# How to Search a Node in a Binary Search Tree

Searching a node in a given Binary Search Tree is a process to search any existing node; let’s say if node A has to be searched then you got to follow below steps –

STEP 1: If there is no node in a given BST then return saying node A is not found as there is no node in the BST.

STEP 2: To find node A in a given Binary Search tree, just compare the value of node A with the root node’s value:

if node A has a value greater than the root node’s value – traverse down the root node in its right node and Go to Step 2 by considering this right node as the root node (Note: if there is no right node straight go to Step 3)

if node A has a value lesser than the root node’s value – traverse down the root node in its left node and Go to Step 2 by considering this left node as the root node (Note: if there is no left node straight go to Step 3)

if node A has a equal to the root node’s value – it just means you have found the node – Just return the same saying Node A found in the Binary Search Tree.

STEP 3: Just return saying node A can not be deleted as it is not present in the BST.

### Above Algorithm can be implemented using two popular ways – Recursive and an Iterative way

BST,java

```package org.gontuseries.bst;

public class BST {

private Node rootNode;

public boolean contains(int value) {
boolean found = false;

found = contains(value, rootNode);
return found;
}

private boolean contains(int value, Node currentNode) {
boolean found = false;

if (currentNode == null)
return false;

if (currentNode.getValue() < value) {
found = contains(value, currentNode.getRightNode());
} else if (currentNode.getValue() > value) {
found = contains(value, currentNode.getLeftNode());
} else {
found = true;
}

return found;
}
}

```
```
package org.gontuseries.bst;

public class BST {

private Node rootNode;

private boolean contains(int value) {
boolean found = false;
Node currentNode = rootNode;

while (true) {
if (currentNode != null) {

if (value > currentNode.getValue()) {
currentNode = currentNode.getRightNode();
} else if (value < currentNode.getValue()) {
currentNode = currentNode.getRightNode();
} else {
found = true; // Node found with the value
break;
}
} else {
}
}
return found;
}
}

```

Node.java

```
package org.gontuseries.bst;

public class Node {

Node(int value) {
this.value = value;
this.leftNode = null;
this.rightNode = null;
}

private int value;
private Node leftNode;
private Node rightNode;
// --- writing all getters and setters for all properties
//i.e for value, leftNode, rightNode
}
```

Time Complexity: The run time complexity of search operation using Recursive way is: O(height of a Binary Search Tree) i.e O(h) [worst-case]

a) In case of a  skewed Binary Search Tree the height is equal to the number of nodes in it; so, it becomes O(n)[worst-case]

b) In case of a Binary Search Tree built using some Tree Balancing Techniques like AVL, RED Black etc the height is equal to log (number of nodes in it); so it becomes log(n) [worst-case]

where, ‘n’ is the number of nodes in a binary search tree.
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