我正在编写一个利用二叉搜索树来存储数据的程序。在之前的程序（无关）中，我能够使用 Java SE6 提供的implementation 实现一个链表。二叉搜索树是否有类似的东西，还是我需要“从头开始”？
【问题讨论】：
标签： java data-structures tree
您可以使用TreeMap data structure。 TreeMap 被实现为 red black tree，这是一个自平衡二叉搜索树。
【讨论】：
根据Collections Framework Overview，您有两个平衡树实现：
【讨论】：
TreeSet 只是一个没有值的TreeMap（所以只有键）。在内部，它们或多或少是相同的。当然，这取决于实现，但大多数 JRE 会将其实现为：public TreeSet() { this(new TreeMap<E,Object>()); }
这是我在 Java SE 1.8 中的简单二叉搜索树实现：
public class BSTNode
{
int data;
BSTNode parent;
BSTNode left;
BSTNode right;
public BSTNode(int data)
{
this.data = data;
this.left = null;
this.right = null;
this.parent = null;
}
public BSTNode()
{
}
}
public class BSTFunctions
{
BSTNode ROOT;
public BSTFunctions()
{
this.ROOT = null;
}
void insertNode(BSTNode node, int data)
{
if (node == null)
{
node = new BSTNode(data);
ROOT = node;
}
else if (data < node.data && node.left == null)
{
node.left = new BSTNode(data);
node.left.parent = node;
}
else if (data >= node.data && node.right == null)
{
node.right = new BSTNode(data);
node.right.parent = node;
}
else
{
if (data < node.data)
{
insertNode(node.left, data);
}
else
{
insertNode(node.right, data);
}
}
}
public boolean search(BSTNode node, int data)
{
if (node == null)
{
return false;
}
else if (node.data == data)
{
return true;
}
else
{
if (data < node.data)
{
return search(node.left, data);
}
else
{
return search(node.right, data);
}
}
}
public void printInOrder(BSTNode node)
{
if (node != null)
{
printInOrder(node.left);
System.out.print(node.data + " - ");
printInOrder(node.right);
}
}
public void printPostOrder(BSTNode node)
{
if (node != null)
{
printPostOrder(node.left);
printPostOrder(node.right);
System.out.print(node.data + " - ");
}
}
public void printPreOrder(BSTNode node)
{
if (node != null)
{
System.out.print(node.data + " - ");
printPreOrder(node.left);
printPreOrder(node.right);
}
}
public static void main(String[] args)
{
BSTFunctions f = new BSTFunctions();
/**
* Insert
*/
f.insertNode(f.ROOT, 20);
f.insertNode(f.ROOT, 5);
f.insertNode(f.ROOT, 25);
f.insertNode(f.ROOT, 3);
f.insertNode(f.ROOT, 7);
f.insertNode(f.ROOT, 27);
f.insertNode(f.ROOT, 24);
/**
* Print
*/
f.printInOrder(f.ROOT);
System.out.println("");
f.printPostOrder(f.ROOT);
System.out.println("");
f.printPreOrder(f.ROOT);
System.out.println("");
/**
* Search
*/
System.out.println(f.search(f.ROOT, 27) ? "Found" : "Not Found");
System.out.println(f.search(f.ROOT, 10) ? "Found" : "Not Found");
}
}
输出是：
3 - 5 - 7 - 20 - 24 - 25 - 27 -
3 - 7 - 5 - 24 - 27 - 25 - 20 -
20 - 5 - 3 - 7 - 25 - 24 - 27 -
Found
Not Found
【讨论】：
这是一个示例实现：
import java.util.*;
public class MyBSTree<K,V> implements MyTree<K,V>{
private BSTNode<K,V> _root;
private int _size;
private Comparator<K> _comparator;
private int mod = 0;
public MyBSTree(Comparator<K> comparator){
_comparator = comparator;
}
public Node<K,V> root(){
return _root;
}
public int size(){
return _size;
}
public boolean containsKey(K key){
if(_root == null){
return false;
}
BSTNode<K,V> node = _root;
while (node != null){
int comparison = compare(key, node.key());
if(comparison == 0){
return true;
}else if(comparison <= 0){
node = node._left;
}else {
node = node._right;
}
}
return false;
}
private int compare(K k1, K k2){
if(_comparator != null){
return _comparator.compare(k1,k2);
}
else {
Comparable<K> comparable = (Comparable<K>)k1;
return comparable.compareTo(k2);
}
}
public V get(K key){
Node<K,V> node = node(key);
return node != null ? node.value() : null;
}
private BSTNode<K,V> node(K key){
if(_root != null){
BSTNode<K,V> node = _root;
while (node != null){
int comparison = compare(key, node.key());
if(comparison == 0){
return node;
}else if(comparison <= 0){
node = node._left;
}else {
node = node._right;
}
}
}
return null;
}
public void add(K key, V value){
if(key == null){
throw new IllegalArgumentException("key");
}
if(_root == null){
_root = new BSTNode<K, V>(key, value);
}
BSTNode<K,V> prev = null, curr = _root;
boolean lastChildLeft = false;
while(curr != null){
int comparison = compare(key, curr.key());
prev = curr;
if(comparison == 0){
curr._value = value;
return;
}else if(comparison < 0){
