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/**
* A symbol table implemented using a left-leaning red-black BST.
*
*/
import java.util.NoSuchElememtException;
public class RedBlackBST<Key extends Comparable<Key>, value> {
private static final boolean RED = true;
private static final boolean BLACK = false;
private Node root; // root of the BST
// BST helper node data type
private class Node {
private Key key; // key
private Value val; // associated data
private Node left, right; // links to left and right subtrees
private boolean color; // color of parent link
private int size; // subtree count
public Node(Key key, Value val, boolean color, int size) {
this.key = key;
this.val = val;
this.color = color;
this.size = size;
}
}
// Initializes an empty symbol table.
public RedBlackBST() {
//
}
/***********************
* Node helper methods *
* *
***********************/
// is node x red
private boolean isRed(Node x) {
if(x == null)
return false;
return x.color == RED;
}
// number of node in subtree rooted at x; 0 if x is null
private int size(Node x) {
if(x == null)
return 0;
return x.size;
}
// Returns the number of key-value pairs in this symbol table.
public int size() {
return size(root);
}
public boolean isEmpty() {
return root == null;
}
/************************
* Standard BST search. *
* *
************************/
// returns the value associated with the given key.
public Value get(Key key) {
if(key == null)
throw new IllegalArgumentException("argument to get() is null");
return get(root, key);
}
private Value get(Node x, Key key) {
while(x != null) {
int cmp = key.compareTo(x.key);
if(cmp < 0)
x = x.left;
else if(cmp > 0)
x = x.right;
else
return x.val;
}
return null;
}
// Does this symbol table contain the given key?
public boolean contains(Key key) {
return get(key) != null;
}
/*****************************
* Red-Black tree insertion. *
* *
*****************************/
// Inserts the specified key-value pair into the symbol table, overwriting the
// old value with the new value if the symbol table already contains the specified
// key.
// Deletes the specified key(and its associated key) from this symbol table if
// the specified value is `null`
public void put(Key key, Value val) {
if(key == null)
throw new IllegalArgumentException("first argument to put() is null");
if(val == null) {
delete(key);
return;
}
root = put(root, key, val);
root.color = BLACK;
}
// inserts the key-value pair in the subtree rooted at h
private Node put(Node h, Key key, Value val) {
if(h == null)
return new Node(key, val, RED, 1);
int cmp = key.compareTo(h.key);
if(cmp < 0)
h.left = put(h.left, key, val);
else if(cmp > 0)
h.right = put(h.right, key, val);
else
h.val = val;
// fix-up any right-leaning links
if(isRed(h.right) && !isRed(h.left))
h = rotateLeft(h);
if(isRed(h.left) && isRed(h.left.left))
h = rotateRight(h);
if(isRed(h.left) && isRed(h.right))
flipColors(h);
h.size = size(h.left) + size(h.right) + 1;
return h;
}
/*****************************
* Red-Black tree deletion. *
* *
*****************************/
// Removes the smallest key and associated value from the symbol table.
public void deleteMin() {
if(isEmpty())
throw new NoSuchElememtException("BST underflow");
// if both children of root are black, set root to red
if(!isRed(root.left) && !isRed(root.right))
root.color = RED;
root = deleteMin(root);
if(!isEmpty())
root.color = BLACK;
}
// delete the key-value pair with the minimum key rooted at h
private Node deleteMin(Node h) {
if(h.left == null)
return null;
if(!isRed(h.left) && !isRed(h.left.left))
h = moveRedLeft(h);
h.left = deleteMin(h.left);
return balance(h);
}
// Removes the largest key and associated value from the symbol table.
