1. Programming with Recursion

2. Example of Recursion (Ask Until the User Gets It Right) import java.util.* ; public class CountDown { private int count; public static void main(String[] args) { CountDown countDowner = new CountDown( ); countDowner.getCount( ); countDowner.showCountDown( ); } public void getCount( ) { System.out.println("Enter a positive number:"); Scanner keyboard = new Scanner(System.in); count = keyboard.nextInt( ); if (count = 0; left--) System.out.print(left + ", "); System.out.println("Blast Off!"); } }

3. Binary Search Using Recursion mid = approximate midpoint between first and last ; if (first > last) return -1; else if (target == a[mid]) return mid; else if (target < a[mid]) return the result of searching a[first] through a[mid-1]. else if (target > a[mid]) return the result of searching a[mid+1] through a[last].

4. Example of Recursion (Binary Search) /** Class for searching an already sorted array of ints. To search the sorted and completely filled array b, use the following: ArraySearcher bSearcher = new ArraySearcher(b); int index = bSearcher.find(target); index will be given an index of where target is located. index will be set to -1 if target is not in the array. */ public class ArraySearcher { private int[] a; /** Precondition: theArray is full and is sorted from lowest to highest. */ public ArraySearcher(int[] theArray) { a = theArray;//a is now another name for theArray. }

5. Example of Recursion (Binary Search) /** If target is in the array, returns the index of an occurrence of target. Returns -1 if target is not in the array. */ public int find(int target) { return search(target, 0, a.length - 1); } //Uses binary search to search for target in a[first] through //a[last] inclusive. Returns the index of target if target //is found. Returns -1 if target is not found. private int search(int target, int first, int last) { int result = -1;//to keep the compiler happy. int mid; if (first > last) result = -1; else { mid = (first + last)/2; if (target == a[mid]) result = mid; else if (target a[mid]) result = search(target, mid + 1, last); } return result; } }

6. Example of Recursion (Binary Search) import java.util.*; public class ArraySearcherDemo { public static void main(String[] args) { int [] a = new int[10]; System.out.println("Enter 10 integers in increasing order."); System.out.println("One per line."); Scanner keyboard = new Scanner(System.in); int i; for (i = 0; i < 10; i++) a[i] = keyboard.nextInt( ); System.out.println( ); for (i = 0; i < 10; i++) System.out.print("a[" + i + "]=" + a[i] + " "); System.out.println( ); System.out.println( ); ArraySearcher finder = new ArraySearcher(a); String ans; do { System.out.println("Enter a value to search for:"); int target = keyboard.nextInt( ); int result = finder.find(target); if (result < 0) System.out.println( target + " is not in the array."); else System.out.println( target + " is at index " + result); System.out.println("Again?"); ans = keyboard.next( ); }while (ans.equalsIgnoreCase("yes")); System.out.println( "May you find what you're searching for."); } }

7. Merge Sort – A Recursive Sorting Method  Merge sort is an example of a divide- and-conquer algorithm.  The array to be sorted is divided in half, and the two halves of the array are sorted by recursive calls.  That process produces two smaller sorted arrays.  The two sorted arrays are then merged to form a single sorted array.

8. Merge Sort – A Recursive Sorting Method Algorithm  If the array a has only one element do nothing (stopping case).  Otherwise, do the following (recursive case): Copy the first half of the elements in a to a smaller array named front. Copy the rest of the elements in the array a to another smaller array named tail. Sort the array front with a recursive call. Sort the array tail with a recursive call. Merge the elements in the arrays front and tail into the array a.

9. Merge Sort – A Recursive Sorting Method Code /** Class for sorting an array of ints from smallest to largest, using the merge sort algorithm. */ public class MergeSort { /** Precondition: Every indexed variable of a has a value. Action: Sorts a so that a[0] = 2) { int halfLength = a.length/2; int[] front = new int[halfLength]; int[] tail = new int[a.length - halfLength]; divide(a, front, tail); sort(front); sort(tail); merge(a, front, tail); } //else do nothing. a.length == 1, so a is sorted. }

10. Merge Sort – A Recursive Sorting Method Code (cont’d) /** Precondition: a.length = front.length + tail.length. Postcondition: All the elements of a are divided between the arrays front and tail. */ private static void divide(int[] a, int[] front, int[] tail) { int i; for (i = 0; i < front.length; i++) front[i] = a[i]; for (i = 0; i < tail.length; i++) tail[i] = a[front.length + i]; }

11. Merge Sort – A Recursive Sorting Method Code (cont’d) /** Precondition: Arrays front and tail are sorted from smallest to largest, and a.length = front.length + tail.length. Postcondition: a contains all the values from front and tail, and a is sorted from smallest to largest. */ private static void merge(int[] a, int[] front, int[] tail) { int frontIndex = 0, tailIndex = 0, aIndex = 0; while ((frontIndex < front.length) && (tailIndex < tail.length)) { if (front[frontIndex] < tail[tailIndex]) { a[aIndex] = front[frontIndex]; aIndex++; frontIndex++; } else { a[aIndex] = tail[tailIndex]; aIndex++; tailIndex++; } } //At least one of front and tail has been //completely copied to a. while (frontIndex < front.length)//Copy rest of front, //if any. { a[aIndex] = front[frontIndex]; aIndex++; frontIndex++; } while (tailIndex < tail.length)//Copy rest of tail, if any. { a[aIndex] = tail[tailIndex]; aIndex++; tailIndex++; } } }

12. Merge Sort – A Recursive Sorting Method Code (cont’d) public class MergeSortDemo { public static void main(String[] args) { int[] b = {7, 5, 11, 2, 16, 4, 18, 14, 12, 30}; System.out.println("Array values before sorting:"); int i; for (i = 0; i < b.length; i++) System.out.print(b[i] + " "); System.out.println( ); MergeSort.sort(b); System.out.println("Array values after sorting:"); for (i = 0; i < b.length; i++) System.out.print(b[i] + " "); System.out.println( ); } }