We Keep Coding

How to get the left and right child of a node in an unordered binary search tree?

I'm stuck with this problem: The method below must return the value in the left child node, or -1 if it not exist.
public int getLeftChild(int el) {...}
/* Same for the right child */
Now, the argument is an int value, that indicates the value of the parent node.
Another issue is that... the tree is not ordered, and there are only positive integer values.
So, I can have a value of 0 in the root, 3 in the left child and 1 in the right child, and so on...
I can't figure out how to resolve this.
I can't use ADTs like LinkedList or Stack for any purpose.
The binary tree class has a field root, of type Node:
public class Node {
private int value;
private Node leftChild;
private Node rightChild;
/*Getters and Setters...*/
}

Something like this would work:
public int getLeftChild(int el) {
int not_found = -1;
Stack<Node> nodes_to_search = new Stack<>();
nodes_to_search.add(this);
while(!stack.isEmpty()){
Node root = nodes_to_search.pop();
if(root.value == el){
return (root.leftChild != null) ? root.leftChild.value : not_found;
}
if(root.leftChild != null) nodes_to_search.push(root.leftChild);
if(root.rightChild != null) nodes_to_search.push(root.rightChild);
}
return not_found;
}
You have to search in both the left and right subtrees since the tree is not sorted. Every time you find a valid subtree (i.e., not null) you added to the stack of elements to search. You stop the search when your searching criteria is meet.

Remove recursively from a binary search tree

This is homework; please don't just give me code
I have two methods: remove(T data) and removeRec(Node<T> node, T data).
In its current state, it seems my code only removes the root node of the BST.
#Override
public T remove(T data) {
if (data == null) {
throw new IllegalArgumentException("Data is null");
}
if (root == null) {
throw new java.util.NoSuchElementException("BST is empty");
} else {
size--;
BSTNode<T> dummy = new BSTNode<T>(null);
return removeRec(root, data, dummy).getData(); //This is probably wrong too
}
}
/**
* Helper method to recursively search for, and remove the BSTNode with
* the given data in it
* #param node is the node we're currently at
* #param data is the data we're looking for
* #param temp I have no idea why
* #return node that was removed
*/
private BSTNode<T> removeRec(BSTNode<T> node, T data, BSTNode<T> temp) {
if (compare(data, node.getData()) < 0) {
temp.setLeft(removeRec(node.getLeft(), data, temp));
} else if (compare(data, node.getData()) > 0) {
temp.setRight(removeRec(node.getRight(), data, temp));
} else if (node.getLeft() != null && node.getRight() != null) {
temp.setData(findMin(node.getRight()).getData());
temp.setRight(removeRec(node.getRight(), data, temp));
} else {
if (node.getLeft() != null) {
temp = node.getLeft();
} else {
temp = node.getRight();
}
}
return temp;
}
private int compare(T a, T b) {
return a.compareTo(b);
}
My instructor has told me (as a hint) that I should see what passing in a third argument into the method, in this case, BSTNode<T> temp. I don't understand how that helps though, or how to utilize it. I don't see how using a third argument helps; and I can't find anything online as to why you'd do this either.

There are three main possibilities when you try to remove data from your Binary Search Tree:
data is less than the current node value: Call remove on the left subtree or throw a NoSuchElementException if it is null.
data is greater than the current node value: Call remove on the right subtree or throw a NoSuchElementException if it is null.
data is equal to the current node value.
1 and 2 are pretty straightforward, but 3 has four more cases to consider:
3.1. current node is a leaf: Both left and right subtrees are null. Just replace the reference to the current node in its parent by null.
3.2. current node has only the left child: You need to make the parent of the current node point to the left subtree, thus removing the current point. To do this, you can implement a function that will check if the current point was on the left or right subtree of the parent and replace it accordingly. Calling it would look like this:
replaceNodeInParent(node, node.getLeft(), parent);
3.3. current node has only the right child: Similar to 3.4, but using getRight() instead of getLeft().
3.4. current node has both the left and right children: You should maintain the property of the BST that all nodes on the left are less than the current node and all nodes on the right are greater than the current node. To do so, you should find the smallest value on the right, copy it to the current node, and delete it from the right subtree. Something like this:
BSTNode<T> successor = findMin(node.getRight());
node.setData(successor.getData());
removeRec(node.getRight(), successor.getData(), node);
It looks like your BSTNode doesn't hold a reference to the parent node. If so, I believe that's what the third argument for removeRec should be. You will need a reference to the parent every time you replace the current node, so you can set the parent left or right subtree as needed.
For further reading, you can check this article on Binary Search Trees from Wikipedia.

