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What changes when implementing lazy deletion into a binary search tree exactly?

Okay so I've been looking into this for days and everytime I think I've gotten it down I start writing code and I get to a point where I just can't figure out what exactly to do.
The tree isn't recursive, so I can follow everything really until I start trying to modify it so it uses lazy deletion instead of real deletion. (Right now it nulls out the node it deletes)
What I have managed to figure out:
I added a flag to the node class to set them as deleted
I've implemented a search method that works, it even seems to register if my nodes are deleted or not(lazily)
I know that the rest of the tree class should treat the nodes that are flagged as deleted such that they are not there.
What I don't know:
I've looked at MANY resources and some say all you need to do is set
the node's deleted flag to true. Does this mean that I don't have to
worry about the linking after their flag is set?
Is an appropriate way to do this very superficial? As in, just don't let the methods report that something is found if the flag is set to deleted even though the methods do find something?
In what method(s) should I change to use lazy deletion? Only the delete() method?
If I only change the delete method, how is this picked up by the other methods?
Does the search method look okay?
Here's the rest of the code so you can see what I'm using. I'm really frustrated because I honestly understand how to delete nodes completely way better then this stupid lazy deletion implementation. It's what they teach in the book! lol
Please help... :(
Search Method
So here's my search method:
public String search(E data){
Node<E> current = root;
String result = "";
while(current != null){
if(data.compareTo(current.e) < 0){
current = current.left;
}
else if (data.compareTo(current.e) > 0){
current = current.right;
}
else{
if (current.isDeleted == false){
return result += "Found node with matching data that is not deleted!";
}
else{
return result += "Found deleted data, not usable, continuing search\n";
}
}
}
return result += "Did not find non-deleted matching node!";
}
Tree Class
Tree Code (The real deletion method is commented out at the end so I could replace it with the lazy deletion):
package mybinarytreeexample;
public class MyBinaryTree> {
private Node<E> root = null;
public class Node<E> {
public boolean isDeleted = false;
public E e = null;
public Node<E> left = null;
public Node<E> right = null;
}
public boolean insert(E e) {
// if empty tree, insert a new node as the root node
// and assign the elementy to it
if (root == null) {
root = new Node();
root.e = e;
return true;
}
// otherwise, binary search until a null child pointer
// is found
Node<E> parent = null;
Node<E> child = root;
while (child != null) {
if (e.compareTo(child.e) < 0) {
parent = child;
child = child.left;
} else if (e.compareTo(child.e) > 0) {
parent = child;
child = child.right;
} else {
if(child.isDeleted){
child.isDeleted = false;
return true;
}
return false;
}
}
// if e < parent.e create a new node, link it to
// the binary tree and assign the element to it
if (e.compareTo(parent.e) < 0) {
parent.left = new Node();
parent.left.e = e;
} else {
parent.right = new Node();
parent.right.e = e;
}
return true;
}
public void inorder() {
System.out.print("inorder: ");
inorder(root);
System.out.println();
}
private void inorder(Node<E> current) {
if (current != null) {
inorder(current.left);
System.out.printf("%3s", current.e);
inorder(current.right);
}
}
public void preorder() {
System.out.print("preorder: ");
preorder(root);
System.out.println();
}
private void preorder(Node<E> current) {
if (current != null) {
System.out.printf("%3s", current.e);
preorder(current.left);
preorder(current.right);
}
}
public void postorder() {
System.out.print("postorder: ");
postorder(root);
System.out.println();
}
private void postorder(Node<E> current) {
if (current != null) {
postorder(current.left);
postorder(current.right);
System.out.printf("%3s", current.e);
}
}
public String search(E data){
Node<E> current = root;
String result = "";
while(current != null){
if(data.compareTo(current.e) < 0){
current = current.left;
}
else if (data.compareTo(current.e) > 0){
current = current.right;
}
else{
if (current.isDeleted == false){
return result += "Found node with matching data that is not deleted!";
}
else{
return result += "Found deleted data, not usable, continuing search\n";
}
}
}
return result += "Did not find non-deleted matching node!";
}
public boolean delete(E e) {
}
// an iterator allows elements to be modified, but can mess with
// the order if element not written with immutable key; it is better
// to use delete to remove and delete/insert to remove or replace a
// node
public java.util.Iterator<E> iterator() {
return new PreorderIterator();
}
private class PreorderIterator implements java.util.Iterator<E> {
private java.util.LinkedList<E> ll = new java.util.LinkedList();
private java.util.Iterator<E> pit= null;
// create a LinkedList object that uses a linked list of nodes that
// contain references to the elements of the nodes of the binary tree
// in preorder
public PreorderIterator() {
buildListInPreorder(root);
pit = ll.iterator();
}
private void buildListInPreorder(Node<E> current) {
if (current != null) {
ll.add(current.e);
buildListInPreorder(current.left);
buildListInPreorder(current.right);
}
}
// check to see if their is another node in the LinkedList
#Override
public boolean hasNext() {
return pit.hasNext();
}
// reference the next node in the LinkedList and return a
// reference to the element in the node of the binary tree
#Override
public E next() {
return pit.next();
}
#Override
public void remove() {
throw new UnsupportedOperationException("NO!");
}
}
}
// binary search until found or not in list
// boolean found = false;
// Node<E> parent = null;
// Node<E> child = root;
//
// while (child != null) {
// if (e.compareTo(child.e) < 0) {
// parent = child;
// child = child.left;
// } else if (e.compareTo(child.e) > 0) {
// parent = child;
// child = child.right;
// } else {
// found = true;
// break;
// }
// }
//
//
// if (found) {
// // if root only is the only node, set root to null
// if (child == root && root.left == null && root.right == null)
// root = null;
// // if leaf, remove
// else if (child.left == null && child.right == null) {
// if (parent.left == child)
// parent.left = null;
// else
// parent.right = null;
// } else
// // if the found node is not a leaf
// // and the found node only has a right child,
// // connect the parent of the found node (the one
// // to be deleted) to the right child of the
// // found node
// if (child.left == null) {
// if (parent.left == child)
// parent.left = child.right;
// else
// parent.right = child.right;
// } else {
// // if the found node has a left child,
// // the node in the left subtree with the largest element
// // (i. e. the right most node in the left subtree)
// // takes the place of the node to be deleted
// Node<E> parentLargest = child;
// Node<E> largest = child.left;
// while (largest.right != null) {
// parentLargest = largest;
// largest = largest.right;
// }
//
// // replace the lement in the found node with the element in
// // the right most node of the left subtree
// child.e = largest.e;
//
// // if the parent of the node of the largest element in the
// // left subtree is the found node, set the left pointer of the
// // found node to point to left child of its left child
// if (parentLargest == child)
// child.left = largest.left;
// else
// // otherwise, set the right child pointer of the parent of
// // largest element in the left subtreeto point to the left
// // subtree of the node of the largest element in the left
// // subtree
// parentLargest.right = largest.left;
// }
//
// } // end if found
//
// return found;

