Recursion examples: Problem 2. (More) Recursion and Lists. Tail recursion. Recursion examples: Problem 2. Recursion examples: Problem 3

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1 Reursion eamples: Problem 2 (More) Reursion and s Reursive funtion to reverse a string publi String revstring(string str) { if(str.equals( )) return str; return revstring(str.substring(1, str.length())) + Leture 4 CS211 Summer 2007 word.harat(0); 1 2 Reursion eamples: Problem 2 Another solution publi String revstr_helper(string str, String sofar) { if(str.equals( )) return sofar; return revstr_helper(str.substring(1, str.length()), str.harat(0) + sofar); Tail reursion In a tail reursive method, the reursive all is the last ommand eeuted by the method Tail reursive eample: return revstr_helper(str.substring(1, str.length()), str.harat(0) + sofar); Non-tail reursive: return revstring(str.substring(1, str.length())) + str.harat(0); publi String reversestring(string str) { return revstr_helper(str, ); 3 Tail reursive methods an be eeuted more effiiently No need to maintain a stak! 4 Reursion eamples: Problem 3 Reursive method to ompute GCD of two integers Uses Eulid s Algorithm publi int gd(int m, int n) { if((m % n) == 0) return n; return gd(n, m % n); Reursion eamples: Problem 4 Method that outputs binary representation of integer publi void printbinary(int n) { if(n == 0 n == 1) System.out.println(n); printbinary(n/2); System.out.print(n % 2); 5 6

2 Reursion eamples: Problem 5 Oveiew Merge two sorted strings of haraters publi String merge(string str1, String str2) { Arrays Random aess (good) Fied size: annot grow on demand after reation (bad) if(str1 == str2 == ) return str1+str2; if(str1.harat(0) <= str2.harat(1)) return str1.harat(0) + But some appliations Do not need random aess Require a data struture that an grow and shrink dynamially to aommodate different amounts of data s satisfy these requirements merge(str1.substring(1), str2); return str2.harat(0) + merge(str1, str2.substring(1); 7 Common operations reation Aessing elements in a list Inserting elements into a list Deleting elements from a list 8 Operations A Simple Interfae An ADT (Abstrat Data Type): Speifies publi funtionality Hides implementation detail from users Allows us to improve/replae implementation Fores us to think about fundamental operations (i.e., the interfae) separately from the implementation Operations: Create Insert objet Delete objet Find objet Replae objet Size? Empty? Usually sequential aess (not random aess) publi interfae { publi void insert(objet element); publi void delete(objet element); publi boolean ontains(objet element); publi int size(); Methods are speified, but no implementation A Java interfae orresponds niely to an ADT 9 10 Data Strutures Class Cell Cell Could use an array Need to speify array size Inserts & Deletes require moving elements Must opy array (to a larger array) when it gets full empty 78 Could use a sequene of linked ells We ll fous on this kind of implementation We define a lass Cell from whih we build lists lass Cell { private Objet datum; private Cell net; publi Cell(Objet d, Cell n){ datum = d; net = n; publi Objet getdatum() {return datum; publi Cell getnet() {return net; publi void setdatum(objet o) {datum = o; publi void setnet(cell ) {net = ; datum Objet: net Cell: getdatum getnet setdatum setnet By onvention, we will not show the instane methods when drawing ells 12

3 Building a Building a (ont d) Cell = new Cell(new Integer(), null); Integer t = new Integer(); Integer s = new Integer(); Integer e = new Integer(); One way to build a list with multiple ells: Cell p = new Cell(t, new Cell(s, new Cell(e, null))); Cell: To keep things simple, we will not show Integer objets epliitly in our pitures, but only show the value ontained in them. p Cell: 7 13 Another way: Integer t = new Integer(); Integer s = new Integer(); Integer e = new Integer(); //Can also use "autoboing" p Cell: Cell p = new Cell(e,null); p = new Cell(s,p); p = new Cell(t,p); Note: assignment of form p = new Cell(s,p); does not reate a irular list! 14 Aessing Elements Aess Eample: Linear Searh s are sequential-aess data strutures. To aess ontents of ell n in sequene, you must aess ells 0...n-1 Aessing data in first ell: p.getdatum() Aessing data in seond ell: p.getnet().getdatum() Aessing net field in seond ell: p.getnet().getnet() p Cell: Writing to fields in ells an be done the same way Update data in first ell: p.setdatum(new Integer(53)); Update data in seond ell: p.getnet().setdatum(new Integer(53)); Chop off third ell: p.getnet().setnet(null); //San list looking for objet, return true if found publi stati boolean searh(objet, Cell ) { for (Cell l = ; l!= null; l = l.getnet()) { if (l.getdatum().equals()) return true; return false; //Here is another version. Why does this work? publi stati boolean searh(objet, Cell ) { for (;!= null; =.getnet()) { if (.getdatum().equals()) return true; return false; A Reursive Version publi stati boolean searh(objet, Cell ) { if ( == null) return false; if (.getdatum().equals()) return true; return searh(,.getnet()); publi stati boolean searh(objet, Cell ) { return!= null && (.getdatum().equals() searh(,.getnet())); Reursion on s Reursion an be done on lists Similar to reursion on integers Almost always Base ase: empty list Reursive ase: Assume you an solve problem on (smaller) list obtained by eliminating first ell Many list operations an be implemented very simply by using this idea Although some operations are easier to implement using iteration 17 18

