YouTipBinary Search Traverse
## Binary Search Tree Depth-First Traversal
Binary search tree traversal is divided into two main categories: depth-first traversal and level-order traversal.
Depth-first traversal is further divided into three types: preorder tree walk, inorder tree walk, and postorder tree walk, which are as follows:
* **1. Preorder Traversal:** Visit the current node first, then recursively visit the left and right subtrees in order.
* **2. Inorder Traversal:** Recursively visit the left subtree first, then visit the node itself, and finally recursively visit the right subtree.
* **3. Postorder Traversal:** Recursively visit the left and right subtrees first, then visit the node itself.
Diagram of preorder traversal result:
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Corresponding code example:
...
// Preorder traversal of the binary search tree rooted at node, recursive algorithm
private void preOrder(Node node){
if( node !=null){
System.out.println(node.key);
preOrder(node.left);
preOrder(node.right);
}
}
...
Diagram of inorder traversal result:
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Corresponding code example:
...
// Inorder traversal of the binary search tree rooted at node, recursive algorithm
private void inOrder(Node node){
if( node !=null){
inOrder(node.left);
System.out.println(node.key);
inOrder(node.right);
}
}
...
Diagram of postorder traversal result:
!(#)
Corresponding code example:
...
// Postorder traversal of the binary search tree rooted at node, recursive algorithm
private void postOrder(Node node){
if( node !=null){
postOrder(node.left);
postOrder(node.right);
System.out.println(node.key);
}
}
...
### Java Example Code
**Source code package download:*## src//binary/Traverse.java file code:
package .binary;
/**
* Traversal
*/
public class Traverse<Key extends Comparable, Value>{
// The node in the tree is a private class, the outside world does not need to understand the specific implementation of the binary search tree node
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, default constructs an empty binary search tree
public Traverse(){
root =null;
count =0;
}
// Returns the number of nodes in the binary search tree
public int size(){
return count;
}
// Returns 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 if the binary search tree contains the key
public boolean contain(Key key){
return contain(root, key);
}
// Search for the value corresponding to the key in the binary search tree. If the value does not exist, return null
public Value search(Key key){
return search( root , key );
}
// Preorder traversal of the binary search tree
public void preOrder(){
preOrder(root);
}
// Inorder traversal of the binary search tree
public void inOrder(){
inOrder(root);
}
// Postorder traversal of the binary search tree
public void postOrder(){
postOrder(root);
}
//********************
//* Helper functions for the binary search tree
//********************
// Insert a node (key, value) into the binary search tree rooted at node, using a 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 if the binary search tree rooted at node contains a node with the key value, using a 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 );
}
// Search for the value corresponding to the key in the binary search tree rooted at node, recursive algorithm
// If the 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 );
}
// Preorder traversal of the binary search tree rooted at node, recursive algorithm
private void preOrder(Node node){
if( node !=null){
System.out.println(node.key);
preOrder(node.left);
preOrder(node.right);
}
}
// Inorder traversal of the binary search tree rooted at node, recursive algorithm
private void inOrder(Node node){
if( node !=null){
inOrder(node.left);
System.out.println(node.key);
inOrder(node.right);
}
}
// Postorder traversal of the binary search tree rooted at node, recursive algorithm
private void postOrder(Node node){
if( node !=null){
postOrder(node.left);
postOrder(node.right);
System.out.println(node.key);
}
}
}