561 lines
18 KiB
Java
561 lines
18 KiB
Java
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/*************************************************************************
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* Compilation: javac RedBlackBST.java
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* Execution: java RedBlackBST < input.txt
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* Dependencies: StdIn.java StdOut.java
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* Data files: http://algs4.cs.princeton.edu/33balanced/tinyST.txt
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*
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* A symbol table implemented using a left-leaning red-black BST.
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* This is the 2-3 version.
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*
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* % more tinyST.txt
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* S E A R C H E X A M P L E
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*
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* % java RedBlackBST < tinyST.txt
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* A 8
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* C 4
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* E 12
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* H 5
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* L 11
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* M 9
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* P 10
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* R 3
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* S 0
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* X 7
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*
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*************************************************************************/
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import java.util.NoSuchElementException;
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import edu.princeton.cs.introcs.StdIn;
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import edu.princeton.cs.introcs.StdOut;
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public class RedBlackBST<Key extends Comparable<Key>, Value> {
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private static final boolean RED = true;
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private static final boolean BLACK = false;
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private Node root; // root of the BST
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// BST helper node data type
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private class Node {
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private Key key; // key
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private Value val; // associated data
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private Node left, right; // links to left and right subtrees
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private boolean color; // color of parent link
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private int N; // subtree count
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public Node(Key key, Value val, boolean color, int N) {
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this.key = key;
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this.val = val;
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this.color = color;
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this.N = N;
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}
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}
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/*************************************************************************
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* Node helper methods
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*************************************************************************/
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// is node x red; false if x is null ?
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private boolean isRed(Node x) {
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if (x == null) return false;
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return (x.color == RED);
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}
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// number of node in subtree rooted at x; 0 if x is null
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private int size(Node x) {
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if (x == null) return 0;
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return x.N;
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}
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/*************************************************************************
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* Size methods
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*************************************************************************/
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// return number of key-value pairs in this symbol table
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public int size() { return size(root); }
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// is this symbol table empty?
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public boolean isEmpty() {
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return root == null;
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}
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/*************************************************************************
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* Standard BST search
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*************************************************************************/
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// value associated with the given key; null if no such key
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public Value get(Key key) { return get(root, key); }
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// value associated with the given key in subtree rooted at x; null if no such key
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private Value get(Node x, Key key) {
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while (x != null) {
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int cmp = key.compareTo(x.key);
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if (cmp < 0) x = x.left;
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else if (cmp > 0) x = x.right;
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else return x.val;
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}
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return null;
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}
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// is there a key-value pair with the given key?
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public boolean contains(Key key) {
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return (get(key) != null);
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}
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// is there a key-value pair with the given key in the subtree rooted at x?
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private boolean contains(Node x, Key key) {
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return (get(x, key) != null);
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}
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/*************************************************************************
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* Red-black insertion
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*************************************************************************/
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// insert the key-value pair; overwrite the old value with the new value
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// if the key is already present
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public void put(Key key, Value val) {
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root = put(root, key, val);
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root.color = BLACK;
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assert check();
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}
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// insert the key-value pair in the subtree rooted at h
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private Node put(Node h, Key key, Value val) {
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if (h == null) return new Node(key, val, RED, 1);
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int cmp = key.compareTo(h.key);
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if (cmp < 0) h.left = put(h.left, key, val);
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else if (cmp > 0) h.right = put(h.right, key, val);
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else h.val = val;
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// fix-up any right-leaning links
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if (isRed(h.right) && !isRed(h.left)) h = rotateLeft(h);
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if (isRed(h.left) && isRed(h.left.left)) h = rotateRight(h);
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if (isRed(h.left) && isRed(h.right)) flipColors(h);
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h.N = size(h.left) + size(h.right) + 1;
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return h;
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}
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/*************************************************************************
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* Red-black deletion
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*************************************************************************/
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// delete the key-value pair with the minimum key
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public void deleteMin() {
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if (isEmpty()) throw new NoSuchElementException("BST underflow");
