RedBlackTree原理分析
RedBlackTree功能介绍
- void insert(x) → Insert x
- void remove(x) → Remove x (unimplemented)
- 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
- void printTree() → Print 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 {}
RedBlackTree的编程实现
/**
* Implements a red-black tree.
* Note that all "matching" is based on the compareTo method.
*/
public class RedBlackTree<T extends Comparable<? super T>> {
private RedBlackNode<T> header;
private RedBlackNode<T> nullNode;
private static final int BLACK = 1; // BLACK must be 1
private static final int RED = 0;
// Used in insert routine and its helpers
private RedBlackNode<T> current;
private RedBlackNode<T> parent;
private RedBlackNode<T> grand;
private RedBlackNode<T> great;
/**
* Construct the tree.
*/
public RedBlackTree() {
nullNode = new RedBlackNode<>(null);
nullNode.left = nullNode.right = nullNode;
header = new RedBlackNode<>(null);
header.left = header.right = nullNode;
}
/**
* Compare item and t.element, using compareTo, with caveat that if t is header, then item is always larger.
* This routine is called if is possible that t is header.
* If it is not possible for t to be header, use compareTo directly.
*/
private int compare(T item, RedBlackNode<T> t) {
if(t == header) {
return 1;
} else {
return item.compareTo(t.element);
}
}
/**
* Insert into the tree.
* @param item the item to insert.
*/
public void insert(T item) {
current = parent = grand = header;
nullNode.element = item;
while(compare(item, current) != 0) {
great = grand; grand = parent; parent = current;
current = compare(item, current) < 0 ? current.left : current.right;
// Check if two red children; fix if so
if(current.left.color == RED && current.right.color == RED) {
handleReorient(item);
}
}
// Insertion fails if already present
if(current != nullNode) {
return;
}
current = new RedBlackNode<>(item, nullNode, nullNode);
// Attach to parent
if(compare(item, parent) < 0) {
parent.left = current;
} else {
parent.right = current;
}
handleReorient(item);
}
/**
* Remove from the tree.
* @param x the item to remove.
* @throws UnsupportedOperationException if called.
*/
public void remove(T x) {
throw new UnsupportedOperationException();
}
/**
* Find the smallest item the tree.
* @return the smallest item or throw UnderflowExcepton if empty.
*/
public T findMin() {
if(isEmpty()) {
throw new UnderflowException();
}
RedBlackNode<T> itr = header.right;
while(itr.left != nullNode) {
itr = itr.left;
}
return itr.element;
}
/**
* Find the largest item in the tree.
* @return the largest item or throw UnderflowExcepton if empty.
*/
public T findMax() {
if(isEmpty()) {
throw new UnderflowException();
}
RedBlackNode<T> itr = header.right;
while(itr.right != nullNode) {
itr = itr.right;
}
return itr.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) {
nullNode.element = x;
current = header.right;
while (true) {
if(x.compareTo(current.element) < 0) {
current = current.left;
} else if(x.compareTo(current.element) > 0) {
current = current.right;
} else if(current != nullNode) {
return true;
} else {
return false;
}
}
}
/**
* Make the tree logically empty.
*/
public void makeEmpty() {
header.right = nullNode;
}
/**
* Print the tree contents in sorted order.
*/
public void printTree() {
if(isEmpty()) {
System.out.println("Empty tree");
} else {
printTree(header.right);
}
}
/**
* Internal method to print a subtree in sorted order.
* @param t the node that roots the subtree.
*/
private void printTree(RedBlackNode<T> t) {
if(t != nullNode) {
printTree(t.left);
System.out.println(t.element);
printTree(t.right);
}
}
/**
* Test if the tree is logically empty.
* @return true if empty, false otherwise.
*/
public boolean isEmpty() {
return header.right == nullNode;
}
/**
* Internal routine that is called during an insertion if a node has two red children. Performs flip and rotations.
* @param item the item being inserted.
*/
private void handleReorient(T item) {
// Do the color flip
current.color = RED;
current.left.color = BLACK;
current.right.color = BLACK;
if(parent.color == RED) { // Have to rotate
grand.color = RED;
if((compare(item, grand) < 0) != (compare(item, parent) < 0)) {
parent = rotate(item, grand); // Start dbl rotate
}
current = rotate(item, great);
current.color = BLACK;
}
header.right.color = BLACK; // Make root black
}
/**
* Internal routine that performs a single or double rotation.
* Because the result is attached to the parent, there are four cases.
* Called by handleReorient.
* @param item the item in handleReorient.
* @param parent the parent of the root of the rotated subtree.
* @return the root of the rotated subtree.
*/
private RedBlackNode<T> rotate(T item, RedBlackNode<T> parent) {
if(compare(item, parent) < 0) {
return parent.left = compare(item, parent.left) < 0 ?
rotateWithLeftChild(parent.left) : // LL
rotateWithRightChild(parent.left) ; // LR
} else {
return parent.right = compare(item, parent.right) < 0 ?
rotateWithLeftChild(parent.right) : // RL
rotateWithRightChild(parent.right); // RR
}
}
/**
* Rotate binary tree node with left child.
*/
private RedBlackNode<T> rotateWithLeftChild(RedBlackNode<T> k2) {
RedBlackNode<T> k1 = k2.left;
k2.left = k1.right;
k1.right = k2;
return k1;
}
/**
* Rotate binary tree node with right child.
*/
private RedBlackNode<T> rotateWithRightChild(RedBlackNode<T> k1) {
RedBlackNode<T> k2 = k1.right;
k1.right = k2.left;
k2.left = k1;
return k2;
}
private static class RedBlackNode<T> {
RedBlackNode(T theElement) {
this(theElement, null, null);
}
RedBlackNode(T theElement, RedBlackNode<T> lt, RedBlackNode<T> rt) {
element = theElement;
left = lt;
right = rt;
color = RedBlackTree.BLACK;
}
T element; // The data in the node
RedBlackNode<T> left; // Left child
RedBlackNode<T> right; // Right child
int color; // Color
}
}
测试
public class RedBlackTreeTest{
public static void main(String[] args) {
RedBlackTree<Integer> t = new RedBlackTree<>();
final int NUMS = 400000;
final int GAP = 35461;
System.out.println("Checking... (no more output means success)");
for(int i = GAP; i != 0; i = (i+GAP) % NUMS) {
t.insert(i);
}
if(t.findMin() != 1 || t.findMax() != NUMS-1) {
System.out.println("FindMin or FindMax error!");
}
for(int i = 1; i < NUMS; i++) {
if(!t.contains(i)) {
System.out.println("Find error1!");
}
}
}
}
