/******************************************************************************
* Compilation: javac BSTDraw.java
* Execution: java BSTDraw
* Dependencies: StdIn.java StdOut.java Queue.java
* Data files: https://algs4.cs.princeton.edu/32bst/tinyST.txt
*
* A symbol table implemented with a binary search tree.
*
* % more tinyST.txt
* S E A R C H E X A M P L E
*
* % java BSTDraw < tinyST.txt
* A 8
* C 4
* E 12
* H 5
* L 11
* M 9
* P 10
* R 3
* S 0
* X 7
*
******************************************************************************/
import java.util.NoSuchElementException;
import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
import edu.princeton.cs.algs4.Queue;
import edu.princeton.cs.algs4.StdDraw;
/**
* The {@code BSTDraw} class represents an ordered symbol table of generic
* key-value pairs.
* It supports the usual <em>put</em>, <em>get</em>, <em>contains</em>,
* <em>delete</em>, <em>size</em>, and <em>is-empty</em> methods.
* It also provides ordered methods for finding the <em>minimum</em>,
* <em>maximum</em>, <em>floor</em>, <em>select</em>, <em>ceiling</em>.
* It also provides a <em>keys</em> method for iterating over all of the keys.
* A symbol table implements the <em>associative array</em> abstraction:
* when associating a value with a key that is already in the symbol table,
* the convention is to replace the old value with the new value.
* Unlike {@link java.util.Map}, this class uses the convention that
* values cannot be {@code null}—setting the
* value associated with a key to {@code null} is equivalent to deleting the key
* from the symbol table.
* <p>
* It requires that
* the key type implements the {@code Comparable} interface and calls the
* {@code compareTo()} and method to compare two keys. It does not call either
* {@code equals()} or {@code hashCode()}.
* <p>
* This implementation uses an (unbalanced) <em>binary search tree</em>.
* The <em>put</em>, <em>contains</em>, <em>remove</em>, <em>minimum</em>,
* <em>maximum</em>, <em>ceiling</em>, <em>floor</em>, <em>select</em>, and
* <em>rank</em> operations each take Θ(<em>n</em>) time in the worst
* case, where <em>n</em> is the number of key-value pairs.
* The <em>size</em> and <em>is-empty</em> operations take Θ(1) time.
* The keys method takes Θ(<em>n</em>) time in the worst case.
* Construction takes Θ(1) time.
* <p>
* For alternative implementations of the symbol table API, see {@link ST},
* {@link BinarySearchST}, {@link SequentialSearchST}, {@link RedBlackBSTDraw},
* {@link SeparateChainingHashST}, and {@link LinearProbingHashST},
* For additional documentation, see
* <a href="https://algs4.cs.princeton.edu/32bst">Section 3.2</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class BSTDraw<Key extends Comparable<Key>, Value> {
private Node root; // root of BSTDraw
private int k; // auxiliary variable for drawing
private class Node {
private Key key; // sorted by key
private Value val; // associated data
private Node left, right; // left and right subtrees
private int size; // number of nodes in subtree
private double xc, yc; // for drawing
public Node(Key key, Value val, int size) {
this.key = key;
this.val = val;
this.size = size;
}
}
/**
* Initializes an empty symbol table.
*/
public BSTDraw() {
}
/**
* Returns true if this symbol table is empty.
* @return {@code true} if this symbol table is empty; {@code false} otherwise
*/
public boolean isEmpty() {
return size() == 0;
}
/**
* Returns the number of key-value pairs in this symbol table.
* @return the number of key-value pairs in this symbol table
*/
public int size() {
return size(root);
}
// return number of key-value pairs in BSTDraw 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?
*
* @param key the key
* @return {@code true} if this symbol table contains {@code key} and
* {@code false} otherwise
* @throws IllegalArgumentException if {@code key} is {@code null}
*/
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.
*
* @param key the key
* @return the value associated with the given key if the key is in the symbol table
* and {@code null} if the key is not in the symbol table
* @throws IllegalArgumentException if {@code key} is {@code null}
*/
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 {@code null}.
*
* @param key the key
* @param val the value
* @throws IllegalArgumentException if {@code key} is {@code 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.
*
* @throws NoSuchElementException if the symbol table is empty
*/
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 associated value from the symbol table.