What changes is that your tree only grows in term of real space used, and never shrinks. This can be very useful if you choose a list as a data-structure to implement your tree, rather than the usual construct Node E {V value; E right; E; left}. I will come back on this later.
I've looked at MANY resources and some say all you need to do is set
the node's deleted flag to true. Does this mean that I don't have to
worry about the linking after their flag is set?
Yes, if by linking you mean node.left, node.right. Delete simply mark as deleted and that's it. It change nothing else, and it should not, because x.CompareTo(y) must be still working even if x or y are marked as deleted
Is an appropriate way to do this very superficial? As in, just don't
let the methods report that something is found if the flag is set to
deleted even though the methods do find something?
Well by definition of this method "something" means a node without the deleted flag. Anything with the deleted flag is "nothing" for the user of the tree.
what method(s) should I change to use lazy deletion? Only the delete()
method?
Of course not. You already changed the search method yourself. Let's take the isEmpty(). You should keep a counter of deleted nodes and one of total nodes. If they are equal the tree is empty. Otherwise the tree is not.
There is a small bug in your algorithm. When you insert and find out that you land on a deleted node, you just unmark that node. You must also set the value of the node. After all compareTo doesnt insure all fields are strictly equal, just that the objects are equivalent.
if(child.isDeleted){
child.isDeleted = false;
child.e = e; <---- missing
return true;
}
There might be others.
Side Note:
As said before one instance where this method is useful is a tree backed by an list (let's say array list). With this method the children of element at position i are at position 2*i+1 and 2*i+2. Usually when you delete a node p with children, you replace that node with the leftmost node q of the right subtree (or rightmost node in the left subtree). Here you can just mark p as deleted and swap the value of the deleted node and leftmost. Your array stays intact in memory

Removing even numbers from a linked list not working at the tail node?

void deleteEven() {
boolean con = false;
Node add;
Node move;
move = head;
if (move.data % 2 == 0) {
head = move.next;
con = true;
}
add = move;
move = move.next;
while (move != null) {
if (move.data % 2 == 0 ) {
add.next = move.next;
con = true;
}
add = move;
move = move.next;
}
if (!con)
System.out.println("No even numbers in list");
}
It works for every node except the tail.
if linked list is [5,4,3,2,2]
the result is [5,3,2]
How to fix that?