java alogrithm: find pre/next leaf node that meet special condition from any node in a tree

I need to write a function to find previous/next leaf node that meet special condition from any node in a singly rooted tree. (in the parent first order)
The API would be something like this:
Node findNextLeafNode(Node currentNode, Condition condition);
Node findPretLeafNode(Node currentNode, Condition condition);
where currentNode is any node in a tree, and Node is defined as:
interface Node{
/** #return the Node's parent or null if Node is root */
Node getParent();
/** #return true if node is root */
boolean isRoot();
/** #return non-null array of child nodes (zero length for leaf nodes) */
Node[] getChildren();
/** #return the number of child nodes. If node is leaf, value is 0 */
int getChildCount();
}
And the Condition interface defines the semantics of checking a constraint against a given Node.
interface Condition{
/** #return true if provided node meets the condition */
boolean check(Node node);
}
My question:
Is there an existing library or algorithm for such a common scenario? I am open to either stack based or recursive algorithms. Pseudocode, links to open source libraries, or if you care to share you own code, would be appreciated.
(If not, I need to spend time to invent the same wheel again and paste it here later for sharing.)
Thanks.
-----------------------------write a method to getNext()........
// currentNode must be descendant of root
public static Node getNextNode(Node currentNode, Node root)
{
// 1. if is has child, next is its first child
if (currentNode.getChildSize() > 0) {
return currentNode.getChildren()[0];
}
// 2. if it has no child, check if its is the last child of his parent
else {
// if it is root and has no children, return null
if (currentNode == root) {
return null;
}
// else should have parent which is or under root;
Node parent = currentNode.getParent();
int index = getIndex(currentNode);
if (!isLastofParent(currentNode)) {
// ----a. if not last, next is his parent's next
return currentNode.getParent().getChildren()[index + 1];
}
else {
// ----b. if it is the last one, return its parent's next right if there is. while until root
Node tmp = parent;
while (tmp != root) {
int parentIndex = getIndex(tmp);
if (!isLastofParent(tmp)) {
return tmp.getParent().getChildren()[parentIndex + 1];
}
tmp = tmp.getParent();
}
}
}
return null;
}
private static boolean isLastofParent(Node node)
{
if (getIndex(node) == node.getParent().getChildSize() - 1) {
return true;
}
return false;
}
private static int getIndex(Node currentNode)
{
Node parent = currentNode.getParent();
for (int i = 0; i < parent.getChildSize(); i++) {
if (parent.getChildren()[i] == currentNode) {
return i;
}
}
//TODO: error condition handling, will not happen if tree not change
return -1;
}
------------------------a full search is much easier............
public static Node getNextFailNode(Node currentNode, Node root, Condition condition)
{
boolean foundCurrentNode = false;
Stack<Node> stack = new Stack<Node>();
stack.push(root);
while (!stack.isEmpty()) {
Node tmp = stack.pop();
System.out.println("-popup---------" +tmp+ " ");
if (foundCurrentNode && checkCondition(tmp, condition)) {
return tmp;
}
if (tmp == currentNode) {
foundCurrentNode = true;
}
if (tmp.getChildSize() > 0) {
for (int i = tmp.getChildSize() - 1; i >= 0; i--) {
stack.push(tmp.getChildren()[i]);
}
}
}
return null;
}

This maybe way overblown for what you need, but it can support what you want:
There is a graph traversal language: Gremlin. Typically bolted on top of something like Neo4j, but any graph data structure (e.g. a singly rooted directed tree) can be wrapped to support the API. Take a look at Blueprints projects to find out how it is done.
[edit: for something less heavy]
Perhaps JGraphT is what you want. Also take a look at this question on SO. It is not an exact duplicate, but you should find it helpful.

