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/******************************************************************************
* Compilation: javac BinarySearchST.java
* Execution: java BinarySearchST
* Dependencies: StdIn.java StdOut.java
* Data files: https://algs4.cs.princeton.edu/31elementary/tinyST.txt
*
* Symbol table implementation with binary search in an ordered array.
*
* % more tinyST.txt
* S E A R C H E X A M P L E
*
* % java BinarySearchST < tinyST.txt
* A 8
* C 4
* E 12
* H 5
* L 11
* M 9
* P 10
* R 3
* S 0
* X 7
*
******************************************************************************/
package edu.princeton.cs.algs4;
import java.util.NoSuchElementException;
/**
* The {@code BST} class represents an ordered symbol table of generic
* key-value pairs.
* It supports the usual put, get, contains,
* delete, size, and is-empty methods.
* It also provides ordered methods for finding the minimum,
* maximum, floor, select, and 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 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.
*
* This implementation uses a sorted array. 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()}.
* The put and remove operations each take linear time in
* the worst case; the contains, ceiling, floor,
* and rank operations take logarithmic time; the size,
* is-empty, minimum, maximum, and select
* operations take constant time. Construction takes constant time.
*
* For additional documentation, see Section 3.1 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
* For other implementations, see {@link ST}, {@link BST},
* {@link SequentialSearchST}, {@link RedBlackBST},
* {@link SeparateChainingHashST}, and {@link LinearProbingHashST},
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*/
public class BinarySearchST, Value> {
private static final int INIT_CAPACITY = 2;
private Key[] keys;
private Value[] vals;
private int n = 0;
/**
* Initializes an empty symbol table.
*/
public BinarySearchST() {
this(INIT_CAPACITY);
}
/**
* Initializes an empty symbol table with the specified initial capacity.
* @param capacity the maximum capacity
*/
public BinarySearchST(int capacity) {
keys = (Key[]) new Comparable[capacity];
vals = (Value[]) new Object[capacity];
}
// resize the underlying arrays
private void resize(int capacity) {
assert capacity >= n;
Key[] tempk = (Key[]) new Comparable[capacity];
Value[] tempv = (Value[]) new Object[capacity];
for (int i = 0; i < n; i++) {
tempk[i] = keys[i];
tempv[i] = vals[i];
}
vals = tempv;
keys = tempk;
}
/**
* 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 n;
}
/**
* 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;
}
/**
* 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 in this symbol table.
*
* @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) {
if (key == null) throw new IllegalArgumentException("argument to get() is null");
if (isEmpty()) return null;
int i = rank(key);
if (i < n && keys[i].compareTo(key) == 0) return vals[i];
return null;
}
/**
* Returns the number of keys in this 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");
int lo = 0, hi = n-1;
while (lo <= hi) {
int mid = lo + (hi - lo) / 2;
int cmp = key.compareTo(keys[mid]);
if (cmp < 0) hi = mid - 1;
else if (cmp > 0) lo = mid + 1;
else return mid;
}
return lo;
}
/**
* 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("first argument to put() is null");
if (val == null) {
delete(key);
return;
}
int i = rank(key);
// key is already in table
if (i < n && keys[i].compareTo(key) == 0) {
vals[i] = val;
return;
}
// insert new key-value pair
if (n == keys.length) resize(2*keys.length);
for (int j = n; j > i; j--) {
keys[j] = keys[j-1];
vals[j] = vals[j-1];
}
keys[i] = key;
vals[i] = val;
n++;
assert check();
}
/**
* Removes the specified key and associated value from this symbol table
* (if the key is in the 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("argument to delete() is null");
if (isEmpty()) return;
// compute rank
int i = rank(key);
// key not in table
if (i == n || keys[i].compareTo(key) != 0) {
return;
}
for (int j = i; j < n-1; j++) {
keys[j] = keys[j+1];
vals[j] = vals[j+1];
}
n--;
keys[n] = null; // to avoid loitering
vals[n] = null;
// resize if 1/4 full
if (n > 0 && n == keys.length/4) resize(keys.length/2);
assert check();
}
/**
* Removes the smallest key and associated value from this symbol table.