curr = curr._left;
lastChildLeft = true;
}
else{
curr = curr._right;
lastChildLeft = false;
}
}
mod++;
if(lastChildLeft){
prev._left = new BSTNode<K, V>(key, value);
}else {
prev._right = new BSTNode<K, V>(key, value);
}
}
private void removeNode(BSTNode<K,V> curr){
if(curr.left() == null && curr.right() == null){
if(curr == _root){
_root = null;
}else{
if(curr.isLeft()) curr._parent._left = null;
else curr._parent._right = null;
}
}
else if(curr._left == null && curr._right != null){
curr._key = curr._right._key;
curr._value = curr._right._value;
curr._left = curr._right._left;
curr._right = curr._right._right;
}
else if(curr._left != null && curr._right == null){
curr._key = curr._left._key;
curr._value = curr._left._value;
curr._right = curr._left._right;
curr._left = curr._left._left;
}
else { // both left & right exist
BSTNode<K,V> x = curr._left;
// find right-most node of left sub-tree
while (x._right != null){
x = x._right;
}
// move that to current
curr._key = x._key;
curr._value = x._value;
// delete duplicate data
removeNode(x);
}
}
public V remove(K key){
BSTNode<K,V> curr = _root;
V val = null;
while(curr != null){
int comparison = compare(key, curr.key());
if(comparison == 0){
val = curr._value;
removeNode(curr);
mod++;
break;
}else if(comparison < 0){
curr = curr._left;
}
else{
curr = curr._right;
}
}
return val;
}
public Iterator<MyTree.Node<K,V>> iterator(){
return new MyIterator();
}
private class MyIterator implements Iterator<Node<K,V>>{
int _startMod;
Stack<BSTNode<K,V>> _stack;
public MyIterator(){
_startMod = MyBSTree.this.mod;
_stack = new Stack<BSTNode<K, V>>();
BSTNode<K,V> node = MyBSTree.this._root;
while (node != null){
_stack.push(node);
node = node._left;
}
}
public void remove(){
throw new UnsupportedOperationException();
}
public boolean hasNext(){
if(MyBSTree.this.mod != _startMod){
throw new ConcurrentModificationException();
}
return !_stack.empty();
}
public Node<K,V> next(){
if(MyBSTree.this.mod != _startMod){
throw new ConcurrentModificationException();
}
if(!hasNext()){
throw new NoSuchElementException();
}
BSTNode<K,V> node = _stack.pop();
BSTNode<K,V> x = node._right;
while (x != null){
_stack.push(x);
x = x._left;
}
return node;
}
}
@Override
public String toString(){
if(_root == null) return "[]";
return _root.toString();
}
private static class BSTNode<K,V> implements Node<K,V>{
K _key;
V _value;
BSTNode<K,V> _left, _right, _parent;
public BSTNode(K key, V value){
if(key == null){
throw new IllegalArgumentException("key");
}
_key = key;
_value = value;
}
public K key(){
return _key;
}
public V value(){
return _value;
}
public Node<K,V> left(){
return _left;
}
public Node<K,V> right(){
return _right;
}
public Node<K,V> parent(){
return _parent;
}
boolean isLeft(){
if(_parent == null) return false;
return _parent._left == this;
}
boolean isRight(){
if(_parent == null) return false;
return _parent._right == this;
}
@Override
public boolean equals(Object o){
if(o == null){
return false;
}
try{
BSTNode<K,V> node = (BSTNode<K,V>)o;
return node._key.equals(_key) && ((_value == null && node._value == null) || (_value != null && _value.equals(node._value)));
}catch (ClassCastException ex){
return false;
}
}
@Override
public int hashCode(){
int hashCode = _key.hashCode();
if(_value != null){
hashCode ^= _value.hashCode();
}
return hashCode;
}
@Override
public String toString(){
String leftStr = _left != null ? _left.toString() : "";
String rightStr = _right != null ? _right.toString() : "";
return "["+leftStr+" "+_key+" "+rightStr+"]";
}
}
}
【讨论】：
这个程序有一个功能
寻找继任者
class BNode{
int data;
BNode left, right;
public BNode(int data){
this.data = data;
this.left = null;
this.right = null;
}
}
public class BST {
static BNode root;
public int add(int value){
BNode newNode, current;
newNode = new BNode(value);
if(root == null){
root = newNode;
current = root;
}
else{
current = root;
while(current.left != null || current.right != null){
if(newNode.data < current.data){
if(current.left != null)
current = current.left;
else
break;
}
else{
if(current.right != null)
current = current.right;
else
break;