The problem is not with the tail node. The problem is with two even nodes in a row irrespective of where they are in the list. When the current node is even you are moving your pointer to the previous node (add) to the current node even though you have just removed it. For the second even node your add.next = move.next statement changes next for the node you have just removed.
The simplest solution is to only move add if the node is not even:
if (move.data % 2 == 1) {
add.next = move.next;
con = true;
} else {
add = move.next;
}
You could simplify your code quite a bit by getting rid of add altogether and just looking one node ahead of move:
while (move.next != null) {
if (move.next.data % 2 == 0) {
move.next = move.next.next;
con = true;
} else {
move = move.next;
}
}
And a programming tip for you: have several test cases before trying to diagnose a problem. I have found it's very easy to jump to an incorrect conclusion based on a small number of test cases and often expanding the range will make the problem clearer. That is one of the (many) reasons that test driven development works as well as it does.

Let's create service Node for attaching other nodes.
Then loop through the list and copy the references in a new list (new Node are not created):
void deleteEven() {
Node tmpHead = new Node(0, null);
Node tmpCopy = tmpHead;
Node tmp = head;
while (tmp != null) {
if (tmp.data % 2 == 1) {
tmpCopy.next = tmp;
tmpCopy = tmpCopy.next;
}
tmp = tmp.next;
}
tmpCopy.next = null;
head = tmpHead.next;
}
Suppose what Node is:
class Node {
int data;
Node next;
public Node(int data, Node next) {
this.data = data;
this.next = next;
}
}

How do I traverse a link list looking two nodes ahead?

I have a link list, and I want to be able to look two nodes ahead. I need to check if the first two nodes have integers, and if they do, and the third node says ADD, then I need to condense that information into one node and free the other two nodes.
I'm confused about what should go in my while loop. I check if the third node points to null, but somehow that's not giving me the right output. I don't know if I'm handling my node.next correctly either. Some of this is pseudocode now.
while(node1.next.next.next != NULL){
if((node1.data.isInteger() && (node2.data.isInteger()){
if(node3.data.equals('add')){
node1.data = node1.data + node2.data;
} else {
//ERROR
}
garbage_ptr1 = node2;
garbage_ptr2 = node3;
node1.next = node3.next;
free(garbage_ptr1);
free(garbage_ptr2);
node2.next = node1.next.next;
node3.next = node2.next.next;
} else {
node1.next = node1.next.next;
node2.next = node1.next.next;
node3.next = node2.next.next;
}

An approach that I find easier is to maintain a small array that acts as a window onto the list, and to look for matches on the array. The code also becomes a lot cleaner and simpler if you move your null checks into utility methods. By doing these things, the loop over the list only needs to check the last element of the window to terminate.
A sketch of this in Java:
/* small utility methods to avoid null checks everywhere */
public static Node getNext(Node n) { return n != null ? n.next : null; }
public static boolean isInteger(Node n) {
return (n != null) && (n.data != null) && (n.data instanceof Integer);
}
public static boolean isAdd(Node n) {
return (n != null) && (n.data != null) && n.data.equals("add");
}
/* checks for a match in the 3-node window */
public boolean isMatch(Node[] w) {
return isInteger(w[0]) && isInteger(w[1]) && isAdd(w[2]);
}
/* Loads the 3-node window with 'n' and the next two nodes on the list */
public void loadWindow(Node[] w, Node n) {
w[0] = n; w[1] = getNext(w[0]); w[2] = getNext(w[1]);
}
/* shifts the window down by one node */
public void shiftWindow(Node[] w) { loadWindow(w, w[1]); }
...
Node[] window = new Node[3];
loadWindow( window, node1 );
while (window[2] != null) {
if (isMatch(window)) {
window[0].data = stack[0].data + stack[1].data;
window[0].next = window[2].next;
loadWindow(window, window[0]); // reload the stack after eliminating two nodes
} else {
shiftWindow( window );
}
}

