I'm trying to write code for a binary search tree, the first method I'm working on is the add (insert) method. The root seems to insert properly, but I'm getting null pointer exception when adding the second node. I'll indicate the exact problem spot in my code with comments.
If you can see how to fix the bugs, or let me know if my overall logic is flawed it would be incredibly helpful.-- I will mention that this is for school, so I'm not looking to make a really impressive model...most of my layout choices simply reflect the way we've been working in class. Also, method names were selected by the teacher and should stay the same. Feel free to edit the formatting, had a little trouble.
BINARY TREE CLASS
public class BinarySearchTree
{
private static Node root;
public BinarySearchTree()
{
root = null;
}
public static void Add (Node newNode)
{
Node k = root;
if (root == null)//-----------------IF TREE IS EMPTY -----------------
{
root = newNode;
}
else // -------TREE IS NOT EMPTY --------
{
if (newNode.value > k.value) //-------NEW NODE IS LARGER THAN ROOT---------
{
boolean searching = true;
while(searching) // SEARCH UNTIL K HAS A LARGER VALUE
{ //***CODE FAILS HERE****
if(k.value > newNode.value || k == null)
{
searching = false;
}
else {k = k.rightChild; }
}
if ( k == null) { k = newNode;}
else if (k.leftChild == null){ k.leftChild = newNode;}
else
{
Node temp = k.leftChild;
k.leftChild = newNode;
newNode = k.leftChild;
if(temp.value > newNode.value )
{
newNode.rightChild = temp;
}
else
{
newNode.leftChild = temp;
}
}
}
if (newNode.value < k.value) //-----IF NEW NODE IS SMALLER THAN ROOT---
{
boolean searching = true;
while(searching) // ----SEARCH UNTIL K HAS SMALLER VALUE
{// **** CODE WILL PROBABLY FAIL HERE TOO ***
if(k.value < newNode.value || k == null) {searching = false;}
else {k = k.leftChild;}
}
if ( k == null) { k = newNode;}
else if (k.rightChild == null){ k.rightChild = newNode;}
else
{
Node temp = k.rightChild;
k.rightChild = newNode;
newNode = k.rightChild;
if(temp.value > newNode.value )
{
newNode.rightChild = temp;
}
else
{
newNode.leftChild = temp;
}
}
}
}} // sorry having formatting issues
}
NODE CLASS
public class Node
{
int value;
Node leftChild;
Node rightChild;
public Node (int VALUE)
{
value = VALUE;
}
}
TEST APPLICATION
public class TestIT
{
public static void main(String[] args)
{
BinarySearchTree tree1 = new BinarySearchTree();
Node five = new Node(5);
Node six = new Node(6);
tree1.Add(five);
tree1.Add(six);
System.out.println("five value: " + five.value);
System.out.println("five right: " + five.rightChild.value);
}
}
The conditional statement is checked from left to right, so you need to check whether k is null before you check whether k.value > newNode.value because if k is null, then it doesn't have a value.
Related
public class doubleLinkedList {
class Node {
String value;
Node prev;
Node next;
Node(String val, Node p, Node n) {
value = val;
prev = p;
next = n;
}
Node(String val) {
value = val;
prev = null;
next = null;
}
}
Node first;
Node last;
public doubleLinkedList() {
first = null;
last = null;
}
public boolean isEmpty() {
if (first == null)
return true;
else
return false;
}
/**The size method returns the length of the linked list
* #return the number of element in the linked list
*/
public int size() {
int count = 0;
Node traverse = first;
while (traverse != null) {
count++;
traverse = traverse.next;
}
return count;
}
public void add(String element) {
if (isEmpty()) {
first = new Node(element);
last = first;
} else {
Node p = first;
Node elementTobeAdded;
while (((p.value).compareTo(element)) > 0 && p.next != null) {
p = p.next;
}
if (p.next != null) {
elementTobeAdded = new Node(element, p, p.next);
p.next.prev = elementTobeAdded;
p = elementTobeAdded.prev;
} else {
elementTobeAdded = new Node(element, p, null);
p.next = elementTobeAdded;
elementTobeAdded.next = null;
last = elementTobeAdded;
}
}
}
public void printForward() {
Node printNode = first;
while (printNode != null) {
System.out.print(printNode.value + ", ");
printNode = printNode.next;
}
}
}
public class test {
public static void main(String[] args) {
doubleLinkedList car = new doubleLinkedList();
car.add("Jeep");
car.add("benz");
car.add("Honda");
car.add("Lexus");
car.add("BMW");
car.printForward();
}
}
My add method is trying to add nodes to a list in alphabetical order. My printForward method prints out each element in the list.
