Binary Tree Algorithm
The Binary Tree Inorder Traversal Algorithm is a depth-first traversal technique used to visit all the nodes in a binary tree in a specific order. In this algorithm, the nodes of the binary tree are visited in the following sequence: first, the left subtree is traversed, then the root node is visited, and finally, the right subtree is traversed. This sequence is applied recursively for each subtree in the binary tree. The result of the inorder traversal is a list of the tree's nodes sorted in ascending order, which makes this algorithm particularly useful when working with binary search trees.
To implement the inorder traversal algorithm, one can use either a recursive or an iterative approach. In the recursive approach, the algorithm first calls itself for the left subtree of the root node, then it processes the root node by adding its value to the resulting list, and finally, it calls itself for the right subtree of the root node. The iterative approach, on the other hand, uses a stack data structure to keep track of the nodes yet to be visited. Starting with the root node, it pushes all the nodes in the left subtree onto the stack, then pops and processes the top node, and repeats the process for the right subtree. This iterative approach can be more efficient in terms of memory usage, as it eliminates the overhead of recursive function calls.
package DataStructures.Trees;
/**
* This entire class is used to build a Binary Tree data structure.
* There is the Node Class and the Tree Class, both explained below.
*/
/**
* A binary tree is a data structure in which an element
* has two successors(children). The left child is usually
* smaller than the parent, and the right child is usually
* bigger.
*
* @author Unknown
*
*/
public class BinaryTree {
/**
* This class implements the nodes that will go on the Binary Tree.
* They consist of the data in them, the node to the left, the node
* to the right, and the parent from which they came from.
*
* @author Unknown
*
*/
class Node {
/** Data for the node */
public int data;
/** The Node to the left of this one */
public Node left;
/** The Node to the right of this one */
public Node right;
/** The parent of this node */
public Node parent;
/**
* Constructor of Node
*
* @param value Value to put in the node
*/
public Node(int value) {
data = value;
left = null;
right = null;
parent = null;
}
}
/** The root of the Binary Tree */
private Node root;
/**
* Constructor
*/
public BinaryTree() {
root = null;
}
/**
* Method to find a Node with a certain value
*
* @param key Value being looked for
* @return The node if it finds it, otherwise returns the parent
*/
public Node find(int key) {
Node current = root;
while (current != null) {
if (key < current.data) {
if (current.left == null)
return current; //The key isn't exist, returns the parent
current = current.left;
} else if (key > current.data) {
if (current.right == null)
return current;
current = current.right;
} else { // If you find the value return it
return current;
}
}
return null;
}
/**
* Inserts certain value into the Binary Tree
*
* @param value Value to be inserted
*/
public void put(int value) {
Node newNode = new Node(value);
if (root == null)
root = newNode;
else {
//This will return the soon to be parent of the value you're inserting
Node parent = find(value);
//This if/else assigns the new node to be either the left or right child of the parent
if (value < parent.data) {
parent.left = newNode;
parent.left.parent = parent;
return;
} else {
parent.right = newNode;
parent.right.parent = parent;
return;
}
}
}
/**
* Deletes a given value from the Binary Tree
*
* @param value Value to be deleted
* @return If the value was deleted
*/
public boolean remove(int value) {
//temp is the node to be deleted
Node temp = find(value);
//If the value doesn't exist
if (temp.data != value)
return false;
//No children
if (temp.right == null && temp.left == null) {
if (temp == root)
root = null;
//This if/else assigns the new node to be either the left or right child of the parent
else if (temp.parent.data < temp.data)
temp.parent.right = null;
else
temp.parent.left = null;
return true;
}
//Two children
else if (temp.left != null && temp.right != null) {
Node successor = findSuccessor(temp);
//The left tree of temp is made the left tree of the successor
successor.left = temp.left;
successor.left.parent = successor;
//If the successor has a right child, the child's grandparent is it's new parent
if(successor.parent!=temp){
if(successor.right!=null){
successor.right.parent = successor.parent;
successor.parent.left = successor.right;
successor.right = temp.right;
successor.right.parent = successor;
}else{
successor.parent.left=null;
successor.right=temp.right;
successor.right.parent=successor;
}
}
if (temp == root) {
successor.parent = null;
root = successor;
return true;
}
//If you're not deleting the root
else {
successor.parent = temp.parent;
//This if/else assigns the new node to be either the left or right child of the parent
if (temp.parent.data < temp.data)
temp.parent.right = successor;
else
temp.parent.left = successor;
return true;
}
}
//One child
else {
//If it has a right child
if (temp.right != null) {
if (temp == root) {
root = temp.right;
return true;
}
temp.right.parent = temp.parent;
//Assigns temp to left or right child
if (temp.data < temp.parent.data)
temp.parent.left = temp.right;
else
temp.parent.right = temp.right;
return true;
}
//If it has a left child
else {
if (temp == root) {
root = temp.left;
return true;
}
temp.left.parent = temp.parent;
//Assigns temp to left or right side
if (temp.data < temp.parent.data)
temp.parent.left = temp.left;
else
temp.parent.right = temp.left;
return true;
}
}
}
/**
* This method finds the Successor to the Node given.
* Move right once and go left down the tree as far as you can
*
* @param n Node that you want to find the Successor of
* @return The Successor of the node
*/
public Node findSuccessor(Node n) {
if (n.right == null)
return n;
Node current = n.right;
Node parent = n.right;
while (current != null) {
parent = current;
current = current.left;
}
return parent;
}
/**
* Returns the root of the Binary Tree
*
* @return the root of the Binary Tree
*/
public Node getRoot() {
return root;
}
/**
* Prints leftChild - root - rightChild
*
* @param localRoot The local root of the binary tree
*/
public void inOrder(Node localRoot) {
if (localRoot != null) {
inOrder(localRoot.left);
System.out.print(localRoot.data + " ");
inOrder(localRoot.right);
}
}
/**
* Prints root - leftChild - rightChild
*
* @param localRoot The local root of the binary tree
*/
public void preOrder(Node localRoot) {
if (localRoot != null) {
System.out.print(localRoot.data + " ");
preOrder(localRoot.left);
preOrder(localRoot.right);
}
}
/**
* Prints rightChild - leftChild - root
*
* @param localRoot The local root of the binary tree
*/
public void postOrder(Node localRoot) {
if (localRoot != null) {
postOrder(localRoot.left);
postOrder(localRoot.right);
System.out.print(localRoot.data + " ");
}
}
}