}
}
if(newNode.data < current.data)
current.left = newNode;
else
current.right = newNode;
}
return value;
}
public void inorder(BNode root){
if (root != null) {
inorder(root.left);
System.out.println(root.data);
inorder(root.right);
}
}
public boolean find(int value){
boolean flag = false;
BNode current;
current = root;
while(current!= null){
if(current.data == value){
flag = true;
break;
}
else if(current.data > value)
current = current.left;
else
current = current.right;
}
System.out.println("Is "+value+" present in tree? : "+flag);
return flag;
}
public void successor(int value){
BNode current;
current = root;
if(find(value)){
while(current.data != value){
if(value < current.data && current.left != null){
System.out.println("Node is: "+current.data);
current = current.left;
}
else if(value > current.data && current.right != null){
System.out.println("Node is: "+current.data);
current = current.right;
}
}
}
else
System.out.println(value+" Element is not present in tree");
}
public static void main(String[] args) {
BST b = new BST();
b.add(50);
b.add(30);
b.add(20);
b.add(40);
b.add(70);
b.add(60);
b.add(80);
b.add(90);
b.inorder(root);
b.find(30);
b.find(90);
b.find(100);
b.find(50);
b.successor(90);
System.out.println();
b.successor(70);
}
}
【讨论】：
这里是二叉搜索树在Java中的完整实现插入，搜索，countNodes，遍历，删除，空，最大和最小节点，找到父节点，打印所有叶子节点，获取级别，获取高度、获取深度、打印左视图、镜像视图
import java.util.NoSuchElementException;
import java.util.Scanner;
import org.junit.experimental.max.MaxCore;
class BSTNode {
BSTNode left = null;
BSTNode rigth = null;
int data = 0;
public BSTNode() {
super();
}
public BSTNode(int data) {
this.left = null;
this.rigth = null;
this.data = data;
}
@Override
public String toString() {
return "BSTNode [left=" + left + ", rigth=" + rigth + ", data=" + data + "]";
}
}
class BinarySearchTree {
BSTNode root = null;
public BinarySearchTree() {
}
public void insert(int data) {
BSTNode node = new BSTNode(data);
if (root == null) {
root = node;
return;
}
BSTNode currentNode = root;
BSTNode parentNode = null;
while (true) {
parentNode = currentNode;
if (currentNode.data == data)
throw new IllegalArgumentException("Duplicates nodes note allowed in Binary Search Tree");
if (currentNode.data > data) {
currentNode = currentNode.left;
if (currentNode == null) {
parentNode.left = node;
return;
}
} else {
currentNode = currentNode.rigth;
if (currentNode == null) {
parentNode.rigth = node;
return;
}
}
}
}
public int countNodes() {
return countNodes(root);
}
private int countNodes(BSTNode node) {
if (node == null) {
return 0;
} else {
int count = 1;
count += countNodes(node.left);
count += countNodes(node.rigth);
return count;
}
}
public boolean searchNode(int data) {
if (empty())
return empty();
return searchNode(data, root);
}
public boolean searchNode(int data, BSTNode node) {
if (node != null) {
if (node.data == data)
return true;
else if (node.data > data)
return searchNode(data, node.left);
else if (node.data < data)
return searchNode(data, node.rigth);
}
return false;
}
public boolean delete(int data) {
if (empty())
throw new NoSuchElementException("Tree is Empty");
BSTNode currentNode = root;
BSTNode parentNode = root;
boolean isLeftChild = false;
while (currentNode.data != data) {
parentNode = currentNode;
if (currentNode.data > data) {
isLeftChild = true;
currentNode = currentNode.left;
} else if (currentNode.data < data) {
isLeftChild = false;
currentNode = currentNode.rigth;
}
if (currentNode == null)
return false;
}
// CASE 1: node with no child
if (currentNode.left == null && currentNode.rigth == null) {
if (currentNode == root)
root = null;
if (isLeftChild)
parentNode.left = null;
else
parentNode.rigth = null;
}
// CASE 2: if node with only one child
else if (currentNode.left != null && currentNode.rigth == null) {
if (root == currentNode) {
root = currentNode.left;
}
if (isLeftChild)
parentNode.left = currentNode.left;
else
parentNode.rigth = currentNode.left;
} else if (currentNode.rigth != null && currentNode.left == null) {
if (root == currentNode)
root = currentNode.rigth;
if (isLeftChild)
parentNode.left = currentNode.rigth;
else