*
* @throws NoSuchElementException if the symbol table is empty
*/
public void deleteMin() {
if (isEmpty()) throw new NoSuchElementException("Symbol table underflow error");
delete(min());
}
/**
* Removes the largest key and associated value from this symbol table.
*
* @throws NoSuchElementException if the symbol table is empty
*/
public void deleteMax() {
if (isEmpty()) throw new NoSuchElementException("Symbol table underflow error");
delete(max());
}
/***************************************************************************
* Ordered symbol table methods.
***************************************************************************/
/**
* Returns the smallest key in this symbol table.
*
* @return the smallest key in this symbol table
* @throws NoSuchElementException if this symbol table is empty
*/
public Key min() {
if (isEmpty()) throw new NoSuchElementException("called min() with empty symbol table");
return keys[0];
}
/**
* Returns the largest key in this symbol table.
*
* @return the largest key in this symbol table
* @throws NoSuchElementException if this symbol table is empty
*/
public Key max() {
if (isEmpty()) throw new NoSuchElementException("called max() with empty symbol table");
return keys[n-1];
}
/**
* Return the kth smallest key in this symbol table.
*
* @param k the order statistic
* @return the {@code k}th smallest key in this symbol table
* @throws IllegalArgumentException unless {@code k} is between 0 and
* n–1
*/
public Key select(int k) {
if (k < 0 || k >= size()) {
throw new IllegalArgumentException("called select() with invalid argument: " + k);
}
return keys[k];
}
/**
* Returns the largest key in this symbol table less than or equal to {@code key}.
*
* @param key the key
* @return the largest key in this 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");
int i = rank(key);
if (i < n && key.compareTo(keys[i]) == 0) return keys[i];
if (i == 0) return null;
else return keys[i-1];
}
/**
* Returns the smallest key in this symbol table greater than or equal to {@code key}.
*
* @param key the key
* @return the smallest key in this 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");
int i = rank(key);
if (i == n) return null;
else return keys[i];
}
/**
* Returns the number of keys in this symbol table in the specified range.
*
* @param lo minimum endpoint
* @param hi maximum endpoint
* @return the number of keys in this 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 all keys in this 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 this symbol table
*/
public Iterable keys() {
return keys(min(), max());
}
/**
* Returns all keys in this symbol table in the given range,
* as an {@code Iterable}.
*
* @param lo minimum endpoint
* @param hi maximum endpoint
* @return all keys in this symbol table between {@code lo}
* (inclusive) and {@code hi} (inclusive)
* @throws IllegalArgumentException if either {@code lo} or {@code hi}
* is {@code null}
*/
public Iterable 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 queue = new Queue();
if (lo.compareTo(hi) > 0) return queue;
for (int i = rank(lo); i < rank(hi); i++)
queue.enqueue(keys[i]);
if (contains(hi)) queue.enqueue(keys[rank(hi)]);
return queue;
}
/***************************************************************************
* Check internal invariants.
***************************************************************************/
private boolean check() {
return isSorted() && rankCheck();
}
// are the items in the array in ascending order?
private boolean isSorted() {
for (int i = 1; i < size(); i++)
if (keys[i].compareTo(keys[i-1]) < 0) return false;
return true;
}
// check that rank(select(i)) = i
private boolean rankCheck() {
for (int i = 0; i < size(); i++)
if (i != rank(select(i))) return false;
for (int i = 0; i < size(); i++)
if (keys[i].compareTo(select(rank(keys[i]))) != 0) return false;
return true;
}
/**
* Unit tests the {@code BinarySearchST} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
BinarySearchST st = new BinarySearchST();
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));
}
}
/******************************************************************************
* Copyright 2002-2018, 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.
******************************************************************************/