In my main method, it prints out "Jeep, benz, Honda, BMW,", which is not in alphabetical order.
Change the not empty case for your add method from this
Node p = first;
Node elementTobeAdded;
while(((p.value).compareTo(element)) > 0 && p.next != null)
{
p = p.next;
}
if(p.next != null)
{
elementTobeAdded = new Node(element,p,p.next);
p.next.prev = elementTobeAdded;
p = elementTobeAdded.prev;
}
else
{
elementTobeAdded = new Node(element, p, null);
p.next = elementTobeAdded;
elementTobeAdded.next = null;
last = elementTobeAdded;
}
to this:
Node p = first;
while (p.value.compareTo(element) < 0 && p.next != null) {
p = p.next;
}
if (p.value.compareTo(element) > 0) {
Node toAdd = new Node(element, p.prev, p);
p.prev = toAdd;
if (toAdd.prev != null) {
toAdd.prev.next = toAdd;
}else {
first = toAdd;
}
}else {
Node toAdd = new Node(element, p, p.next);
p.next = toAdd;
if (toAdd.next != null) {
toAdd.next.prev = toAdd;
}else {
last = toAdd;
}
}
There were many errors here. The biggest one was that you never checked for the case where the new element should be inserted at the beginning of the list. A new element was always inserted after the first element even if it should have come first.
Note that "benz" comes at the end because the String.compareTo method treats capitals as coming before lower case letters.
It is not an a linked list... You wrote some sort of Queue (with optional possibility to make it Dequeue).
About your question - you have an error in your 'add' method - at least you don't check if it is necessary to move head forward. It is possible that you have another bugs, but it is too hard to read such styled sources (please fix your question formatting)...
So i have 3 methods 1 that adds a node to the binary tree using the traverseAdd method, and another method which finds the location of where a value would be placed within the tree based on its parent node. I would like to eliminate the traverseAdd method and use the findLocation method within the add method to add the new value to the BST.
public void add(int val) {
/*Adds a new node to the binary tree after traversing the tree and figuring out where it belongs*/
Node nodeObjToAdd = new Node(val);
if(root == null){
//if node root is not null root = new node value
root = nodeObjToAdd;
}
Node nodeTraversed = root;
traverseAdd(nodeTraversed, nodeObjToAdd);
}
private void traverseAdd(Node node, Node nodeObjToAdd){
/*Traverses tree and finds a place to add the node to be added by comparing values of the left child and right child of the
* focus node*/
if(nodeObjToAdd.value < node.value){
if(node.leftChild == null){
node.leftChild = nodeObjToAdd;
}
else {
//if the val < the root.value set int he constructor
traverseAdd(node.leftChild, nodeObjToAdd);
}
}
else if(nodeObjToAdd.value > node.value) {
if (node.rightChild == null) {
node.rightChild = nodeObjToAdd;
} else {
traverseAdd(node.rightChild, nodeObjToAdd);
}
}
}
public Node findNodeLocation(Node rootNode, int val) {
/*returns where a the Node after which the value would be added.*/
if(val < rootNode.value && rootNode.leftChild != null){
return rootNode.leftChild;
}
if(val >= rootNode.value && rootNode.rightChild != null){
return rootNode.rightChild;
}
else
return this.root;
}
public void add(int val) {
if (root == null) {
root = new Node(val);
}
Node cur = root;
Node next = null;
while (true) {
next = findNodeLocation(cur, val);
if (next != cur) {
cur = next;
} else {
break;
}
}
if (val < cur.value) {
cur.leftChild = new Node(val);
} else {
cur.rightChild = new Node(val);
}
}
I think this should work
Iterator words = treeSearch.getItems().iterator();
int addCount = 0;
while (words.hasNext())
{
numWords++;
rootNode = add(objectToReference, addCount++, (ITreeSearch) words.next(), 0, rootNode);
}
//Add to the Tree
private TernaryTreeNode add(Object storedObject, int wordNum, ITreeSearch treeSearch, int pos, TernaryTreeNode parentNode) throws NoSearchValueSetException
{
if (parentNode == null)
{
parentNode = new TernaryTreeNode(treeSearch.getNodeValue(pos));
}
if (parentNode.lessThan(treeSearch, pos))
{
parentNode.left = add(storedObject, wordNum, treeSearch, pos, parentNode.left);
}
else if (parentNode.greaterThan(treeSearch, pos))
{
parentNode.right = add(storedObject, wordNum, treeSearch, pos, parentNode.right);
}
else
{
if (pos < treeSearch.getNumberNodeValues())
{
parentNode.mid = add(storedObject, wordNum, treeSearch, pos + 1, parentNode.mid);
}
else
{
numberOfObjectsStored++;
parentNode.addStoredData(storedObject);
}
}
return parentNode;
}
This a snippet of my code in my Ternary Tree which I use for inserting a Name of a person(can hav multiple words in a name, like Michele Adams, Tina Joseph George, etc). I want to convert the above recursion to a for loop / while iterator.
