1 Examples of class: Recursive data structures Instructor: Mainak Chaudhuri

2 Recursive data structures Refers to a “connected” set of similar objects –Object A “connects” or “refers” to object B –For example, in a list of integers you can imagine each integer in the list as an object and each object connects to its next object thereby forming a list –The structure is called recursive because an object of type class A connects to another object of the same class type –Very important to build complex connected structures e.g., a network of cities where a “connection” could mean rail or road

3 List structure Why not just an array? –Basic operations needed on a list: search, insertion, deletion –All these are time consuming in arrays e.g., searching is O(n), insertion at head is O(n), and deletion from head is also O(n) –With lists, arbitrary insertion and deletion can be made in O(1) time; searching is still costly (we will discuss techniques to improve it on average and in the worst case) Insertion and deletion involve changing a few references (independent of n)

4 List structure Consider insertion sort –For each element, we compared it with all elements on its left until a comparison failed and then shifted up all the elements on the right to make a hole for insertion –If the numbers are stored in a list, the last shift-up step can be completely avoided Just insert one element and delete another: O(1) –Recall that with a reverse-sorted array, the number of comparisons is minimum while with a sorted array, the number of comparisons is maximum But former spends more time in shift-up leading to both cases requiring roughly the same amount of time –With a list implementation, the first case will indeed be the fastest

5 List structure public class IntegerList { private int data; private IntegerList next; public IntegerList (int x, IntegerList rest) { data = x; next = rest; } // next slide

6 List structure public IntegerList (int x) { data = x; next = null; } public int GetHead () { return data; } // next slide

7 List structure public IntegerList GetBody () { return next; } public int Length () { if (next==null) return 1; return (1 + GetBody().Length()); } public int GetTail () { if (next==null) return data; return GetBody().GetTail(); }

8 List structure public IntegerList Search (int x) { if (data==x) return this; if (next==null) return null; return GetBody().Search(x); } public int ExtractElement (int index) { // This is slower compared to array if (index==0) return data; if (next==null) { System.out.println (“Query index too large!”); return -1; } return GetBody().ExtractElement (index-1); }

9 List structure public void Enqueue (int x) { if (next==null) { next = new IntegerList (x); } else { GetBody().Enqueue(x); } // next slide

10 List structure public IntegerList Dequeue () { return next; } public IntegerList Reverse () { if (next==null) return this; IntegerList temp = GetBody().Reverse(); temp.Enqueue (data); return temp; } // next slide

11 List structure public void SetBody (IntegerList x) { next = x; }

12 List structure public void Print () { if (next==null) { System.out.println (data); } else { System.out.print (data + “, ”); GetBody().Print(); } // next slide

13 List structure public IntegerList SearchAndDelete (int x) { // return the new head of the list IntegerList temp = this; IntegerList prev = null; while ((temp != null) && (temp.GetHead() != x)) { prev = temp; temp = temp.GetBody(); } // next slide

14 List structure if (temp != null) { // found x if (prev == null) { // first one is x return temp.GetBody(); // new head of list } else { prev.SetBody (temp.GetBody()); return this; } else { // did not find x return this; } } // next slide

15 List structure public IntegerList SortedInsert (int x) { // return the new head of the list IntegerList temp = this; IntegerList prev = null; IntegerList newBorn = new IntegerList (x); while ((temp != null) && (temp.GetHead() < x)) { prev = temp; temp = temp.GetBody(); } // next slide

16 List structure if (temp != null) { if (prev == null) { // Insert at head newBorn.SetBody(this); return newBorn; } else { // Insert in middle prev.SetBody(newBorn); newBorn.SetBody(temp); return this; } // next slide

17 List structure else { // Insert at end prev.SetBody(newBorn); return this; } } // end class Need for maintaining a tail reference –Could enqueue at end without traversing the entire list

18 List structure class ListBuilder { public static void main (String a[]) { IntegerList iL = new IntegerList (5); iL = new IntegerList (6, iL); iL = new IntegerList (-2, iL); iL.Enqueue (13); System.out.println (“Length: ” + iL.Length()); System.out.println (“Position 2: ” + iL.ExtractElement (2)); iL.Print ();// next slide

19 List structure iL = iL.Reverse(); iL.Print(); iL = iL.SearchAndDelete(-2); iL.Print(); iL = iL.SortedInsert(10); iL.Print(); }