Implementazione Alberi Binari. mediante. Linked Structure ( 7.3.4)

Transcription

1 Implementazione Alberi Binari mediante Linked Structure ( 7.3.4) 1 Implementazione di AlberoBinario Vedi testo pag. 290 B A D C E 2 1

2 Implementazione di AlberoBinario Position Tree extends BTPosition extends BinaryTree BTNode implements implements LinkedBinaryTree 3 interface Position L ADT Posizione formalizza la nozione di "posto" ove inserire un elemento in un contenitore posizionale (sequenza, albero, grafo, etc.); oggetti posizione sono, ad esempio, un nodo in una lista, un nodo in un albero, un vertice in un grafo public interface Position<E> { public E element() throws InvalidPositionException; Il metodo element() ritorna l'elemento memorizzato nella "this" posizione; viene lanciata una InvalidPositionException se la this posizione non è valida 4 2

3 interface BTPosition public interface BTPosition<E> extends Position<E> { //eredita element() public void setelement (E e); parent public BTPosition<E> getleft (); public void setleft (BTPosition<E> v); public BTPosition<E> getright (); public void setright (BTPosition<E> v); left element right public BTPosition<E> getparent (); public void setparent (BTPosition<E> v); 5 class BTNode (1) public class BTNode<E> implements BTPosition<E> { private E element; //element stored at this node private BTPosition<E> left, right, parent; //adjacent nodes public BTNode<E> (E element, BTPosition<E> parent, BTPosition<E> left, BTPosition<E> right) { //COSTRUTTORE setelement(element); parent setparent(parent); setleft(left); setright(right); element left right 6 3

4 class BTNode (2) public E element() { return element; public void setelement (E e) { element = e; public BTPosition<E> getleft() { return left; public void setleft (BTPosition<E> v) { left = v; public BTPosition<E> getright() { return right; public void setright (BTPosition<E> v) { right = v; public BTPosition<E> getparent () { return parent; public void setparent (BTPosition<E> v) { parent = v; 7 class LinkedBinaryTree public class LinkedBinaryTree<E> implements BinaryTree<E> { protected BTPosition<E> root; //reference to the root protected int size; //number of nodes public LinkedBinaryTree() { //COSTRUTTORE root = (BTPosition<E>) addroot(null); // empty tree size = 0; T LinkedBinaryTree<E> root size 0 8 4

5 Metodi di interrogazione public int size() { return size; public boolean isempty() { return (size==0); T (LinkedBinaryTree) public boolean isinternal (Position<E> v) checkposition(v); //auxiliary method return ( hasleft(v) hasright(v) ); public boolean isexternal (Position<E> v) return! isinternal(v); public boolean isroot (Position<E> v) checkposition(v); return ( v == root() ); root size 9 9 Metodi di interrogazione public boolean hasleft (Position<E> v) BTPosition<E> = checkposition(v); return (.getleft()!= null ); T (LinkedBinaryTree) root size 9 public boolean hasright (Position<E> v) BTPosition<E> = checkposition(v); return (.getright()!= null ); 10 5

6 Metodi di navigazione public Position<E> root() throws EmptyTreeException { if ( root == null ) throw new EmptyTreeException("he tree has no root ); return root; public Position<E> left( Position<E> v ) throws InvalidPositionException, BoundaryViolationException { if (! hasleft(v) ) throw new BoundaryViolationException("No left child ); return ( (BTPosition<E>) v).getleft(); 11 Metodi di navigazione public Position<E> right(position<e> v) throws InvalidPositionException, BoundaryViolationException { if (! hasright(v) ) throw new BoundaryViolationException("No right child"); return ( (BTPosition<E>) v ).getright(); public Position<E> parent(position<e> v) throws InvalidPositionException, BoundaryViolationException { if (isroot(v)) throw new BoundaryViolationException("Root has no parent"); return ( (BTPosition<E>) v ).getparent(); 12 6

7 Metodi di navigazione public Position<E> sibling ( Position<E> v ) throws InvalidPositionException, BoundaryViolationException { try { BTPosition<E> p = parent(v); p BTPosition<E> lc = left(p); if ( v == lc ) return right(p); else return lc; lc v catch ( BoundaryViolationException e ) { throw new BoundaryViolationException("Node has no sibling"); 13 Metodi di aggiornamento public E replace ( Position<E> v, E obj ) BTPosition<E> = checkposition(v); E temp = v.element(); root size.setelement(obj); 1 return temp; public Position<E> addroot ( E e ) throws NonEmptyTreeException { if(! isempty()) throw new NonEmptyTreeException("Tree already has a root ); size = 1; root = createnode(e,null,null,null); return root; 14 7

8 Metodi di aggiornamento public Position<E> insertleft ( Position<E> v, E e ) if ( hasleft(v) ) throw new InvalidPositionException("Node already has a left child ); BTPosition<E> = (BTPosition) v; BTPosition<E> ww = createnode(e,, null, null);.setleft(ww); size++; return ww; ww ww 15 Metodi di aggiornamento public Position<E> insertright (Position<E> v, E e) if (hasright(v)) throw new InvalidPositionException("Node already has a right child"); BTPosition<E> = (BTPosition)v; BTPosition<E> ww = createnode(e,, null, null);.setright(ww); size++; return ww; ww ww 16 8

9 Metodi di aggiornamento - remove (1) /** Removes a node with zero or one child. */ public E remove ( Position<E> v ) if ( hasleft(v) && hasright(v) ) throw new InvalidPositionException("Cannot remove node w/ 2 children" ); BTPosition<E> = (BTPosition) v; BTPosition<E> ww; // the only child of v, if any if ( hasleft(v) ) ww = (BTPosition) left(v); else if ( hasright(v) ) ww = (BTPosition) right(v); ww else ww = null; 17 Metodi di aggiornamento remove (2) if ( v == root() ) { if ( ww!= null ) ww.setparent(null); root = ww; else { // v!= root() BTPosition<E> uu = (BTPosition) parent(v); if ( hasleft(uu) && v == left(uu) ) uu.setleft(ww); else uu.setright(ww); if( ww!= null) ww.setparent(uu); size--; return v.element(); root v uu ww ww 18 9

10 Metodi di aggiornamento public void swapelements ( Position<E> v, Position<E> w ) BTPosition<E> = checkposition(v); BTPosition<E> ww = checkposition(w); E temp = w.element(); ww.setelement( v.element() ) ;.setelement(temp); ww 19 Metodi di aggiornamento public void expandexternal ( Position<E> v, E l, E r ) if (! isexternal(v) ) throw new InvalidPositionException( "Node is not external ); insertleft (v, l); insertright(v, r); v v 20 10

11 Metodi di aggiornamento public void removeaboveexternal ( Position<E> v ) if (! isexternal(v) ) throw new InvalidPositionException( "Node is not external ); if ( isroot(v) ) remove(v); else { Position<E> u = parent(v); remove(v); remove(u); u v 21 Metodi di aggiornamento protected BTPosition<E> checkposition<e> (Position<E> v) throws InvalidPositionException { if (v == null! (v instanceof BTPosition)) throw new InvalidPositionException("The Position is invalid"); return (BTPosition<E>) v; protected BTPosition<E> createnode (E elem, BTPosition<E> p, BTPosition<E> lft, BTPosition<E> rgt) { return new BTNode(elem,p,lft,rgt); 22 11

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