public void deleteMax() {
if(isEmpty())
throw new NoSuchElememtException("BST underflow");
if(!isRed(root.left) && !isRed(root.right))
root.color = RED;
root = deleteMax(root);
if(!isEmpty())
root.color = BLACK;
}
// delete the key-value pair with the maximum key rooted at h
private Node deleteMax(Node h) {
if(isRed(h.left))
h = rotateRight(h);
if(h.right == null)
return null;
if(!isRed(h.right) && !isRed(h.right.left))
h = moveRedRight(h);
h.right = deleteMax(h.right);
return balance(h);
}
// Removes the specified key and its associated value from this symbol table
public void delete(Key key) {
if(key == null)
throw new IllegalArgumentException("argument to delete() is null");
if(!contains(key))
return;
if(!isRed(root.left) && !isRed(root.right))
root.color = RED;
root = delete(root, key);
if(!isEmpty())
root.color = BLACK;
}
// delete the key-value pair with the given key rooted at h
private Node delete(Node h, Key key) {
if(key.compareTo(h.key) < 0) {
if(!isRed(h.left) && !isRed(h.left.left))
h = moveRedLeft(h);
h.left = delete(h.left, key);
} else {
if(isRed(h.left))
h = rotateRight(h);
if(key.compareTo(h.key) == 0 && (h.right == null))
return null;
if(!isRed(h.right) && !isRed(h.right.left))
h = moveRedRight(h);
if(key.compareTo(h.key) == 0) {
Node x = min(h.right);
h.key = x.key;
h.val = x.val;
h.right = deleteMin(h.right);
} else {
h.right = delete(h.right, key);
}
}
return balance(h);
}
/*******************************
* Red-Black helper functions. *
* *
*******************************/
// make a left-leaning link lean to the right
private Node rotateRight(Node h) {
Node x = h.left;
h.left = x.right;
x.right = h;
x.color = x.right.color;
x.right.color = RED;
x.size = h.size;
h.size = size(h.left) + size(h.right) + 1;
return x;
}
// make a right-leaning link lean to the left
private Node rotateLeft(Node h) {
Node x = h.right;
h.right = x.left;
x.left = h;
x.color = x.left.color;
x.left.color = RED;
x.size = h.size;
h.size = size(h.left) + size(h.right) + 1;
return x;
}
// flip the colors of a node and its two children
private void flipColors(Node h) {
h.color = !h.color;
h.left.color = !h.left.color;
h.right.color = !h.right.color;
}
// Assuming that h is red and both h.left and h.left.left are black, make h.left
// or one of its children red.
private Node moveRedLeft(Node h) {
flipColors(h);
if(isRed(h.right.left)) {
h.right = rotateRight(h.right);
h = rotateLeft(h);
flipColors(h);
}
return h;
}
// Assuming that h is red and both h.right and h.right.left are black, make h.right
// or one of its children red.
private Node moveRedRight(Node h) {
flipColors(h);
if(isRed(h.left.left)) {
h = rotateRight(h);
flipColors(h);
}
return h;
}
// restore red-black tree invariant
private Node balance(Node h) {
if(isRed(h.right))
h = rotateLeft(h);
if(isRed(h.left) && isRed(h.left.left))
h = rotateRight(h);
if(isRed(h.left) && isRed(h.right))
flipColors(h);
h.size = size(h.left) + size(h.right) + 1;
return h;
}
/**********************
* Utility functions *
* *
**********************/
// Returns the height of the BST
public int height() {
return height(root);
}
private int height(Node x) {
if(x == null)
return -1;
return Math.max(height(x.left), height(x.right)) + 1;
}
/*********************************
* Ordered symbol tqble methods *
* *
*********************************/
// Returns the smallest key in the symbol table.
public Key min() {
if(isEmpty())
trow new NoSuchElememtException("calls min() with empty symbol table");
return min(root).key;
}
// the smallest key in subtree rooted at x;
private Node min(Node x) {
if(x.left == null)
return x;
else
return min(x.left);
}
// Returns the largest key in the symbol table.
public Key max() {
if(isEmpty())
throw new NoSuchElememtException("calls max() with empty symbol table");
return max(root).key;
}
// the largest key in the subtree rooted at x;
private Node max(Node x) {
if(x.right == null)\
return x;
else
return max(x.right);
}
// Returns the largest key in the symbol table less than or equal to `key`
public Key floor(Key key) {
if(key == null)
throw new IllegalArgumentException("argument to floor() is null");
if(isEmpty())
throw new NoSuchElememtException("calls floor() with empty symbol table");
Node x = floor(root, key);
if(x == null)
return null;
else
return x.key;
}
// the largest key in the subtree rooted at x less than or equal to the given key
private Node floor(Node x, Key key) {
if(x == null)
return null;
int cmp = key.compareTo(x.key);
if(cmp == 0)
return x;
if(cmp < 0)
return floor(x.left, key);
Node t = floor(x.right, key);
if(t != null)
return t;
else
return x;
}
// Returns the smallest key in the symbol table greater than or equal to `key`
public Key ceiling(Key key) {
if(key == null)
throw new IllegalArgumentException("argument to ceiling() is null");
if(isEmpty())
throw new NoSuchElememtException("calls ceiling() with empty symbol table");
Node x = ceiling(root, key);
if(x == null)
return null;
else
return x.key;
}
// the smallest key in the subtree rooted at x greater than or equal to the given key.