java Delete a Binary Tree node containing two children

This is the last case where the node to be deleted has two children. I cant figure out what I am doing wrong . Please help.
//BTNode has two children
else if (u.getLeft() != null && u.getRight() != null){
//if node to delete is root
BTNode<MyEntry<K,V>> pred = u.getRight();
while (pred.getLeft().element() != null){
pred = pred.getLeft();
}
BTNode<MyEntry<K,V>> predParent = pred.getParent();
if (!hasRightChild(pred)){
predParent.setLeft(new BTNode<MyEntry<K,V>>(null,predParent,null,null));}
if (hasRightChild(pred)){
BTNode<MyEntry<K,V>> predChild = pred.getRight();
predParent.setLeft(predChild);
predChild.setParent(predParent);
}
return returnValue;
ok so modify it like this ??
u.setElement(succ.element());
BTNode<MyEntry<K,V>> succParent = succ.getParent();
if (!hasLeftChild(succ)){
succParent.setRight(new BTNode<MyEntry<K,V>>(null,succParent,null,null));}
if (hasLeftChild(succ)){
BTNode<MyEntry<K,V>> predChild = succ.getLeft();
succParent.setRight(predChild);
predChild.setParent(succParent);
}
return returnValue;

From wikipedia:
Deleting a node with two children: Call the node to be deleted N. Do
not delete N. Instead, choose either its in-order successor node or
its in-order predecessor node, R. Replace the value of N with the
value of R, then delete R.
So, take for example the left children, and then find the rightmost leaf in that subtree, then replace the information of the node to delete with that of the leaf, and then delete that leaf easily.
You might want to create a function that returns the rightmost leaf from a subtree.

I have given the code for deletion of a node in a BST which would work for any condition and that too using a for loop.
public void delete(int key) {
Node<E> temp = find(key);
System.out.println(temp.key);
for (;;) {
// case 1 : external node
if (temp.isExternal()) {
if (temp.getParent().getrChild() == temp) {
temp.parent.rightchild = null;
temp = null;
} else {
temp = null;
}
break;
}
// case2 : one child is null
else if ((temp.getlChild() == null) || (temp.getrChild() == null)) {
if ((temp.parent.leftchild != null) && temp.getParent().getlChild().key == temp.key) {
if (temp.getlChild() == null) {
temp.getParent().setLeft(temp.getrChild());
temp.getrChild().setParent(temp.getParent());
break;
}
else
temp.getParent().setLeft(temp.getlChild());
temp.getlChild().setParent(temp.getParent());
}
else {
if (temp.rightchild != null) {
System.out.println("in");
temp.getParent().setRight(temp.getrChild());
temp.getrChild().setParent(temp.getParent());
break;
}
else
temp.getParent().setRight(temp.getlChild());
temp.getlChild().setParent(temp.getParent());
}
break;
}
// case 3 : has both the children
else {
int t = temp.key;
temp.key = temp.getlChild().key;
temp.getlChild().key = t;
temp = temp.getlChild();
continue;
}
}
}

Converting an ordered binary tree to a doubly circular link list

I have a ordered binary tree:
4
|
|-------|
2 5
|
|-------|
1 3
The leaves point to null. I have to create a doubly link list which should look like
1<->2<->3<->4<->5
(Obviously 5 should point to 1)
The node class is as follows:
class Node {
Node left;
Node right;
int value;
public Node(int value)
{
this.value = value;
left = null;
right = null;
}
}
As you can see the doubly link list is ordered (sorted) as well.
Question: I have to create the linked list form the tree without using any extra pointers. The left pointer of the tree should be the previous pointer of the list and the right pointer of the tree should be the next pointer of the list.
What I thought off: Since the tree is an ordered tree, the inorder traversal would give me a sorted list. But while doing the inorder traversal I am not able to see, where and how to move the pointers to form a doubly linked list.
P.S I checked some variations of this question but none of them gave me any clues.

