SplayTree
SplayTree功能介绍
- void insert(x) → Insert x
- void remove(x) → Remove x
- boolean contains(x) → Return true if x is found
- Comparable findMin() → Return smallest item
- Comparable findMax() → Return largest item
- boolean isEmpty() → Return true if empty; else false
- void makeEmpty() → Remove all items
异常类
当集合容器为空的时候就不能够删除或获取元素，这时就会出现一种异常，命名为UnderflowException：
/**
* Exception class for access in empty containers
* such as stacks, queues, and priority queues.
*/
public class UnderflowException extends RuntimeException {}
SplayTree的编程实现
/**
* Implements a top-down splay tree.
* Note that all "matching" is based on the compareTo method.
*/
public class SplayTree<T extends Comparable<? super T>> {
/**
* Construct the tree.
*/
public SplayTree() {
nullNode = new BinaryNode<T>(null);
nullNode.left = nullNode.right = nullNode;
root = nullNode;
}
private BinaryNode<T> newNode = null; // Used between different inserts
/**
* Insert into the tree.
* @param x the item to insert.
*/
public void insert(T x) {
if(newNode == null) {
newNode = new BinaryNode<T>(null);
}
newNode.element = x;
if(root == nullNode) {
newNode.left = newNode.right = nullNode;
root = newNode;
} else {
root = splay(x, root);
int compareResult = x.compareTo(root.element);
if(compareResult < 0) {
newNode.left = root.left;
newNode.right = root;
root.left = nullNode;
root = newNode;
} else if(compareResult > 0) {
newNode.right = root.right;
newNode.left = root;
root.right = nullNode;
root = newNode;
} else {
return; // No duplicates
}
}
newNode = null; // So next insert will call new
}
/**
* Remove from the tree.
* @param x the item to remove.
*/
public void remove(T x) {
if(!contains(x)) {
return;
}
BinaryNode<T> newTree;
// If x is found, it will be splayed to the root by contains
if(root.left == nullNode) {
newTree = root.right;
} else {
// Find the maximum in the left subtree
// Splay it to the root; and then attach right child
newTree = root.left;
newTree = splay(x, newTree);
newTree.right = root.right;
}
root = newTree;
}
/**
* Find the smallest item in the tree.
* Not the most efficient implementation (uses two passes), but has correct amortized behavior.
* A good alternative is to first call find with parameter smaller than any item in the tree, then call findMin.
* @return the smallest item or throw UnderflowException if empty.
*/
public T findMin() {
if(isEmpty()) {
throw new UnderflowException();
}
BinaryNode<T> ptr = root;
while(ptr.left != nullNode) {
ptr = ptr.left;
}
root = splay(ptr.element, root);
return ptr.element;
}
/**
* Find the largest item in the tree.
* Not the most efficient implementation (uses two passes), but has correct amortized behavior.
* A good alternative is to first call find with parameter larger than any item in the tree, then call findMax.
* @return the largest item or throw UnderflowException if empty.
*/
public T findMax() {
if(isEmpty()) {
throw new UnderflowException();
}
BinaryNode<T> ptr = root;
while(ptr.right != nullNode) {
ptr = ptr.right;
}
root = splay(ptr.element, root);
return ptr.element;
}
/**
* Find an item in the tree.
* @param x the item to search for.
* @return true if x is found; otherwise false.
*/
public boolean contains(T x) {
if(isEmpty()) {
return false;
}
root = splay(x, root);
return root.element.compareTo(x) == 0;
}
/**
* Make the tree logically empty.
*/
public void makeEmpty() {
root = nullNode;
}
/**
* Test if the tree is logically empty.
* @return true if empty, false otherwise.
*/
public boolean isEmpty() {
return root == nullNode;
}
private BinaryNode<T> header = new BinaryNode<T>(null); // For splay
/**
* Internal method to perform a top-down splay.
* The last accessed node becomes the new root.
* @param x the target item to splay around.
* @param t the root of the subtree to splay.
* @return the subtree after the splay.
*/
private BinaryNode<T> splay(T x, BinaryNode<T> t) {
BinaryNode<T> leftTreeMax, rightTreeMin;
header.left = header.right = nullNode;
leftTreeMax = rightTreeMin = header;
nullNode.element = x; // Guarantee a match
while (true) {
int compareResult = x.compareTo(t.element);
if(compareResult < 0) {
if( x.compareTo(t.left.element) < 0) {
t = rotateWithLeftChild(t);
}
if(t.left == nullNode) {
break;
}
// Link Right
rightTreeMin.left = t;
rightTreeMin = t;
t = t.left;
} else if(compareResult > 0) {
if( x.compareTo(t.right.element) > 0) {
t = rotateWithRightChild(t);
}
if(t.right == nullNode) {
break;
}
// Link Left
leftTreeMax.right = t;
leftTreeMax = t;
t = t.right;
} else {
break;
}
}
leftTreeMax.right = t.left;
rightTreeMin.left = t.right;
t.left = header.right;
t.right = header.left;
return t;
}
/**
* Rotate binary tree node with left child.
* For AVL trees, this is a single rotation for case 1.
*/
private static <T> BinaryNode<T> rotateWithLeftChild(BinaryNode<T> k2) {
BinaryNode<T> k1 = k2.left;
k2.left = k1.right;
k1.right = k2;
return k1;
}
/**
* Rotate binary tree node with right child.
* For AVL trees, this is a single rotation for case 4.
*/
private static <T> BinaryNode<T> rotateWithRightChild(BinaryNode<T> k1 ) {
BinaryNode<T> k2 = k1.right;
k1.right = k2.left;
k2.left = k1;
return k2;
}
// Basic node stored in unbalanced binary search trees
private static class BinaryNode<T> {
BinaryNode(T theElement) {
this(theElement, null, null);
}
BinaryNode(T theElement, BinaryNode<T> lt, BinaryNode<T> rt) {
element = theElement;
left = lt;
right = rt;
}
T element; // The data in the node
BinaryNode<T> left; // Left child
BinaryNode<T> right; // Right child
}
private BinaryNode<T> root;
private BinaryNode<T> nullNode;
}
SplayTree测试
public class SplayTreeTest {
public static void main(String [] args) {
SplayTree<Integer> t = new SplayTree<>();
final int NUMS = 40000;
final int GAP = 307;
System.out.println("Checking... (no bad output means success)");
for(int i = GAP; i != 0; i = (i+GAP) % NUMS) {
t.insert(i);
}
System.out.println("Insert completely");
for(int i = 1; i < NUMS; i += 2) {
t.remove(i);
}
System.out.println("Remove completely");
if(t.findMin() != 2 || t.findMax() != NUMS-2) {
System.out.println("FindMin or FindMax error!");
}
for(int i = 2; i < NUMS; i += 2) {
if(!t.contains(i)) {
System.out.println("Error: find fails for " + i);
}
}
for(int i = 1; i < NUMS; i += 2) {
if(t.contains(i)) {
System.out.println("Error: Found deleted item " + i);
}
}
}
}
