Treap
随机数生成器
Treap的功能介绍
- 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
- void printTree() → Print tree in sorted order
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 {}
Treap的编程实现
/**
* Implements a treap.
* Note that all "matching" is based on the compareTo method.
*/
public class Treap<T extends Comparable<? super T>> {
private TreapNode<T> root;
private TreapNode<T> nullNode;
/**
* Construct the treap.
*/
public Treap() {
nullNode = new TreapNode<>(null);
nullNode.left = nullNode.right = nullNode;
nullNode.priority = Integer.MAX_VALUE;
root = nullNode;
}
/**
* Insert into the tree. Does nothing if x is already present.
* @param x the item to insert.
*/
public void insert(T x) {
root = insert(x, root);
}
/**
* Remove from the tree. Does nothing if x is not found.
* @param x the item to remove.
*/
public void remove(T x) {
root = remove(x, root);
}
/**
* Find the smallest item in the tree.
* @return the smallest item, or throw UnderflowException if empty.
*/
public T findMin() {
if(isEmpty()) {
throw new UnderflowException();
}
TreapNode<T> ptr = root;
while(ptr.left != nullNode) {
ptr = ptr.left;
}
return ptr.element;
}
/**
* Find the largest item in the tree.
* @return the largest item, or throw UnderflowException if empty.
*/
public T findMax() {
if(isEmpty()) {
throw new UnderflowException();
}
TreapNode<T> ptr = root;
while(ptr.right != nullNode) {
ptr = ptr.right;
}
return ptr.element;
}
/**
* Find an item in the tree.
* @param x the item to search for.
* @return true if x is found.
*/
public boolean contains(T x) {
TreapNode<T> current = root;
nullNode.element = x;
while(true) {
int compareResult = x.compareTo(current.element);
if(compareResult < 0) {
current = current.left;
} else if(compareResult > 0) {
current = current.right;
} else {
return current != nullNode;
}
}
}
/**
* 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;
}
/**
* Print the tree contents in sorted order.
*/
public void printTree() {
if(isEmpty()) {
System.out.println("Empty tree");
} else {
printTree(root);
}
}
/**
* Internal method to insert into a subtree.
* @param x the item to insert.
* @param t the node that roots the subtree.
* @return the new root of the subtree.
*/
private TreapNode<T> insert(T x, TreapNode<T> t) {
if(t == nullNode) {
return new TreapNode<>(x, nullNode, nullNode);
}
int compareResult = x.compareTo(t.element);
if(compareResult < 0) {
t.left = insert(x, t.left);
if(t.left.priority < t.priority) {
t = rotateWithLeftChild(t);
}
} else if(compareResult > 0) {
t.right = insert(x, t.right);
if(t.right.priority < t.priority) {
t = rotateWithRightChild(t);
}
}
// Otherwise, it's a duplicate; do nothing
return t;
}
/**
* Internal method to remove from a subtree.
* @param x the item to remove.
* @param t the node that roots the subtree.
* @return the new root of the subtree.
*/
private TreapNode<T> remove(T x, TreapNode<T> t) {
if(t != nullNode) {
int compareResult = x.compareTo(t.element);
if(compareResult < 0) {
t.left = remove(x, t.left);
} else if(compareResult > 0) {
t.right = remove(x, t.right);
} else {
// Match found
if(t.left.priority < t.right.priority) {
t = rotateWithLeftChild(t);
} else {
t = rotateWithRightChild(t);
}
if(t != nullNode) { // Continue on down
t = remove(x, t);
} else {
t.left = nullNode; // At a leaf
}
}
}
return t;
}
/**
* Internal method to print a subtree in sorted order.
* @param t the node that roots the tree.
*/
private void printTree(TreapNode<T> t) {
if(t != t.left) {
printTree(t.left);
System.out.println(t.element.toString());
printTree(t.right);
}
}
/**
* Rotate binary tree node with left child.
*/
private TreapNode<T> rotateWithLeftChild(TreapNode<T> k2) {
TreapNode<T> k1 = k2.left;
k2.left = k1.right;
k1.right = k2;
return k1;
}
/**
* Rotate binary tree node with right child.
*/
private TreapNode<T> rotateWithRightChild(TreapNode<T> k1) {
TreapNode<T> k2 = k1.right;
k1.right = k2.left;
k2.left = k1;
return k2;
}
private static class TreapNode<T> {
TreapNode(T theElement) {
this(theElement, null, null);
}
TreapNode(T theElement, TreapNode<T> lt, TreapNode<T> rt) {
element = theElement;
left = lt;
right = rt;
priority = randomObj.randomInt();
}
// Friendly data; accessible by other package routines
T element; // The data in the node
TreapNode<T> left; // Left child
TreapNode<T> right; // Right child
int priority; // Priority
private static Random randomObj = new Random();
}
}
测试
public class TreapTest{
public static void main(String[] args) {
Treap<Integer> t = new Treap<>();
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(NUMS < 40) {
t.printTree();
}
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);
}
}
}
}