Please guide me on this.
General idea in replacing recursion with iteration is to create a state variable, and update it in the loop by following the same rules that you follow in your recursive program. This means that when you pick a left subtree in the recursive program, you update the state to reference the left subtree; when you go to the right subtree, the state changes to reference the right subtree, and so on.
Here is an example of how to rewrite the classic insertion into binary tree without recursion:
public TreeNode add(TreeNode node, int value) {
// Prepare the node that we will eventually insert
TreeNode insert = new TreeNode();
insert.data = value;
// If the parent is null, insert becomes the new parent
if (node == null) {
return insert;
}
// Use current to traverse the tree to the point of insertion
TreeNode current = node;
// Here, current represents the state
while (true) {
// The conditional below will move the state to the left node
// or to the right node, depending on the current state
if (value < current.data) {
if (current.left == null) {
current.left = insert;
break;
} else {
current = current.left;
}
} else {
if (current.right == null) {
current.right = insert;
break;
} else {
current = current.right;
}
}
}
// This is the original node, not the current state
return node;
}
Demo.
Thanks dasblinkenlight..
This is my logic for replacing the above recursive function for a ternary tree.
Iterator words = treeSearch.getItems().iterator();
while (words.hasNext())
{
for (int i = 0; i < word.getNumberNodeValues(); i++)
{
add_Non_Recursive(objectToReference, word, i);
}
}
//Add to Tree
private void add_Non_Recursive(Object storedObject, ITreeSearch treeSearch, int pos) throws NoSearchValueSetException
{
TernaryTreeNode currentNode = rootNode;
// Start from a node(parentNode). If there is no node, then we create a new node to insert into the tree.
// This could even be the root node.
if (rootNode == null)
{
rootNode = new TernaryTreeNode(treeSearch.getNodeValue(pos));
}
else
{
while (currentNode != null)
{
if (currentNode.lessThan(treeSearch, pos))
{
if (currentNode.left == null)
{
currentNode.left = new TernaryTreeNode(treeSearch.getNodeValue(pos));
currentNode = null;
}
else
{
currentNode = currentNode.left;
}
}
else if (currentNode.greaterThan(treeSearch, pos))
{
if (currentNode.right == null)
{
currentNode.right = new TernaryTreeNode(treeSearch.getNodeValue(pos));
currentNode = null;
}
else
{
currentNode = currentNode.right;
}
}
else
{
if (currentNode.mid == null)
{
currentNode.mid = new TernaryTreeNode(treeSearch.getNodeValue(pos));
currentNode = null;
}
else
{
currentNode = currentNode.mid;
}
}
}
}
}
But I dropped this logic as it wasnt great in performing, it took more time than the recursive counterpart.
I am implementing a Red Black Tree with insert, search and delete functions in O (log n) time. Insert and search are working fine. However I am stuck on delete. I found this ppt slide on the internet which shows the algorithm of RBT deletion: http://www.slideshare.net/piotrszymanski/red-black-trees#btnNext on page 56 onwards. I know I am asking a bit too much but I have been stuck on this for over 2 weeks and I can't find the problem. The way I'm understanding Top-Down deletion that you have to rotate and recolor nodes accordingly until you find the predecessor of the node to be deleted. When you do find this node - which would be either a leaf or a node with one right child, replace node to be deleted data by the data of this node and delete this node like normal BST deletion, right?
