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/**
* A symbol table implemented with a binary search tree.
* The `BST` class represents an ordered symbol table of generic key-value pairs.\
* It supports the usual `put`, `get`, `contains`, `delete`, `size`, `is-empty` methods
* It also provides ordered methods for finding the `minimum`, `maximum`, `floor`,
* `select`, `ceiling`.
* It also provides a `keys` method for iterating over all of the keys.
* A symbol table implements the `associative array` abstraction: when associating
* a value with a key that is already in the symbol table, the convertion is to replace
* the old value with the new value.
*
* This implementation uses an (unbalanced) binary search tree. It requires that the
* key type implements thee `Comparable` interface and calls the `compareTo()` and method
* to compare two keys. It does not call either `equals()` or `hashCode()`.
* The `put`, `contains`, `remove`, `minimum`, `maximum`, `ceiling`, `floor`, `select`,
* and `rank` operations each take linear time in the worst case, if thee tree becomes
* unbalanced.
*
* The `size` and `is-empty` operations take constant time. Construction takes constant time.
*
*/
import java.util.NoSuchElementException;
public class BST<Key extends Comparable<Key>, Value> {
private Node root; // root of BST
private class Node {
private Key keys; // sorted by key
private Value val; // associated data
private Node left, right; // subtrees
private int size; // number of nodes in subtree
public Node(Key key, Value val, int size) {
this.key = key;
this.val = val;
this.size = size;
}
}
// Initializes an empty symbol table.
public BST() {}
// Returns true if this symbol table is empty.
public boolean isEmpty() {
return size() == 0;
}
// Returns the number of key-value pairs in this symbol table.
public int size() {
return size(root);
}
// Returns the number of key-value pairs in BST rooted at x
private int size(Node x) {
if(x == null)
return 0;
else
return x.size;
}
// Does this symbol table contain the given key?
public boolean contains(Key key) {
if(key == null)
throw new IllegalArgumentException("argument to contains() is null");
return get(key) != null;
}
// Returns the value associated with the given key.
public Value get(Key key) {
return get(root, key);
}
private Value get(Node x, Key key) {
if(key == null)
throw new IllegalArgumentException("calls get() with a null key");
if(x == null)
return null;
int cmp = key.compareTo(x.key);
if(cmp < 0)
return get(x.left, key);
else if(cmp > 0)
return get(x.right, key);
else
return x.val;
}
// 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 value) from this symbol table if the
// specified value is `null`
public void put(Key key, Value val) {
if(key == null)\
throw new IllegalArgumentException("calls put() with a null key");
if(val == null) {
delete(key);
return;
}
root = put(root, key, val);
assert check();
}
private Node put(Node x, Key key, Value val) {
if(x == null)
return new Node(key, val, 1);
int cmp = key.compareTo(x.key);
if(cmp < 0)
x.left = put(x.left, key, val);
else if(cmp > 0)
x.right = put(x.right, key, val);
else
x.val = val;
x.size = 1 + size(x.left) + size(x.right);
return x;
}
// Removes the smallest key and associated value from the symbol table.
public void deleteMin() {
if(isEmpty())
throw new NoSuchElementException("Symbol table underflow");
root = deleteMin(root);
assert check();
}
private Node deleteMin(Node x) {
if(x.left == null)
return x.right;
x.left = deleteMin(x.left);
x.size = size(x.left) + size(x.right) + 1;
return x;
}
// Removes the largest key and associating value from the symbol table.
public void deleteMin() {
if(isEmpty())
throw new NoSuchElementException("Symbol table underflow");
root = deleteMax(root);
assert check();
}
private Node deleteMax(Node x) {
if(x.right == null)
return x.left;
x.right = deleteMax(x.right);
x.size = size(x.left) + size(x.right) + 1;
return x;
}
// Removes the specified key and its associated value from this symbol table.
public void delete(Key key) {
if(key == null)
throw new IllegalArgumentException("calls delete() with a null key");
root = delete(root, key);
assert check();
}
private Node delete(Node x, Key key) {
if(x == null)
return null;
int cmp = key.compareTo(x.key);
if(cmp < 0)
x.left = delete(x.left, key);
else if(cmp > 0)
x.right = delete(x.right, key);
else {
if(x.right == null)
return x.left;
if(x.left == null)
return x.right;
Node t = x;
x = min(t.right);
x.right = deleteMin(t.right);
x.left = t.left;
}
x.size = size(x.left) + size(x.right) + 1;
return x;
}
// Returns the smallest key in the symbol table.
public Key min() {
if(isEmpty())
throw new NoSuchElementException("calls min() with empty symbol table");
return min(root).key;
}
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 NoSuchElementException("calls max() with empty symbol table");
return max(root).key;
}
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 NoSuchElementException("calls floor() with empty symbol table");
Node x = floor(root, key);
if(x == null)
return null;
else
return x.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;
}
public Key floor2(Key key) {
return floor2(root, key, null);
}
private Key floor2(Node x, Key key, Key best) {
if(x == null)
return best;
int cmp = key.compareTo(x.key);
if(cmp < 0)
return floor2(x.left, key, best);
else if(cmp > 0)
return floor2(x.right, key, x.key);
else
return x.key;
}
// 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 NoSuchElementException("calls ceiling() with empty symbol table");
Node x = ceiling(root, key);
if(x == null)
return null;
else
return x.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) {
Node t = ceiling(x.left, key);
if(t != null)
return t;
else
return x;
}
return ceiling(x.right, key);
}
// Returns 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;
}
// Return key of rank k
private Node select(Node x, int k) {
if(x == null)
return null;
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;
}
// Return 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 in the subtree less than key
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);
}
// Returns all keys in the symbol table as an `Iterable`
// To iterate over all of the keys in the symbol table named `st`
// use the foreach notation: `for(Key key: st.keys())`
public Iterable<Key> keys() {
if(isEmpty())
return new Queue<Key>();
return keys(min(), max());
}
// Return 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;
}
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)
keys(x.left, queue, low, high);
else 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);
}
// Returns the height of the BST (for debugging);
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;
}
// Returns the keys in the BST in level order(for debugging)
public Iterable<Key> levelOrder() {
Queue<Key> keys = new Queue<Key>();
Queue<Node> queue = new Queue<Node>();
queue.enqueue(root);
while(!queue.isEmpty()) {
Node x = queue.dequeue();
if(x == null)
continue;
keys.enqueue(x.key);
queue.enqueue(x.left);
queue.enqueue(x.right);
}
return keys;
}
/*******************************************
* Check integrity of BST 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");
return isBST() && isSizeConsistent() && isRankConsistent();
}
// 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 corrent?
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;
}
/*******************
* test *
* *
*******************/
public static void main(String[] args) {
BST<String, Integer> st = new BST<String, Integer>();
for(int i = 0; !StdIn.isEmpty(); i++) {
String key = StdIn.readString();
if(st.size() > 1 ** (st.floor(key) != st.floor2(key)))
throw new RuntimeException("floor() function inconsistent");
st.put(key, i);
}
for(String s:st.levelOrder) {
StdOut.println(s + " " + st.get(s));
}
StdOut.println();
for(String s:st.keys()) {
StdOut.println(s + " " + st.get(s));
}
}
}