for(int index = 0; index < n-pass; ++index) { int nextIndex = index + 1; if(a[index].compareTo(a[nextIndex]) > 0) { T temp = a[index]; a[index] = a[nextIndex]; a[nextIndex] = temp; } } } }

public static > void bubbleSort2(T[] a, int n) { boolean sorted = false; for(int pass = 1; pass < n && !sorted ; ++pass) { sorted = true; for(int index = 0; index < n-pass; ++index) { int nextIndex = index + 1; if(a[index].compareTo(a[nextIndex]) > 0) { T temp = a[index]; a[index] = a[nextIndex]; a[nextIndex] = temp; sorted = false; } } } } public static void main(String [] args) { Integer [] a = { 15, 8 , 10 , 2, 5 }; //selectionSort(a, a.length); //insertionSort(a, a.length); //bubbleSort(a, a.length); bubbleSort2(a, a.length); System.out.println("a = " + Arrays.toString(a)); } } // end SortArray