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// if both children of root are black, set root to red
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if (!isRed(root.left) && !isRed(root.right))
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root.color = RED;
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root = deleteMin(root);
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if (!isEmpty()) root.color = BLACK;
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assert check();
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}
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// delete the key-value pair with the minimum key rooted at h
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private Node deleteMin(Node h) {
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if (h.left == null)
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return null;
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if (!isRed(h.left) && !isRed(h.left.left))
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h = moveRedLeft(h);
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h.left = deleteMin(h.left);
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return balance(h);
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}
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// delete the key-value pair with the maximum key
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public void deleteMax() {
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if (isEmpty()) throw new NoSuchElementException("BST underflow");
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// if both children of root are black, set root to red
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if (!isRed(root.left) && !isRed(root.right))
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root.color = RED;
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root = deleteMax(root);
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if (!isEmpty()) root.color = BLACK;
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assert check();
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}
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// delete the key-value pair with the maximum key rooted at h
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private Node deleteMax(Node h) {
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if (isRed(h.left))
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h = rotateRight(h);
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if (h.right == null)
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return null;
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if (!isRed(h.right) && !isRed(h.right.left))
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h = moveRedRight(h);
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h.right = deleteMax(h.right);
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return balance(h);
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}
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// delete the key-value pair with the given key
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public void delete(Key key) {
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if (!contains(key)) {
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System.err.println("symbol table does not contain " + key);
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return;
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}
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// if both children of root are black, set root to red
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if (!isRed(root.left) && !isRed(root.right))
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root.color = RED;
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root = delete(root, key);
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if (!isEmpty()) root.color = BLACK;
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assert check();
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}
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// delete the key-value pair with the given key rooted at h
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private Node delete(Node h, Key key) {
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assert contains(h, key);
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if (key.compareTo(h.key) < 0) {
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if (!isRed(h.left) && !isRed(h.left.left))
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h = moveRedLeft(h);
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h.left = delete(h.left, key);
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}
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else {
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if (isRed(h.left))
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h = rotateRight(h);
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if (key.compareTo(h.key) == 0 && (h.right == null))
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return null;
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if (!isRed(h.right) && !isRed(h.right.left))
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h = moveRedRight(h);
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if (key.compareTo(h.key) == 0) {
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Node x = min(h.right);
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h.key = x.key;
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h.val = x.val;
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// h.val = get(h.right, min(h.right).key);
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// h.key = min(h.right).key;
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h.right = deleteMin(h.right);
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}
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else h.right = delete(h.right, key);
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}
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return balance(h);
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}
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/*************************************************************************
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* red-black tree helper functions
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*************************************************************************/
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// make a left-leaning link lean to the right
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private Node rotateRight(Node h) {
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assert (h != null) && isRed(h.left);
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Node x = h.left;
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h.left = x.right;
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x.right = h;
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x.color = x.right.color;
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x.right.color = RED;
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x.N = h.N;
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h.N = size(h.left) + size(h.right) + 1;
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return x;
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}
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// make a right-leaning link lean to the left
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private Node rotateLeft(Node h) {
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assert (h != null) && isRed(h.right);
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Node x = h.right;
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h.right = x.left;
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x.left = h;
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x.color = x.left.color;
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x.left.color = RED;
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x.N = h.N;
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h.N = size(h.left) + size(h.right) + 1;
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return x;
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}
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// flip the colors of a node and its two children
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private void flipColors(Node h) {
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// h must have opposite color of its two children
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assert (h != null) && (h.left != null) && (h.right != null);
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assert (!isRed(h) && isRed(h.left) && isRed(h.right))
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|| (isRed(h) && !isRed(h.left) && !isRed(h.right));
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h.color = !h.color;
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h.left.color = !h.left.color;
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h.right.color = !h.right.color;
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}
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// Assuming that h is red and both h.left and h.left.left
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// are black, make h.left or one of its children red.
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private Node moveRedLeft(Node h) {
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assert (h != null);
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assert isRed(h) && !isRed(h.left) && !isRed(h.left.left);
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flipColors(h);
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if (isRed(h.right.left)) {
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h.right = rotateRight(h.right);
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h = rotateLeft(h);
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}
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return h;
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}
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// Assuming that h is red and both h.right and h.right.left
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// are black, make h.right or one of its children red.
