363 lines
11 KiB
Java
363 lines
11 KiB
Java
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/*************************************************************************
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* Compilation: javac BST.java
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* Execution: java BST
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* Dependencies: StdIn.java StdOut.java Queue.java
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* Data files: http://algs4.cs.princeton.edu/32bst/tinyST.txt
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*
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* A symbol table implemented with a binary search tree.
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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 BST < 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 BST<Key extends Comparable<Key>, Value> {
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private Node root; // root of BST
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private class Node {
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private Key key; // sorted by key
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private Value val; // associated data
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private Node left, right; // left and right subtrees
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private int N; // number of nodes in subtree
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public Node(Key key, Value val, int N) {
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this.key = key;
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this.val = val;
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this.N = N;
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}
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}
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// is the symbol table empty?
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public boolean isEmpty() {
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return size() == 0;
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}
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// return number of key-value pairs in BST
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public int size() {
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return size(root);
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}
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// return number of key-value pairs in BST rooted at x
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private int size(Node x) {
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if (x == null) return 0;
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else return x.N;
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}
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/***********************************************************************
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* Search BST for given key, and return associated value if found,
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* return null if not found
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***********************************************************************/
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// does there exist a key-value pair with 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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// return value associated with the given key, or null if no such key exists
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public Value get(Key key) {
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return get(root, key);
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}
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private Value get(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 get(x.left, key);
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else if (cmp > 0) return get(x.right, key);
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else return x.val;
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}
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/***********************************************************************
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* Insert key-value pair into BST
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* If key already exists, update with new value
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***********************************************************************/
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public void put(Key key, Value val) {
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if (val == null) { delete(key); return; }
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root = put(root, key, val);
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assert check();
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}
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private Node put(Node x, Key key, Value val) {
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if (x == null) return new Node(key, val, 1);
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int cmp = key.compareTo(x.key);
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if (cmp < 0) x.left = put(x.left, key, val);
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else if (cmp > 0) x.right = put(x.right, key, val);
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else x.val = val;
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x.N = 1 + size(x.left) + size(x.right);
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return x;
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}
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/***********************************************************************
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* Delete
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***********************************************************************/
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public void deleteMin() {
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if (isEmpty()) throw new NoSuchElementException("Symbol table underflow");
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root = deleteMin(root);
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assert check();
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}
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private Node deleteMin(Node x) {
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if (x.left == null) return x.right;
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x.left = deleteMin(x.left);
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x.N = size(x.left) + size(x.right) + 1;
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return x;
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}
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public void deleteMax() {
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if (isEmpty()) throw new NoSuchElementException("Symbol table underflow");
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root = deleteMax(root);
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assert check();
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}
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private Node deleteMax(Node x) {
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if (x.right == null) return x.left;
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x.right = deleteMax(x.right);
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x.N = size(x.left) + size(x.right) + 1;
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return x;
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}
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public void delete(Key key) {
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root = delete(root, key);
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assert check();
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}
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private Node delete(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) x.left = delete(x.left, key);
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else if (cmp > 0) x.right = delete(x.right, key);
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else {
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if (x.right == null) return x.left;
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if (x.left == null) return x.right;
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Node t = x;
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x = min(t.right);
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x.right = deleteMin(t.right);
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x.left = t.left;
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}
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x.N = size(x.left) + size(x.right) + 1;
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return x;
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}
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/***********************************************************************
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* Min, max, floor, and ceiling
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***********************************************************************/
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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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private Node min(Node x) {
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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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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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private Node max(Node x) {
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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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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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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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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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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) {
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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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return ceiling(x.right, key);
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}
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/***********************************************************************
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* Rank and selection
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***********************************************************************/
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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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// Return key of rank k.
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private Node select(Node x, int k) {
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if (x == null) return null;
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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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public int rank(Key key) {
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return rank(key, root);
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}
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// Number of keys in the subtree less than key.
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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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public Iterable<Key> keys() {
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return keys(min(), max());
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}
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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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keys(root, queue, lo, hi);
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return queue;
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}
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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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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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// height of this BST (one-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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// level order traversal
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public Iterable<Key> levelOrder() {
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Queue<Key> keys = new Queue<Key>();
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Queue<Node> queue = new Queue<Node>();
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queue.enqueue(root);
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while (!queue.isEmpty()) {
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Node x = queue.dequeue();
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if (x == null) continue;
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keys.enqueue(x.key);
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queue.enqueue(x.left);
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queue.enqueue(x.right);
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}
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return keys;
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}
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/*************************************************************************
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* Check integrity of 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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return isBST() && isSizeConsistent() && isRankConsistent();
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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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/*****************************************************************************
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* Test client
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*****************************************************************************/
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public static void main(String[] args) {
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BST<String, Integer> st = new BST<String, Integer>();
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for (int i = 0; !StdIn.isEmpty(); i++) {
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String key = StdIn.readString();
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st.put(key, i);
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}
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for (String s : st.levelOrder())
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StdOut.println(s + " " + st.get(s));
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StdOut.println();
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for (String s : st.keys())
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StdOut.println(s + " " + st.get(s));
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}
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}
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