Write an iterator for your tree that can be initialized from any node and uses pre/in/post-order traversal (Of course it should be bi-directional).
This is basically writing one simple algorithm that at least to me seem basic.
Once you have an iterator all you need is to iterate your way to the next node which is a leaf and the condition holds for it.
If you have trouble with any specific part just ask and I'll improve my answer.

Based on the fact that you already have defined your interfaces, and you say the graph-traversal libraries are too heavyweight, you probably should just write it yourself. It would be an absolutely trivial amount of code. (This page contains some code if you need help.)
(One suggestion for your API: don't put a boolean isRoot(); method on Node, that's a waste of bits unless you have a very good reason to do so. The code that builds the tree should just refer to the root node.)

How do I iterate over Binary Tree?

Right now I have
private static void iterateall(BinaryTree foo) {
if(foo!= null){
System.out.println(foo.node);
iterateall(foo.left);
iterateall(foo.right);
}
}
Can you change it to Iteration instead of a recursion?

What you're looking for is a successor algorithm.
Here's how it can be defined:
First rule: The first node in the tree is the leftmost node in the tree.
Next rule: The successor of a node is:
Next-R rule: If it has a right subtree, the leftmost node in the right subtree.
Next-U rule: Otherwise, traverse up the tree
If you make a right turn (i.e. this node was a left child), then that parent node is the successor
If you make a left turn (i.e. this node was a right child), continue going up.
If you can't go up anymore, then there's no successor
As you can see, for this to work, you need a parent node pointer.
Example:
First rule: The first node in the tree is the leftmost node in the tree: (1)
Next-U rule: Since (1) has no right subtree, we go up to (3). This is a right turn, so (3) is next.
Next-R rule: Since (3) has a right subtree, the leftmost node in that subtree is next: (4).
Next-U rule: Since (4) has no right subtree, we go up to (6). This is a right turn, so next is (6).
Next-R rule: Since (6) has a right subtree, the leftmost node in that subtree is next: (7).
Next-U rule: Since (7) has no right subtree, we go up to (6). This is a left turn, so we continue going up to (3). This is a left turn, so we continue going up to (8). This is a right turn, so next is (8).
Next-R rule: Since (8) has a right subtree, the leftmost node in that subtree is next: (10).
Next-R rule: Since (10) has a right subtree, the leftmost node in that subtree is next: (13).
Next-U rule: Since (13) has no right subtree, we go up to (14). This is a right turn, so next is (14).
Next-U rule: Since (14) has no right subtree, we go up to (10). This is a left turn, so we continue going up to (8). This is a left turn, so we want to continue going up, but since (8) has no parent, we've reached the end. (14) has no successor.
Pseudocode
Node getLeftMost(Node n)
WHILE (n.leftChild != NULL)
n = n.leftChild
RETURN n
Node getFirst(Tree t)
IF (t.root == NULL) RETURN NULL
ELSE
RETURN getLeftMost(t.root);
Node getNext(Node n)
IF (n.rightChild != NULL)
RETURN getLeftMost(n.rightChild)
ELSE
WHILE (n.parent != NULL AND n == n.parent.rightChild)
n = n.parent;
RETURN n.parent;
PROCEDURE iterateOver(Tree t)
Node n = getFirst(t);
WHILE n != NULL
visit(n)
n = getNext(n)
Java code
Here's a simple implementation of the above algorithm:
public class SuccessorIteration {
static class Node {
final Node left;
final Node right;
final int key;
Node parent;
Node(int key, Node left, Node right) {
this.key = key;
this.left = left;
this.right = right;
if (left != null) left.parent = this;
if (right != null) right.parent = this;
}
Node getLeftMost() {
Node n = this;
while (n.left != null) {
n = n.left;
}
return n;
}
Node getNext() {
if (right != null) {
return right.getLeftMost();
} else {
Node n = this;
while (n.parent != null && n == n.parent.right) {
n = n.parent;
}
return n.parent;
}
}
}
}
Then you can have a test harness like this:
static Node C(int key, Node left, Node right) {
return new Node(key, left, right);
}
static Node X(int key) { return C(key, null, null); }
static Node L(int key, Node left) { return C(key, left, null); }
static Node R(int key, Node right) { return C(key, null, right); }
public static void main(String[] args) {
Node n =
C(8,
C(3,
X(1),
C(6,
X(4),
X(7)
)
),
R(10,
L(14,
X(13)
)
)
);
Node current = n.getLeftMost();
while (current != null) {
System.out.print(current.key + " ");
current = current.getNext();
}
}
This prints:
1 3 4 6 7 8 10 13 14
See also
Complete Java listing and output on ideone.com