This is the code I did, based on what I learnt from that slide. If anyone would be so kind to go over it, I would be more than grateful! Or at least if you think there's a better algorithm than what I'm using, please tell me!
public void delete(int element){
if (root == null){
System.out.println("Red Black Tree is Empty!");
} else {
Node X = root;
parent = null;
grandParent = null;
sibling = null;
if (isLeaf(X)){
if (X.getElement() == element){
emptyRBT();
}
} else {
if (checkIfBlack(root.getLeftChild()) && checkIfBlack(root.getRightChild())){
root.setIsBlack(false);
if (X.getElement() > element && X.getLeftChild() != null){
X = moveLeft(X);
} else if (X.getElement() < element && X.getRightChild() != null){
X = moveRight(X);
}
Step2(X, element);
} else {
Step2B(X, element);
}
}
}
root.setIsBlack(true);
}
public void Step2(Node X, int element)
{
int dir = -1;
while (!isLeaf(X)){
if (predecessor == null){ // still didn't find Node to delete
if (X.getElement() > element && X.getLeftChild() != null){
X = moveLeft(X);
dir = 0;
} else if (X.getElement() < element && X.getRightChild() != null){
X = moveRight(X);
dir = 1;
} else if (X.getElement() == element){
toDelete = X;
predecessor = inorderPredecessor(X.getRightChild());
X = moveRight(X);
}
} else { // if node to delete is already found and X is equal to right node of to delete
// move always to the left until you find predecessor
if (X != predecessor){
X = moveLeft(X);
dir = 0;
}
}
if (!isLeaf(X)){
if (!hasOneNullNode(X)){
if (checkIfBlack(X.getLeftChild()) && checkIfBlack(X.getRightChild())){
Step2A(X, element, dir);
} else {
Step2B(X, element);
}
}
}
}
removeNode(X);
if (predecessor != null){
toDelete.setElement(X.getElement());
}
}
public Node Step2A(Node X, int element, int dir) {
if (checkIfBlack(sibling.getLeftChild()) && checkIfBlack(sibling.getRightChild())) {
X = Step2A1(X);
} else if ((checkIfBlack(sibling.getLeftChild()) == false) && checkIfBlack(sibling.getRightChild())) {
X = Step2A2(X);
} else if ((checkIfBlack(sibling.getLeftChild()) && (checkIfBlack(sibling.getRightChild()) == false))) {
X = Step2A3(X);
} else if ((checkIfBlack(sibling.getLeftChild()) == false) && (checkIfBlack(sibling.getRightChild()) == false)) {
X = Step2A3(X);
}
return X;
}
public Node Step2A1(Node X) {
X.setIsBlack(!X.IsBlack());
parent.setIsBlack(!parent.IsBlack());
sibling.setIsBlack(!sibling.IsBlack());
return X;
}
public Node Step2A2(Node X) {
if (parent.getLeftChild() == sibling){
LeftRightRotation(sibling.getLeftChild(), sibling, parent);
} else RightLeftRotation(sibling.getRightChild(), sibling, parent);
X.setIsBlack(!X.IsBlack());
parent.setIsBlack(!parent.IsBlack());
return X;
}
public Node Step2A3(Node X) {
if (parent.getLeftChild() == sibling){
leftRotate(sibling);
} else if (parent.getRightChild() == sibling){
rightRotate(sibling);
}
X.setIsBlack(!X.IsBlack());
parent.setIsBlack(!parent.IsBlack());
sibling.setIsBlack(!sibling.IsBlack());
sibling.getRightChild().setIsBlack(!sibling.getRightChild().IsBlack());
return X;
}
public void Step2B(Node X, int element){
if (predecessor == null){
if (X.getElement() > element && X.getLeftChild() != null){
X = moveLeft(X);
} else if (X.getElement() < element && X.getRightChild() != null){
X = moveRight(X);
} else if (X.getElement() == element){
Step2(X, element);
}
} else {
if (X != predecessor)
X = moveLeft(X);
else Step2(X, element);
}
if (X.IsBlack()){
if (parent.getLeftChild() == sibling){
leftRotate(sibling);
} else if (parent.getRightChild() == sibling){
rightRotate(sibling);
}
parent.setIsBlack(!parent.IsBlack());
sibling.setIsBlack(!sibling.IsBlack());
Step2(X, element);
} else {
Step2B(X, element);
}
}
public void removeNode(Node X) {
if (isLeaf(X)) {
adjustParentPointer(null, X);
count--;
} else if (X.getLeftChild() != null && X.getRightChild() == null) {
adjustParentPointer(X.getLeftChild(), X);
count--;
} else if (X.getRightChild() != null && X.getLeftChild() == null) {
adjustParentPointer(X.getRightChild(), X);
count--;
}
}
public Node inorderPredecessor(Node node){
while (node.getLeftChild() != null){
node = node.getLeftChild();
