YouTipBinary Search Level Traverse
## Binary Search Tree Level Order Traversal
The level-order traversal of a binary search tree, also known as level-by-level traversal, means storing the nodes of each level in a queue, then performing dequeue (taking out nodes) and enqueue (storing the next level's nodes) operations to achieve the purpose of traversal.
**Introducing a queue to support level-order traversal:**
* If the root node is null, there is nothing to traverse;
* If the root node is not null:
* First, enqueue the root node;
* As long as the queue is not empty:
* Dequeue the front node and traverse it;
* If the front node has a left child, enqueue the left child;
* If the front node has a right child, enqueue the right child;
The following demonstrates the steps in order:
**(1)** First, take out the root node and put it into the queue
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**(2)** Take out 29, enqueue the left and right child nodes
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**(3)** Dequeue 17 from the front, enqueue child nodes 14 and 23.
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**(4)** Dequeue 31, enqueue child nodes 30 and 43
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**(5)** Finally, dequeue all
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Core code example:
...
// Level-order traversal of binary search tree
public void levelOrder(){
// We use LinkedList as our queue
LinkedList q =new LinkedList();
q.add(root);
while(!q.isEmpty()){
Node node = q.remove();
System.out.println(node.key);
if( node.left!=null)
q.add( node.left);
if( node.right!=null)
q.add( node.right);
}
}
...
### Java Example Code
**Source Package Download:*## src/tutorial/binary/LevelTraverse.java File Code:
package tutorial.binary;
import java.util.LinkedList;
/**
* Level Order Traversal
*/
public class LevelTraverse<Key extends Comparable, Value>{
// The nodes in the tree are private class, the outside world does not need to know the specific implementation of binary search tree nodes
private class Node {
private Key key;
private Value value;
private Node left, right;
public Node(Key key, Value value){
this.key= key;
this.value= value;
left = right =null;
}
}
private Node root;// Root node
private int count;// Number of nodes in the tree
// Constructor, construct an empty binary search tree by default
public LevelTraverse(){
root =null;
count =0;
}
// Return the number of nodes in the binary search tree
public int size(){
return count;
// Return whether the binary search tree is empty
public boolean isEmpty(){
return count ==0;
}
// Insert a new (key, value) data pair into the binary search tree
public void insert(Key key, Value value){
root = insert(root, key, value);
}
// Check whether key exists in the binary search tree
public boolean contain(Key key){
return contain(root, key);
}
// Search for the value corresponding to key in the binary search tree. If the value does not exist, return null
public Value search(Key key){
return search( root , key );
}
// Pre-order traversal of binary search tree
public void preOrder(){
preOrder(root);
}
// In-order traversal of binary search tree
public void inOrder(){
inOrder(root);
}
// Post-order traversal of binary search tree
public void postOrder(){
postOrder(root);
}
// Level-order traversal of binary search tree
public void levelOrder(){
// We use LinkedList as our queue
LinkedList q =new LinkedList();
q.add(root);
while(!q.isEmpty()){
Node node = q.remove();
System.out.println(node.key);
if( node.left!=null)
q.add( node.left);
if( node.right!=null)
q.add( node.right);
}
}
//********************
//* Helper functions for binary search tree
//********************
// Insert node (key, value) into the binary search tree with node as root, using recursive algorithm
// Return the root of the binary search tree after inserting the new node
private Node insert(Node node, Key key, Value value){
if( node ==null){
count ++;
return new Node(key, value);
}
if( key.compareTo(node.key)==0)
node.value= value;
else if( key.compareTo(node.key) node->key
node.right= insert( node.right, key, value);
return node;
}
// Check whether the binary search tree with node as root contains a node with key value, using recursive algorithm
private boolean contain(Node node, Key key){
if( node ==null)
return false;
if( key.compareTo(node.key)==0)
return true;
else if( key.compareTo(node.key) node->key
return contain( node.right , key );
}
// Find the value corresponding to key in the binary search tree with node as root, recursive algorithm
// If value does not exist, return NULL
private Value search(Node node, Key key){
if( node ==null)
return null;
if( key.compareTo(node.key)==0)
return node.value;
else if( key.compareTo(node.key) node->key
return search( node.right, key );
}
// Pre-order traversal of binary search tree with node as root, recursive algorithm
private void preOrder(Node node){
if( node !=null){
System.out.println(node.key);
preOrder(node.left);
preOrder(node.right);
}
}
// In-order traversal of binary search tree with node as root, recursive algorithm
private void inOrder(Node node){
if( node !=null){
inOrder(node.left);
System.out.println(node.key);
inOrder(node.right);
}
}
// Post-order traversal of binary search tree with node as root, recursive algorithm
private void postOrder(Node node){
if( node !=null){
postOrder(node.left);
postOrder(node.right);
System.out.println(node.key);
}
}
}