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private Node moveRedRight(Node h) {
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assert (h != null);
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assert isRed(h) && !isRed(h.right) && !isRed(h.right.left);
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flipColors(h);
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if (isRed(h.left.left)) {
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h = rotateRight(h);
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}
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return h;
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}
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// restore red-black tree invariant
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private Node balance(Node h) {
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assert (h != null);
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if (isRed(h.right)) h = rotateLeft(h);
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if (isRed(h.left) && isRed(h.left.left)) h = rotateRight(h);
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if (isRed(h.left) && isRed(h.right)) flipColors(h);
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h.N = size(h.left) + size(h.right) + 1;
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return h;
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}
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/*************************************************************************
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* Utility functions
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*************************************************************************/
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// height of tree (1-node tree has height 0)
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public int height() { return height(root); }
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private int height(Node x) {
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if (x == null) return -1;
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return 1 + Math.max(height(x.left), height(x.right));
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}
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/*************************************************************************
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* Ordered symbol table methods.
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*************************************************************************/
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// the smallest key; null if no such key
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public Key min() {
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if (isEmpty()) return null;
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return min(root).key;
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}
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// the smallest key in subtree rooted at x; null if no such key
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private Node min(Node x) {
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assert x != null;
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if (x.left == null) return x;
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else return min(x.left);
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}
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// the largest key; null if no such key
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public Key max() {
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if (isEmpty()) return null;
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return max(root).key;
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}
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// the largest key in the subtree rooted at x; null if no such key
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private Node max(Node x) {
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assert x != null;
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if (x.right == null) return x;
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else return max(x.right);
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}
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// the largest key less than or equal to the given key
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public Key floor(Key key) {
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Node x = floor(root, key);
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if (x == null) return null;
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else return x.key;
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}
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// the largest key in the subtree rooted at x less than or equal to the given key
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private Node floor(Node x, Key key) {
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if (x == null) return null;
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int cmp = key.compareTo(x.key);
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if (cmp == 0) return x;
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if (cmp < 0) return floor(x.left, key);
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Node t = floor(x.right, key);
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if (t != null) return t;
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else return x;
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}
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// the smallest key greater than or equal to the given key
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public Key ceiling(Key key) {
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Node x = ceiling(root, key);
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if (x == null) return null;
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else return x.key;
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}
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// the smallest key in the subtree rooted at x greater than or equal to the given key
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private Node ceiling(Node x, Key key) {
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if (x == null) return null;
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int cmp = key.compareTo(x.key);
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if (cmp == 0) return x;
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if (cmp > 0) return ceiling(x.right, key);
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Node t = ceiling(x.left, key);
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if (t != null) return t;
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else return x;
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}
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// the key of rank k
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public Key select(int k) {
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if (k < 0 || k >= size()) return null;
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Node x = select(root, k);
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return x.key;
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}
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// the key of rank k in the subtree rooted at x
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private Node select(Node x, int k) {
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assert x != null;
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assert k >= 0 && k < size(x);
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int t = size(x.left);
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if (t > k) return select(x.left, k);
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else if (t < k) return select(x.right, k-t-1);
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else return x;
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}
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// number of keys less than key
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public int rank(Key key) {
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return rank(key, root);
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}
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// number of keys less than key in the subtree rooted at x
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private int rank(Key key, Node x) {
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if (x == null) return 0;
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int cmp = key.compareTo(x.key);
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if (cmp < 0) return rank(key, x.left);
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else if (cmp > 0) return 1 + size(x.left) + rank(key, x.right);
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else return size(x.left);
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}
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/***********************************************************************
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* Range count and range search.