}
return node;
}
public void adjustParentPointer(Node node, Node current) {
if (parent != null) {
if (parent.getElement() < current.getElement()) {
parent.setRightChild(node);
} else if (parent.getElement() > current.getElement()) {
parent.setLeftChild(node);
}
} else {
root = node;
}
}
public boolean checkIfBlack(Node n){
if (n == null || n.IsBlack() == true){
return true;
} else return false;
}
public Node leftRotate(Node n)
{
parent.setLeftChild(n.getRightChild());
n.setRightChild(parent);
Node gp = grandParent;
if (gp != null){
if (gp.getElement() > n.getElement()){
gp.setLeftChild(n);
} else if (gp.getElement() < n.getElement()){
gp.setRightChild(n);
}
} else root = n;
return n;
}
public Node rightRotate(Node n)
{
parent.setRightChild(n.getLeftChild());
n.setLeftChild(parent);
Node gp = grandParent;
if (gp != null){
if (gp.getElement() > n.getElement()){
gp.setLeftChild(n);
} else if (gp.getElement() < n.getElement()){
gp.setRightChild(n);
}
} else root = n;
return n;
}
The node is being deleted, but the tree after deletion would be black violated, which is very wrong.
The eternally confuzzled blog has top-down implementations of both insert and delete for red-black trees. It also goes through case-by-case why it works. I won't replicate it here (it's rather lengthy).
I've used that blog as a reference for implementing red-black trees in both c++ and java. As I discussed in an earlier answer, I found the implementation to be faster than std::map's bottom-up implementation of red-black trees (whatever STL came with gcc at the time).
Here's an untested, direct translation of the code to Java. I would highly suggest you test it and morph it to match your style.
private final static int LEFT = 0;
private final static int RIGHT = 1;
private static class Node {
private Node left,right;
private boolean red;
...
// any non-zero argument returns right
Node link(int direction) {
return (direction == LEFT) ? this.left : this.right;
}
// any non-zero argument sets right
Node setLink(int direction, Node n) {
if (direction == LEFT) this.left = n;
else this.right = n;
return n;
}
}
boolean remove(int data) {
if ( this.root != null ) {
final Node head = new Node(-1, null, null); /* False tree root */
Node cur, parent, grandpa; /* Helpers */
Node found = null; /* Found item */
int dir = RIGHT;
/* Set up helpers */
cur = head;
grandpa = parent = null;
cur.setLink(RIGHT, this.root);
/* Search and push a red down */
while ( cur.link(dir) != null ) {
int last = dir;
/* Update helpers */
grandpa = parent, parent = cur;
cur = cur.link(dir);
dir = cur.data < data ? RIGHT : LEFT;
/* Save found node */
if ( cur.data == data )
found = cur;
/* Push the red node down */
if ( !is_red(cur) && !is_red(cur.link(dir)) ) {
if ( is_red(cur.link(~dir)) )
parent = parent.setLink(last, singleRotate(cur, dir));
else if ( !is_red(cur.link(~dir)) ) {
Node s = parent.link(~last);
if ( s != null ) {
if (!is_red(s.link(~last)) && !is_red(s.link(last))) {
/* Color flip */
parent.red = false;
s.red = true;
cur.red = true;
}
else {
int dir2 = grandpa.link(RIGHT) == parent ? RIGHT : LEFT;
if ( is_red(s.link(last)) )
grandpa.setLink(dir2, doubleRotate(parent, last));
else if ( is_red(s.link(~last)) )
grandpa.setLink(dir2, singleRotate(parent, last));
/* Ensure correct coloring */
cur.red = grandpa.link(dir2).red = true;
grandpa.link(dir2).link(LEFT).red = false;
grandpa.link(dir2).link(RIGHT).red = false;
}
}
}
}
}
/* Replace and remove if found */
if ( found != null ) {
found.data = cur.data;
parent.setLink(
parent.link(RIGHT) == cur ? RIGHT : LEFT,
cur.link(cur.link(LEFT) == null ? RIGHT : LEFT));
}
/* Update root and make it black */
this.root = head.link(RIGHT);
if ( this.root != null )
this.root.red = false;
}
return true;
}
quick link :
http://algs4.cs.princeton.edu/33balanced/RedBlackBST.java.html
--> Caution : the code on the site is relying on two jars. In the datastructures however the dependency might be minimal. Sometimes it's enough to comment out the main method (that only serves as a test client)
If not : the jars are downloadable on the same site.