Can you change it to Iteration instead of a recursion?
You can, using an explicit stack. Pseudocode:
private static void iterateall(BinaryTree foo) {
Stack<BinaryTree> nodes = new Stack<BinaryTree>();
nodes.push(foo);
while (!nodes.isEmpty()) {
BinaryTree node = nodes.pop();
if (node == null)
continue;
System.out.println(node.node);
nodes.push(node.right);
nodes.push(node.left);
}
}
But this isn’t really superior to the recursive code (except for the missing base condition in your code).

Sure, you have two general algorithms, depth first search and breadth first search.
If order of traversal is not important to you, go for breadth first, it's easier to implement for iteration. You're algorithm should look something like this.
LinkedList queue = new LinkedList();
queue.add(root);
while (!queue.isEmpty()){
Object element = queue.remove();
queue.add(element.left);
queue.add(element.right);
// Do your processing with element;
}

As with every recursion, you can use additional data structure - i.e. the stack.
A sketch of the solution:
private static void visitall(BinaryTree foo) {
Stack<BinaryTree> iterationStack = new Stack<BinaryTree>();
iterationStack.push(foo);
while (!iterationStack.isEmpty()) {
BinaryTree current = iterationStack.pop();
System.out.println(current.node);
current.push(current.right); // NOTE! The right one comes first
current.push(current.left);
}
}

I had a tree (not binary) and eventually solved it with this very simple algorithm. The other solutions used left and right that were not relevant or even implemented in the examples.
My structure was: nodes with each parent containing list of children, and each child containing a pointer back to the parent. Pretty common...
After a bunch of refactoring, I came up with the following example using Kotlin. It should be trivial to convert to your language of choice.
Helper Functions
First, the node must provide 2 simple functions. This will vary depending on your Node class' implementation:
leftMost - This is the first child node. If that node has children, it's first child, etc. If no children, return this.
fun leftMost(): Node {
if (children.isEmpty()) {
return this
}
var n = this
while (n.children.isNotEmpty()) {
n = n.children[0]
}
return n
}
nextSibling - The next sibling of this node, or NULL
fun nextSibling(): Node? {
if (parent == null) return null
val siblingIndex = parent.children.indexOf(this) + 1
return if (siblingIndex < parent.children.size) {
parent.children[siblingIndex]
} else {
null
}
}
The Iteration
The iteration starts with the leftMost of the root.
Then inspect the next sibling.
If NOT NULL the sibling's leftMostChild
If NULL, the parent, and if the parent is NULL, we are done.
That's it.
Here is a Kotlin iterator function.
fun iterator(): Iterator<Node> {
var next: Node? = this.leftMost()
return object : Iterator<Node> {
override fun hasNext(): Boolean {
return next != null
}
override fun next(): Node {
val ret = next ?: throw NoSuchElementException()
next = ret.nextSibling()?.leftMost() ?: ret.parent
return ret
}
}
}
Here is the same next() function, but without the Kotlin shorthand for dealing with NULL values, for those that are not hip to the syntax.
fun next(): Node {
val ret = next
if (ret == null) throw NoSuchElementException()
val nextSibling = ret.nextSibling()
if (nextSibling != null) {
next = nextSibling.leftMost()
}
else {
next = ret.parent
}
return ret
}