*
* @throws NoSuchElementException if the symbol table is empty
*/
public void deleteMax() {
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
* (if the key is in this symbol table).
*
* @param key the key
* @throws IllegalArgumentException if {@code key} is {@code null}
*/
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.
*
* @return the smallest key in the symbol table
* @throws NoSuchElementException if the symbol table is empty
*/
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.
*
* @return the largest key in the symbol table
* @throws NoSuchElementException if the symbol table is empty
*/
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 {@code key}.
*
* @param key the key
* @return the largest key in the symbol table less than or equal to {@code key}
* @throws NoSuchElementException if there is no such key
* @throws IllegalArgumentException if {@code key} is {@code null}
*/
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) throw new NoSuchElementException("argument to floor() is too small");
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) {
Key x = floor2(root, key, null);
if (x == null) throw new NoSuchElementException("argument to floor() is too small");
else return x;
}
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 {@code key}.
*
* @param key the key
* @return the smallest key in the symbol table greater than or equal to {@code key}
* @throws NoSuchElementException if there is no such key
* @throws IllegalArgumentException if {@code key} is {@code null}
*/
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) throw new NoSuchElementException("argument to floor() is too large");
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);
}
/**
* Return the key in the symbol table of a given {@code rank}.
* This key has the property that there are {@code rank} keys in
* the symbol table that are smaller. In other words, this key is the
* ({@code rank}+1)st smallest key in the symbol table.
*
* @param rank the order statistic
* @return the key in the symbol table of given {@code rank}
* @throws IllegalArgumentException unless {@code rank} is between 0 and
* <em>n</em>–1
*/
public Key select(int rank) {
if (rank < 0 || rank >= size()) {
throw new IllegalArgumentException("argument to select() is invalid: " + rank);
}
return select(root, rank);
}
// Return key in BSTDraw rooted at x of given rank.
// Precondition: rank is in legal range.
private Key select(Node x, int rank) {
if (x == null) return null;
int leftSize = size(x.left);
if (leftSize > rank) return select(x.left, rank);
else if (leftSize < rank) return select(x.right, rank - leftSize - 1);
else return x.key;
}
/**
* Return the number of keys in the symbol table strictly less than {@code key}.
*
* @param key the key
* @return the number of keys in the symbol table strictly less than {@code key}
* @throws IllegalArgumentException if {@code key} is {@code null}
*/
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 1 + size(x.left) + rank(key, x.right);
else return size(x.left);
}
/**
* Returns all keys in the symbol table as an {@code Iterable}.
* To iterate over all of the keys in the symbol table named {@code st},
* use the foreach notation: {@code for (Key key : st.keys())}.
*
* @return all keys in the symbol table
*/
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 {@code Iterable}.
*
* @param lo minimum endpoint
* @param hi maximum endpoint
* @return all keys in the symbol table between {@code lo}
* (inclusive) and {@code hi} (inclusive)
* @throws IllegalArgumentException if either {@code lo} or {@code hi}
* is {@code null}
*/
public Iterable<Key> keys(Key lo, Key hi) {
if (lo == null) throw new IllegalArgumentException("first argument to keys() is null");
if (hi == null) throw new IllegalArgumentException("second argument to keys() is null");
Queue<Key> queue = new Queue<Key>();
keys(root, queue, lo, hi);
return queue;
}
private void keys(Node x, Queue<Key> queue, Key lo, Key hi) {
if (x == null) return;
int cmplo = lo.compareTo(x.key);
int cmphi = hi.compareTo(x.key);
if (cmplo < 0) keys(x.left, queue, lo, hi);
if (cmplo <= 0 && cmphi >= 0) queue.enqueue(x.key);
if (cmphi > 0) keys(x.right, queue, lo, hi);
}
/**
* Returns the number of keys in the symbol table in the given range.
*
* @param lo minimum endpoint
* @param hi maximum endpoint
* @return the number of keys in the symbol table between {@code lo}
* (inclusive) and {@code hi} (inclusive)
* @throws IllegalArgumentException if either {@code lo} or {@code hi}
* is {@code null}
*/
public int size(Key lo, Key hi) {
if (lo == null) throw new IllegalArgumentException("first argument to size() is null");
if (hi == null) throw new IllegalArgumentException("second argument to size() is null");
if (lo.compareTo(hi) > 0) return 0;
if (contains(hi)) return rank(hi) - rank(lo) + 1;
else return rank(hi) - rank(lo);
}
/**
* Returns the height of the BSTDraw (for debugging).