parentNode.rigth = currentNode.rigth;
}
// CASE 3: node with two child
else if (currentNode.left != null && currentNode.rigth != null) {
// Now we have to find minimum element in rigth sub tree
// that is called successor
BSTNode successor = getSuccessor(currentNode);
if (currentNode == root)
root = successor;
if (isLeftChild)
parentNode.left = successor;
else
parentNode.rigth = successor;
successor.left = currentNode.left;
}
return true;
}
private BSTNode getSuccessor(BSTNode deleteNode) {
BSTNode successor = null;
BSTNode parentSuccessor = null;
BSTNode currentNode = deleteNode.left;
while (currentNode != null) {
parentSuccessor = successor;
successor = currentNode;
currentNode = currentNode.left;
}
if (successor != deleteNode.rigth) {
parentSuccessor.left = successor.left;
successor.rigth = deleteNode.rigth;
}
return successor;
}
public int nodeWithMinimumValue() {
return nodeWithMinimumValue(root);
}
private int nodeWithMinimumValue(BSTNode node) {
if (node.left != null)
return nodeWithMinimumValue(node.left);
return node.data;
}
public int nodewithMaximumValue() {
return nodewithMaximumValue(root);
}
private int nodewithMaximumValue(BSTNode node) {
if (node.rigth != null)
return nodewithMaximumValue(node.rigth);
return node.data;
}
public int parent(int data) {
return parent(root, data);
}
private int parent(BSTNode node, int data) {
if (empty())
throw new IllegalArgumentException("Empty");
if (root.data == data)
throw new IllegalArgumentException("No Parent node found");
BSTNode parent = null;
BSTNode current = node;
while (current.data != data) {
parent = current;
if (current.data > data)
current = current.left;
else
current = current.rigth;
if (current == null)
throw new IllegalArgumentException(data + " is not a node in tree");
}
return parent.data;
}
public int sibling(int data) {
return sibling(root, data);
}
private int sibling(BSTNode node, int data) {
if (empty())
throw new IllegalArgumentException("Empty");
if (root.data == data)
throw new IllegalArgumentException("No Parent node found");
BSTNode cureent = node;
BSTNode parent = null;
boolean isLeft = false;
while (cureent.data != data) {
parent = cureent;
if (cureent.data > data) {
cureent = cureent.left;
isLeft = true;
} else {
cureent = cureent.rigth;
isLeft = false;
}
if (cureent == null)
throw new IllegalArgumentException("No Parent node found");
}
if (isLeft) {
if (parent.rigth != null) {
return parent.rigth.data;
} else
throw new IllegalArgumentException("No Sibling is there");
} else {
if (parent.left != null)
return parent.left.data;
else
throw new IllegalArgumentException("No Sibling is there");
}
}
public void leafNodes() {
if (empty())
throw new IllegalArgumentException("Empty");
leafNode(root);
}
private void leafNode(BSTNode node) {
if (node == null)
return;
if (node.rigth == null && node.left == null)
System.out.print(node.data + " ");
leafNode(node.left);
leafNode(node.rigth);
}
public int level(int data) {
if (empty())
throw new IllegalArgumentException("Empty");
return level(root, data, 1);
}
private int level(BSTNode node, int data, int level) {
if (node == null)
return 0;
if (node.data == data)
return level;
int result = level(node.left, data, level + 1);
if (result != 0)
return result;
result = level(node.rigth, data, level + 1);
return result;
}
public int depth() {
return depth(root);
}
private int depth(BSTNode node) {
if (node == null)
return 0;
else
return 1 + Math.max(depth(node.left), depth(node.rigth));
}
public int height() {
return height(root);
}
private int height(BSTNode node) {
if (node == null)
return 0;
else
return 1 + Math.max(height(node.left), height(node.rigth));
}
public void leftView() {
leftView(root);
}
private void leftView(BSTNode node) {
if (node == null)
return;
int height = height(node);
for (int i = 1; i <= height; i++) {
printLeftView(node, i);
}
}
private boolean printLeftView(BSTNode node, int level) {
if (node == null)
return false;
if (level == 1) {
System.out.print(node.data + " ");
return true;
} else {
boolean left = printLeftView(node.left, level - 1);
if (left)
return true;
else
return printLeftView(node.rigth, level - 1);