Yes, you can change it to iteration instead of a recursion, but then it gets much more complicated, since you need to have some way to remember where to go back from the current node. In the recursive case, the Java call stack handles that, but in an iterative solution you need to build your own stack, or perhaps store back pointers in the nodes.

Java, Binary tree remove method

I am trying to write a remove(node cRoot, Object o) function for a sorted binary tree.
Here is what I have so far:
private boolean remove(Node cRoot, Object o) {
if (cRoot == null) {
return false;
}
else if (cRoot.item.equals(o)) {
//erase node fix tree
return true;
}
else if (((Comparable)item).compareTo(cRoot.item)<=0){
return remove(cRoot.lChild, o);
}
else {
return remove(cRoot.rChild,o);
}
}
It does not work correctly. To delete a node you have to repair the tree to fix the hole. How should this be done?

There are generally two ways of performing a remove on the tree:
First method:
Remove the node, then replace it with either child. Then, resort the tree by doing parent-child swapping until the tree is once again sorted.
The second method:
Traverse the tree to find the next (highest or lowest) value that belongs as the root*, if it is a leaf node, swap that with the root, then trim off the value you want to remove. If it is an internal node, you will have to recursively call remove on that node. Repeat until a leaf node is removed.
*What I mean is, if you convert your BST into a sorted list, then you will want to pick either value to the left or right of the root as the new root. I.e. leftmost child of the right subtree, or right most child of the left subtree.

The basic pseudo-code for erasing a node from a sorted tree is pretty simple:
erase the node value
find child node with maximum value
make it the root node
if it had children - goto 2 recursively
Basically what you are doing is bubbling nodes up the tree, each time the maximum of the children node in each node, so that in the end you stay with a sorted tree, and only one node missing at the end of the full path you went.
Also - see wikipedia on the subject, they have some sample code in C as well.

In the simple case3 you can use next algorithm:
if(removed node had left child)
{
place left child instead of removed node;
most_right = most right leaf in the left subtree;
move right child of removed node as right child of most_right;
}
else
{
place right child instead of removed node
}
In more complicated case you may need to rebalance your tree (see AVL trees, http://www.cmcrossroads.com/bradapp/ftp/src/libs/C++/AvlTrees.html for C++ example)

leaf-delete node
1-child Promote the subtree
2-child case replace the node with either
in order successor or predecessor
left most of the right subtree or
right most of the left subtree

I found this code on Habrahabr. I've just added comments.
public void remove (T1 k){
Node<T1,T2> x = root, y = null;
// from while to if(x == null) - searching for key
while(x != null){
int cmp = k.compareTo(x.key);
if(cmp == 0){
break; // quit cycle if key element is found
} else {
y = x;
if(cmp < 0){
x = x.left;
} else {
x = x.right;
}
}
}
if(x == null) return; // if key is not found or tree is empty
if(x.right == null){ // if element found has not right child
if(y == null){ // if element found is root & has not right child
root = x.left;
} else { // if element found is not root & has not right child
if(x == y.left) y.left = x.left;
else y.right = x.left;
}
} else { // element found has right child, so search for most left of rights
Node<T1,T2> mostLeft = x.right;
y = null;
while(mostLeft.left != null) {
y = mostLeft;
mostLeft = mostLeft.left;
}
if(y == null){ // if right child of element found has not left child
x.right = mostLeft.right;
} else { // if right child of element found has left child
y.left = mostLeft.right;
}
x.key = mostLeft.key;
x.value = mostLeft.value;
}
}