*
* @return the height of the BSTDraw (a 1-node tree has height 0)
*/
public int height() {
return height(root);
}
private int height(Node x) {
if (x == null) return -1;
return 1 + Math.max(height(x.left), height(x.right));
}
/**
* Returns the keys in the BSTDraw in level order (for debugging).
*
* @return the keys in the BSTDraw in level order traversal
*/
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 BSTDraw data structure.
***************************************************************************/
private boolean check() {
if (!isBSTDraw()) StdOut.println("Not in symmetric order");
if (!isSizeConsistent()) StdOut.println("Subtree counts not consistent");
if (!isRankConsistent()) StdOut.println("Ranks not consistent");
return isBSTDraw() && isSizeConsistent() && isRankConsistent();
}
// does this binary tree satisfy symmetric order?
// Note: this test also ensures that data structure is a binary tree since order is strict
private boolean isBSTDraw() {
return isBSTDraw(root, null, null);
}
// is the tree rooted at x a BSTDraw with all keys strictly between min and max
// (if min or max is null, treat as empty constraint)
// Credit: Bob Dondero's elegant solution
private boolean isBSTDraw(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 isBSTDraw(x.left, min, x.key) && isBSTDraw(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;
}
/***************************************************************************
* Drawing routines.
***************************************************************************/
public void draw(double y, double lineWidth, double nodeSize)
{
StdDraw.clear(StdDraw.LIGHT_GRAY);
k = 0;
setCoords(root, y);
StdDraw.setPenColor(StdDraw.BLACK);
StdDraw.setPenRadius(lineWidth);
drawLines(root);
StdDraw.setPenColor(StdDraw.WHITE);
drawNodes(root, nodeSize);
}
public void setCoords(Node x, double d)
{
if (x == null) return;
setCoords(x.left, d - .04);
x.xc = (16.0 / 9.0)*(2 + k++)/(size() + 3); // ad hoc scaling
x.yc = d - .04;
setCoords(x.right, d - .04);
}
public void drawLines(Node x)
{
if (x == null) return;
drawLines(x.left);
if (x.left != null)
{
StdDraw.setPenColor(StdDraw.BLACK);
StdDraw.line(x.xc, x.yc, x.left.xc, x.left.yc);
}
if (x.right != null)
{
StdDraw.setPenColor(StdDraw.BLACK);
StdDraw.line(x.xc, x.yc, x.right.xc, x.right.yc);
}
drawLines(x.right);
}
public void drawNodes(Node x, double nodeSize)
{
if (x == null) return;
drawNodes(x.left, nodeSize);
StdDraw.filledCircle(x.xc, x.yc, nodeSize);
drawNodes(x.right, nodeSize);
}
public void drawPrepare(int width) {
StdDraw.setCanvasSize(width, (int)Math.round((9.0 / 16.0) * width));
double ymax = 1.0;
double xmax = 16.0 / 9.0; // ad hoc scaling
StdDraw.setXscale(0.0, xmax);
StdDraw.setYscale(0.0, ymax);
}
/***************************************************************************
* Other parameters.
***************************************************************************/
public int iplP() {
return iplP(root);
}
public int iplP(Node x) {
if (x == null) return 0;
return x.size - 1 + iplP(x.left) + iplP(x.right);
}
/***************************************************************************
* Unit tests the {@code BSTDraw} data type.
*
* @param args the command-line arguments
***************************************************************************/
public static void main(String[] args) {
BSTDraw<String, Integer> st = new BSTDraw<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();
// for (String s : st.levelOrder())
// StdOut.println(s + " " + st.get(s));
StdOut.println("N = " + st.size());
StdOut.println("Plain height = " + st.height());
StdOut.println("IPL = " + st.iplP());
st.drawPrepare(800);
StdDraw.enableDoubleBuffering();
st.draw(.95, .003, .004);
StdDraw.show();
}
}
/******************************************************************************
* Copyright 2002-2020, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/