}
}
public void mirroeView() {
BSTNode node = mirroeView(root);
preorder(node);
System.out.println();
inorder(node);
System.out.println();
postorder(node);
System.out.println();
}
private BSTNode mirroeView(BSTNode node) {
if (node == null || (node.left == null && node.rigth == null))
return node;
BSTNode temp = node.left;
node.left = node.rigth;
node.rigth = temp;
mirroeView(node.left);
mirroeView(node.rigth);
return node;
}
public void preorder() {
preorder(root);
}
private void preorder(BSTNode node) {
if (node != null) {
System.out.print(node.data + " ");
preorder(node.left);
preorder(node.rigth);
}
}
public void inorder() {
inorder(root);
}
private void inorder(BSTNode node) {
if (node != null) {
inorder(node.left);
System.out.print(node.data + " ");
inorder(node.rigth);
}
}
public void postorder() {
postorder(root);
}
private void postorder(BSTNode node) {
if (node != null) {
postorder(node.left);
postorder(node.rigth);
System.out.print(node.data + " ");
}
}
public boolean empty() {
return root == null;
}
}
public class BinarySearchTreeTest {
public static void main(String[] l) {
System.out.println("Weleome to Binary Search Tree");
Scanner scanner = new Scanner(System.in);
boolean yes = true;
BinarySearchTree tree = new BinarySearchTree();
do {
System.out.println("\n1. Insert");
System.out.println("2. Search Node");
System.out.println("3. Count Node");
System.out.println("4. Empty Status");
System.out.println("5. Delete Node");
System.out.println("6. Node with Minimum Value");
System.out.println("7. Node with Maximum Value");
System.out.println("8. Find Parent node");
System.out.println("9. Count no of links");
System.out.println("10. Get the sibling of any node");
System.out.println("11. Print all the leaf node");
System.out.println("12. Get the level of node");
System.out.println("13. Depth of the tree");
System.out.println("14. Height of Binary Tree");
System.out.println("15. Left View");
System.out.println("16. Mirror Image of Binary Tree");
System.out.println("Enter Your Choice :: ");
int choice = scanner.nextInt();
switch (choice) {
case 1:
try {
System.out.println("Enter Value");
tree.insert(scanner.nextInt());
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
case 2:
System.out.println("Enter the node");
System.out.println(tree.searchNode(scanner.nextInt()));
break;
case 3:
System.out.println(tree.countNodes());
break;
case 4:
System.out.println(tree.empty());
break;
case 5:
try {
System.out.println("Enter the node");
System.out.println(tree.delete(scanner.nextInt()));
} catch (Exception e) {
System.out.println(e.getMessage());
}
case 6:
try {
System.out.println(tree.nodeWithMinimumValue());
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
case 7:
try {
System.out.println(tree.nodewithMaximumValue());
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
case 8:
try {
System.out.println("Enter the node");
System.out.println(tree.parent(scanner.nextInt()));
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
case 9:
try {
System.out.println(tree.countNodes() - 1);
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
case 10:
try {
System.out.println("Enter the node");
System.out.println(tree.sibling(scanner.nextInt()));
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
case 11:
try {
tree.leafNodes();
} catch (Exception e) {
System.out.println(e.getMessage());
}
case 12:
try {
System.out.println("Enter the node");
System.out.println("Level is : " + tree.level(scanner.nextInt()));
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
case 13:
try {
System.out.println(tree.depth());
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
case 14:
try {
System.out.println(tree.height());
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
case 15:
try {
tree.leftView();
System.out.println();
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
case 16:
try {
tree.mirroeView();
} catch (Exception e) {
System.out.println(e.getMessage());
}
break;
default:
break;
}
tree.preorder();
System.out.println();
tree.inorder();
System.out.println();
tree.postorder();
} while (yes);
scanner.close();
}
}
【讨论】：