If you are looking for two weeks and studying algoritms, chances are you know about
http://algs4.cs.princeton.edu/
the website that is accompanying the famous
Algorithms, by Robert Sedgewick and Kevin Wayne
book.
On this website, there is this implementation of a red black (balances) tree :
http://algs4.cs.princeton.edu/33balanced/RedBlackBST.java.html
I didnot look into it yet (I will later on this year) , but I fully trust it to be a working implementation of a RBTree.
Some sidenote that might be interesting for visitors of this topic:
MIT placed excellent courses concerning algoritms online. The one concerning rbtrees is
http://www.youtube.com/watch?v=iumaOUqoSCk
I have this school assignment that I'm a little confused about.
Here's what it's saying:
"Write a program that uses the technique of 'chaining' for hashing.
The program will read in the length of an array which will contain the reference to each
linked list that will be generated. Furthermore, all values that are to be stored, is read.
The program shall have a separate function for hashing where the index exists. When the program have generated the linked lists, the theoretical 'load factor' is to be calculated and printed out. The whole array should be easily printed out."
The thing that I'm confused about, is the part about the program will read in the length of an array which will contain the reference to each linked list that will be generated. Is it possible to generate multiple linked lists? In that case, how do you do that?
This is the classes I'm told to use:
public class EnkelLenke {
private Node head = null;
private int numOfElements = 0;
public int getNum()
{
return numOfElements;
}
public Node getHead()
{
return head;
}
public void insertInFront(double value)
{
head = new Node (value, head);
++numOfElements;
}
public void insertInBack(double value)
{
if (head != null)
{
Node this = head;
while (this.next != null)
this = this.next;
this.next = new Node(value, null);
}
else
head = new Node(value, null);
++numOfElements;
}
public Node remove(Node n)
{
Node last = null;
Node this = head;
while (this != null && this != n)
{
last = this;
this = this.next;
}
if (this != null)
{
if (last != null)
last.next = this.next;
else
head = this.next;
this.next = null;
--numOfElements;
return this;
}
else
return null;
}
public Node findNr(int nr)
{
Node this = head;
if (nr < numOfElements)
{
for (int i = 0; i < nr; i++)
this = this.next;
return this;
}
else
return null;
}
public void deleteAll()
{
head = null;
numOfElements = 0;
}
public String printAllElements() {
String streng = new String();
Node this = head;
int i = 1;
while(this != null)
{
streng = streng + this.element + " ";
this = this.findNext();
i++;
if(i > 5)
{
i = 1;
streng = streng + "\n";
}
}
return streng;
}
public double getValueWithGivenNode (Node n)
{
Node this = head;
while (this != null && this != n)
{
this = this.next;
}
if (this == n)
return this.element;
else
return (Double) null;
}
}
public class Node {
double element;
Node next;
public Node(double e, Node n)
{
element = e;
next = n;
}
public double findElement()
{
return element;
}
public Node findNext()
{
return next;
}
}
Your data structure will look something like this (where "LL" is a linked list):
i | a[i]
-------------------------------
0 | LL[obj1 -> obj5 -> obj3]
1 | LL[obj2]
2 | LL[]
... | ...
N-1 | LL[obj4 -> obj6]
At each array index, you have a linked list of objects which hash to that index.
Is it possible to generate multiple linked lists? In that case, how do you do that?
Yes. Create your array, and initialize each element to a new linked list.
EnkelLenke[] a = new EnkelLenke[N];
for ( int i = 0; i < N; i++ ) {
a[i] = new EnkelLenke();
}