private Node ceiling(Node x, Key key) {
if(x == null)
return null;
int cmp = key.compareTo(x.key);
if(cmp == 0)
return x
if(cmp > 0)
return ceiling(x.right, key);
Node t = ceiling(x.left, key);
if(t != null)
return t;
else
return x;
}
// Return the key in the symbol table whose rank is `k`
public Key select(int k) {
if(k < 0 || k >= size)
throw new IllegalArgumentException("argument to select() is invalid: " + k);
Node x = select(root, k);
return x.key;
}
// the key of rank k in the subtree rooted at x
private Node select(Node x, int k) {
int t = size(x.left);
if(t > k)
return select(x.left, k);
else if(t < k)
return select(x.right, k - t - 1);
else
return x;
}
// Returns the number of keys in the symbol table strictly less than `key`
public int rank(Key key) {
if(key == null)
throw new IllegalArgumentException("argument to rank() is null");
return rank(key, root);
}
// number of keys less than key in the subtree rooted at x.
private int rank(Key key, Node x) {
if(x == null)
return 0;
int cmp = key.compareTo(x.key);
if(cmp < 0)
return rank(key, x.left);
else if(cmp > 0)
return size(x.left) + rank(key, x.right) + 1;
else
return size(x.left);
}
/*********************************
* Range count and range search *
* *
*********************************/
// Returns all keys in the symbol table as an `Iterable`
// To iterate over all of the keys in the symbol table named `st`
public Iterable<Key> keys() {
if(isEmpty())
return new Queue<Key>();
return keys(min(), max());
}
// Returns all keys in the symbol table in the given range, as an `Iterable`
public Iterable<Key> keys(Key low, Key high) {
if(low == null)
throw new IllegalArgumentException("first argument to keys() is null");
if(high == null)
throw new IllegalArgumentException("second argument to keys() is null");
Queue<Key> queue = new Queue<Key>();
keys(root, queue, low, high);
return queue;
}
// add the keys bewteen low and high in the subtree rooted at x.
private void keys(Node x, Queue<Key> queue, Key low, Key high) {
if(x == null)
return;
int cmpLow = low.compareTo(x.key);
int cmpHigh = high.compareTo(x.key);
if(cmpLow < 0 && cmpHigh >= 0)
queue.enqueue(x.key);
if(cmpHigh > 0)
keys(x.right, queue, low, high);
}
// Returns the number of keys in the symbol table in the given range
public int size(Key low, Key high) {
if(low == null)
throw new IllegalArgumentException("first argument to size() is null");
if(high == null)
throw new IllegalArgumentException("second argument to size() is null");
if(low.compareTo(high) > 0)
return 0;
if(contains(high))
return rank(high) - rank(low) + 1;
else
return rank(high) - rank(low);
}
// check integrity of red-black tree data structure.
private boolean check() {
if(!isBST())
StdOut.println("Not in symmetric order!");
if(!isSizeConsistent)
StdOut.println("Subtree counts not consistent");
if(!isRankConsistent)
StdOut.println("Ranks not consistent");
if(!is23())
StdOut.println("Not a 2-3 tree");
if(!isBalanced())
StdOut.println("Not balanced");
return isBST() && isSizeConsistent() && isRankConsistent() && is23() && isBalanced();
}
// does this binary tree satisfy symmetric order?
// (this test also ensures that data structure is a binary tree since order is strict)
private boolean isBST() {
return isBST(root, null, null);
}
// is the tree rooted at x a BST with all keys strictly between min and max
// (if min or max is null, treat as empty constraint)
private boolean isBST(Node x, Key min, Key max) {
if(x == null)
return true;
if(min != null && x.key.compareTo(min) <= 0)
return false;
if(max != null && x.key.compareTo(max) >= 0)
return false;
return isBST(x.left, min, x.key) && isBST(x.right, x.key, max);
}
// are the size fields correct?
private boolean isSizeConsistent() {
return isSizeConsistent(root);
}
private boolean isSizeConsistent(Node x) {
if(x == null)
return true;
if(x.size != size(x.left) + size(x.right) + 1)
return false;
return isSizeConsistent(x.left) && isSizeConsistent(x.right);
}
// check that ranks are consistent
private boolean isRankConsistent() {
for(int i = 0; i < size(); i++) {
if(i != rank(select(i)))
return false;
}
for(Key key: keys()) {
if(key.compareTo(select(rank(key))) != 0)
return false;
}
return true;
}
// Does the tree have no red right links, and at most one(left) red links in a
// row on any path?
private boolean is23() {
return is23(root);
}
private boolean is23(Node x) {
if(x == null)
return true;
if(isRed(x.right))
return false;
if(x != root && isRed(x) && isRed(x.left))
return false;
return is23(x.left) && is23(x.right);
}
// do all paths from root to leaf have some number of black edges?
private boolean isBalanced() {
int black = 0;
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
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();
}
}