Binary search tree operations - Java
Binary Search Tree, is a node-based binary tree data structure which has the following properties:
- The left subtree of a node contains only nodes with keys less than the node’s key.
- The right subtree of a node contains only nodes with keys greater than the node’s key.
- The left and right subtree each must also be a binary search tree.
There must be no duplicate nodes.
The above properties of Binary Search Tree provide an ordering among keys so that the operations like search, minimum and maximum can be done fast. If there is no ordering, then we may have to compare every key to search a given key.
Searching a key
To search a given key in Bianry Search Tree, we first compare it with root, if the key is present at root, we return root. If key is greater than root’s key, we recur for right subtree of root node. Otherwise we recur for left subtree.
To search a given key in Bianry Search Tree, we first compare it with root, if the key is present at root, we return root. If key is greater than root’s key, we recur for right subtree of root node. Otherwise we recur for left subtree.
// A utility function to search a given key in BST
public Node search(Node root, int key)
{
// Base Cases: root is null or key is present at root
if (root==null || root.key==key)
return root;
// val is greater than root's key
if (root.key > key)
return search(root.left, key);
// val is less than root's key
return search(root.right, key);
}
Insertion of a key
A new key is always inserted at leaf. We start searching a key from root till we hit a leaf node. Once a leaf node is found, the new node is added as a child of the leaf node.
A new key is always inserted at leaf. We start searching a key from root till we hit a leaf node. Once a leaf node is found, the new node is added as a child of the leaf node.
100 100
/ \ Insert 40 / \
20 500 ---------> 20 500
/ \ / \
10 30 10 30
\
40
// Java program to demonstrate insert operation in binary search treeclass BinarySearchTree { /* Class containing left and right child of current node and key value*/ class Node { int key; Node left, right; public Node(int item) { key = item; left = right = null; } } // Root of BST Node root; // Constructor BinarySearchTree() { root = null; } // This method mainly calls insertRec() void insert(int key) { root = insertRec(root, key); } /* A recursive function to insert a new key in BST */ Node insertRec(Node root, int key) { /* If the tree is empty, return a new node */ if (root == null) { root = new Node(key); return root; } /* Otherwise, recur down the tree */ if (key < root.key) root.left = insertRec(root.left, key); else if (key > root.key) root.right = insertRec(root.right, key); /* return the (unchanged) node pointer */ return root; } // This method mainly calls InorderRec() void inorder() { inorderRec(root); } // A utility function to do inorder traversal of BST void inorderRec(Node root) { if (root != null) { inorderRec(root.left); System.out.println(root.key); inorderRec(root.right); } } // Driver Program to test above functions public static void main(String[] args) { BinarySearchTree tree = new BinarySearchTree(); /* Let us create following BST 50 / \ 30 70 / \ / \ 20 40 60 80 */ tree.insert(50); tree.insert(30); tree.insert(20); tree.insert(40); tree.insert(70); tree.insert(60); tree.insert(80); // print inorder traversal of the BST tree.inorder(); }}
When we delete a node, there possibilities arise.
1) Node to be deleted is leaf: Simply remove from the tree.
50 50
/ \ delete(20) / \
30 70 ---------> 30 70
/ \ / \ \ / \
20 40 60 80 40 60 80
2) Node to be deleted has only one child: Copy the child to the node and delete the child
50 50
/ \ delete(30) / \
30 70 ---------> 40 70
\ / \ / \
40 60 80 60 80
3) Node to be deleted has two children: Find inorder successor of the node. Copy contents of the inorder successor to the node and delete the inorder successor. Note that inorder predecessor can also be used.
50 60
/ \ delete(50) / \
40 70 ---------> 40 70
/ \ \
60 80 80
The important thing to note is, inorder successor is needed only when right child is not empty. In this particular case, inorder successor can be obtained by finding the minimum value in right child of the node.
// Java program to demonstrate delete operation in binary search tree
class BinarySearchTree
{
/* Class containing left and right child of current node and key value*/
class Node
{
int key;
Node left, right;
public Node(int item)
{
key = item;
left = right = null;
}
}
// Root of BST
Node root;
// Constructor
BinarySearchTree()
{
root = null;
}
// This method mainly calls deleteRec()
void deleteKey(int key)
{
root = deleteRec(root, key);
}
/* A recursive function to insert a new key in BST */
Node deleteRec(Node root, int key)
{
/* Base Case: If the tree is empty */
if (root == null) return root;
/* Otherwise, recur down the tree */
if (key < root.key)
root.left = deleteRec(root.left, key);
else if (key > root.key)
root.right = deleteRec(root.right, key);
// if key is same as root's key, then This is the node
// to be deleted
else
{
// node with only one child or no child
if (root.left == null)
return root.right;
else if (root.right == null)
return root.left;
// node with two children: Get the inorder successor (smallest
// in the right subtree)
root.key = minValue(root.right);
// Delete the inorder successor
root.right = deleteRec(root.right, root.key);
}
return root;
}
int minValue(Node root)
{
int minv = root.key;
while (root.left != null)
{
minv = root.left.key;
root = root.left;
}
return minv;
}
// This method mainly calls insertRec()
void insert(int key)
{
root = insertRec(root, key);
}
/* A recursive function to insert a new key in BST */
Node insertRec(Node root, int key)
{
/* If the tree is empty, return a new node */
if (root == null)
{
root = new Node(key);
return root;
}
/* Otherwise, recur down the tree */
if (key < root.key)
root.left = insertRec(root.left, key);
else if (key > root.key)
root.right = insertRec(root.right, key);
/* return the (unchanged) node pointer */
return root;
}
// This method mainly calls InorderRec()
void inorder()
{
inorderRec(root);
}
// A utility function to do inorder traversal of BST
void inorderRec(Node root)
{
if (root != null)
{
inorderRec(root.left);
System.out.print(root.key + " ");
inorderRec(root.right);
}
}
// Driver Program to test above functions
public static void main(String[] args)
{
BinarySearchTree tree = new BinarySearchTree();
/* Let us create following BST
50
/ \
30 70
/ \ / \
20 40 60 80 */
tree.insert(50);
tree.insert(30);
tree.insert(20);
tree.insert(40);
tree.insert(70);
tree.insert(60);
tree.insert(80);
System.out.println("Inorder traversal of the given tree");
tree.inorder();
System.out.println("\nDelete 20");
tree.deleteKey(20);
System.out.println("Inorder traversal of the modified tree");
tree.inorder();
System.out.println("\nDelete 30");
tree.deleteKey(30);
System.out.println("Inorder traversal of the modified tree");
tree.inorder();
System.out.println("\nDelete 50");
tree.deleteKey(50);
System.out.println("Inorder traversal of the modified tree");
tree.inorder();
}
}
Output:
Inorder traversal of the given tree
20 30 40 50 60 70 80
Delete 20
Inorder traversal of the modified tree
30 40 50 60 70 80
Delete 30
Inorder traversal of the modified tree
40 50 60 70 80
Delete 50
Inorder traversal of the modified tree
40 60 70 80
Ref: Geeksforgeeks
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