This is java. Please use the BST class provided in algs4.jar. If you do not use
ID: 3599714 • Letter: T
Question
This is java. Please use the BST class provided in algs4.jar. If you do not use the BST class and post a polynonaimal program I will give a negative review.
Run empirical studies to compute the average and standard deviation of the average length of a path to a random node in a BST built by insertion of N random keys into an initially empty tree, for N from 100 to 12,800 (with N doubling from 100, 200, 400 ...)
Details:
- I recommend developing your own BST implementation in MyBST.java, building on the code in the BST class provided in algs4.jar.
- For each tree size, do 1000 trial trees. That means: create an empty BST object, generate N keys, and put them into the BST.
- Once you have a filled BST, the average path length on this tree (mt) is the sum of all node depths divided by the number of nodes, plus 1. You'll need to create a function in your BST implementation to compute and return this.
- I'm asking you to compute the average and standard deviations of those mt values.
- Print those values to a table, captured in your README file
Algs4.jar can be downloaded here
Explanation / Answer
import java.util.NoSuchElementException;
public class BST<Key extends Comparable<Key>, Value> {
private Node root;
private class Node {
private Key key;
private Value val;
private Node left, right;
private int size;
public Node(Key key, Value val, int size) {
this.key = key;
this.val = val;
this.size = size;
}
}
public BST() {
}
public boolean isEmpty() {
return size() == 0;
}
public int size() {
return size(root);
}
// return number of key-value pairs in BST rooted at x
private int size(Node x) {
if (x == null) return 0;
else return x.size;
}
public boolean contains(Key key) {
if (key == null) throw new IllegalArgumentException("argument to contains() is null");
return get(key) != 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;
}
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;
}
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;
}
/**
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;
}
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;
}
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);
}
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);
}
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;
}
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);
}
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;
}
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);
}
public Iterable<Key> keys() {
if (isEmpty()) return new Queue<Key>();
return keys(min(), max());
}
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);
}
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);
}
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));
}
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;
}
***************************************************************************/
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?
// Note: this test also ensures that data structure is a binary tree since order is strict
private boolean isBST() {
return isBST(root, null, null);
}
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;
}
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();
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));
}
}
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