It sounds like you need a method that accepts a Node reference to the root of the tree and returns a Node reference to the head of a circular list, where no new Node objects are created. I would approach this recursively, starting with the simple tree:
2
|
|-----|
1 3
You don't say whether the tree is guaranteed to be full, so we need to allow for 1 and/or 3 being null. The following method should work for this simple tree:
Node simpleTreeToList(Node root) {
if (root == null) {
return null;
}
Node left = root.left;
Node right = root.right;
Node head;
if (left == null) {
head = root;
} else {
head = left;
left.right = root;
// root.left is already correct
}
if (right == null) {
head.left = root;
root.right = head;
} else {
head.left = right;
right.right = head;
right.left = root;
}
return head;
}
Once it is clear how this works, it isn't too hard to generalize it to a recursive method that works for any tree. It is a very similar method:
Node treeToList(Node root) {
if (root == null) {
return null;
}
Node leftTree = treeToList(root.left);
Node rightTree = treeToList(root.right);
Node head;
if (leftTree == null) {
head = root;
} else {
head = leftTree;
leftTree.left.right = root;
root.left = leftTree.left;
}
if (rightTree == null) {
head.left = root;
root.right = head;
} else {
head.left = rightTree.left;
rightTree.left.right = head;
rightTree.left = root;
root.right = rightTree;
}
return head;
}
If I got all the link assignments covered correctly, this should be all you need.

Do an in-order traversal of the list, adding each list item to the doubly linked list as you encounter it. When done, add an explicit link between the first and last items.
Update 3/6/2012: Since you must reuse the Node objects you already have, after you put the node objects into the the list, you can then iterate over the list and reset the left and right pointers of the Node objects to point to their siblings. Once that is done, you can get rid of the list and simply return the first node object.

This should also work:
NodeLL first = null;
NodeLL last = null;
private void convertToLL(NodeBST root) {
if (root == null) {
return;
}
NodeLL newNode = new NodeLL(root.data);
convertToLL(root.left);
final NodeLL l = last;
last = newNode;
if (l == null)
first = newNode;
else {
l.next = newNode;
last.prev = l;
}
convertToLL(root.right);
}

Let your recursion return the left and right end of formed list. Then you link your current node to the last of the left list, and first of the right list. Basic case it, when there is no left or right element, which is the node it self for both. Once all is done, you can link the first and last of the final result. Below is the java code.
static void convertToSortedList(TreeNode T){
TreeNode[] r = convertToSortedListHelper(T);
r[1].next = r[0];
r[0].prev= r[1];
}
static TreeNode[] convertToSortedListHelper(TreeNode T){
TreeNode[] ret = new TreeNode[2];
if (T == null) return ret;
if (T.left == null && T.right == null){
ret[0] = T;
ret[1] = T;
return ret;
}
TreeNode[] left = TreeNode.convertToSortedListHelper(T.left);
TreeNode[] right = TreeNode.convertToSortedListHelper(T.right);
if (left[1] != null) left[1].next = T;
T.prev = left[1];
T.next = right[0];
if (right[0] != null) right[0].prev = T;
ret[0] = left[0]==null? T:left[0];
ret[1] = right[1]==null? T:right[1];
return ret;
}

Add the following method to your Node class
public Node toLinked() {
Node leftmost = this, rightmost = this;
if (right != null) {
right = right.toLinked();
rightmost = right.left;
right.left = this;
}
if (left != null) {
leftmost = left.toLinked();
left = leftmost.left;
left.right = this;
}
leftmost.left = rightmost;
rightmost.right = leftmost;
return leftmost;
}
EDIT By maintaining the invariant that the list returned by toLinked() has the proper form, you can easily get the left- and rightmost nodes in the sublist returned by the recursive call on the subtrees

/* input: root of BST. Output: first node of a doubly linked sorted circular list. **Constraints**: do it in-place. */
public static Node transform(Node root){
if(root == null){
return null;
}
if(root.isLeaf()){
root.setRight(root);
root.setLeft(root);
return root;
}
Node firstLeft = transform(root.getLeft());
Node firstRight = transform(root.getRight());
Node lastLeft = firstLeft == null ? null : firstLeft.getLeft();
Node lastRight= firstRight == null ? null : firstRight.getLeft();
if(firstLeft != null){
lastLeft.setRight(root);
root.setLeft(lastLeft);
if(lastRight == null){
firstLeft.setLeft(root);
}
else{
firstLeft.setLeft(lastRight);
root.setRight(firstRight);
}
}
if(firstRight != null){
root.setRight(firstRight);
firstRight.setLeft(root);
if(lastLeft == null){
root.setLeft(lastRight);
lastRight.setLeft(root);
firstLeft = root;
}
else{
root.setLeft(lastLeft);
lastRight.setRight(firstLeft);
}
}
return firstLeft;
}