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***********************************************************************/
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// all of the keys, as an Iterable
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public Iterable<Key> keys() {
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return keys(min(), max());
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}
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// the keys between lo and hi, as an Iterable
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public Iterable<Key> keys(Key lo, Key hi) {
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Queue<Key> queue = new Queue<Key>();
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// if (isEmpty() || lo.compareTo(hi) > 0) return queue;
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keys(root, queue, lo, hi);
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return queue;
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}
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// add the keys between lo and hi in the subtree rooted at x
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// to the queue
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private void keys(Node x, Queue<Key> queue, Key lo, Key hi) {
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if (x == null) return;
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int cmplo = lo.compareTo(x.key);
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int cmphi = hi.compareTo(x.key);
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if (cmplo < 0) keys(x.left, queue, lo, hi);
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if (cmplo <= 0 && cmphi >= 0) queue.enqueue(x.key);
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if (cmphi > 0) keys(x.right, queue, lo, hi);
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}
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// number keys between lo and hi
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public int size(Key lo, Key hi) {
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if (lo.compareTo(hi) > 0) return 0;
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if (contains(hi)) return rank(hi) - rank(lo) + 1;
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else return rank(hi) - rank(lo);
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}
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/*************************************************************************
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* Check integrity of red-black BST data structure
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*************************************************************************/
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private boolean check() {
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if (!isBST()) StdOut.println("Not in symmetric order");
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if (!isSizeConsistent()) StdOut.println("Subtree counts not consistent");
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if (!isRankConsistent()) StdOut.println("Ranks not consistent");
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if (!is23()) StdOut.println("Not a 2-3 tree");
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if (!isBalanced()) StdOut.println("Not balanced");
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return isBST() && isSizeConsistent() && isRankConsistent() && is23() && isBalanced();
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}
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// does this binary tree satisfy symmetric order?
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// Note: this test also ensures that data structure is a binary tree since order is strict
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private boolean isBST() {
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return isBST(root, null, null);
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}
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// is the tree rooted at x a BST with all keys strictly between min and max
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// (if min or max is null, treat as empty constraint)
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// Credit: Bob Dondero's elegant solution
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private boolean isBST(Node x, Key min, Key max) {
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if (x == null) return true;
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if (min != null && x.key.compareTo(min) <= 0) return false;
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if (max != null && x.key.compareTo(max) >= 0) return false;
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return isBST(x.left, min, x.key) && isBST(x.right, x.key, max);
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}
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// are the size fields correct?
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private boolean isSizeConsistent() { return isSizeConsistent(root); }
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private boolean isSizeConsistent(Node x) {
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if (x == null) return true;
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if (x.N != size(x.left) + size(x.right) + 1) return false;
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return isSizeConsistent(x.left) && isSizeConsistent(x.right);
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}
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// check that ranks are consistent
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private boolean isRankConsistent() {
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for (int i = 0; i < size(); i++)
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if (i != rank(select(i))) return false;
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for (Key key : keys())
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if (key.compareTo(select(rank(key))) != 0) return false;
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return true;
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}
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// Does the tree have no red right links, and at most one (left)
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// red links in a row on any path?
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private boolean is23() { return is23(root); }
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private boolean is23(Node x) {
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if (x == null) return true;
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if (isRed(x.right)) return false;
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if (x != root && isRed(x) && isRed(x.left))
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return false;
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return is23(x.left) && is23(x.right);
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}
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// do all paths from root to leaf have same number of black edges?
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private boolean isBalanced() {
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int black = 0; // number of black links on path from root to min
|
|
Node x = root;
|
|
while (x != null) {
|
|
if (!isRed(x)) black++;
|
|
x = x.left;
|
|
}
|
|
return isBalanced(root, black);
|
|
}
|
|
|
|
// does every path from the root to a leaf have the given number of black links?
|
|
private boolean isBalanced(Node x, int black) {
|
|
if (x == null) return black == 0;
|
|
if (!isRed(x)) black--;
|
|
return isBalanced(x.left, black) && isBalanced(x.right, black);
|
|
}
|
|
|
|
|
|
/*****************************************************************************
|
|
* Test client
|
|
*****************************************************************************/
|
|
public static void main(String[] args) {
|
|
RedBlackBST<String, Integer> st = new RedBlackBST<String, Integer>();
|
|
for (int i = 0; !StdIn.isEmpty(); i++) {
|
|
String key = StdIn.readString();
|
|
st.put(key, i);
|
|
}
|
|
for (String s : st.keys())
|
|
StdOut.println(s + " " + st.get(s));
|
|
StdOut.println();
|
|
}
|
|
}
|