4 Base ase: empty list return false Reursive Searh Reursive ase: non-empty list if data in first ell equals objet, return true return result of doing linear searh on rest of list Eeution of Reursive Program publi stati boolean searh(objet, Cell ) { if ( == null) return false; if (.getdatum().equals()) return true; return searh(,.getnet()); Eeution of Reursive Program publi stati boolean searh(objet, Cell ) { if ( == null) return false; if (.getdatum().equals()) return true; return searh(,.getnet()); Eeution of Reursive Program publi stati boolean searh(objet, Cell ) { if ( == null) return false; if (.getdatum().equals()) return true; return searh(,.getnet()); Eeution of Reursive Program Eeution of Reursive Program publi stati boolean searh(objet, Cell ) { if ( == null) return false; if (.getdatum().equals()) return true; return searh(,.getnet()); publi stati boolean searh(objet, Cell ) { if ( == null) return false; if (.getdatum().equals()) return true; return searh(,.getnet()); false 23

5 Eeution of Reursive Program publi stati boolean searh(objet, Cell ) { if ( == null) return false; if (.getdatum().equals()) return true; return searh(,.getnet()); Eeution of Reursive Program publi stati boolean searh(objet, Cell ) { if ( == null) return false; if (.getdatum().equals()) return true; return searh(,.getnet()); false 25 false 26 Eeution of Reursive Program Iterative eample: reversing a list publi stati boolean searh(objet, Cell ) { if ( == null) return false; if (.getdatum().equals()) return true; return searh(,.getnet()); Given a list, reate a new list with elements in reverse order Intuition: think of reversing a pile of oins publi stati Cell reverse(cell ) { Cell rev = null; for (;!= null; =.getnet()) { rev = new Cell(.getDatum(), rev); return rev; false Reursive eample: Delete from a with Header Delete first ourrene of from list Reursive delete Iterative delete Intuitive idea of reursive ode If list is empty, return null If first element of is, return rest of list Otherwise, return list onsisting of First element of, and that results from deleting from rest of list Some authors prefer to have a lass that is distint from Cell lass. The objet is like a element that always eists even if list itself is empty. lass { proteted Cell ; publi (Cell ) { = ; publi Cell gethead() publi void sethead(cell ) //reursive delete publi stati Cell delete(objet, Cell ) { if ( == null) return null; if (.getdatum().equals()) return.getnet();.setnet(delete(,.getnet())); return ; 29 30

6 Variations on with Header Speial Cases to Worry About Header an also keep other info Referene to last ell of list Number of elements in list Searh/insertion/ deletion as instane methods tail tail size 3 Empty list add find delete Front of list insert End of list find delete s with just one element Doubly-Linked s In some appliations, it is onvenient to have a Cell that has referenes to both its predeessor and its suessor in the list. lass DLLCell { private Objet datum; private DLLCell net; private DLLCell prev; prev net tail 33 Doubly-Linked vs. Singly-Linked Advantages of doubly-linked lists over singly-linked lists some things are easier e.g., reversing a doubly-linked list an be done simply by swapping the previous and net fields of eah ell Disadvantages doubly-linked lists require more heap spae than singlylinked lists insert and delete take more time 34 Cirularly-linked s In other appliations, it is onvenient if the list forms a yle, with no beginning or end Entire list an be traversed from any given node 35