Compare Cpu Scheduling of Linux and Unix.

Binary Search Trees basic implementations randomized BSTs deletion in BSTs

References: Algorithms in Java, Chapter 12 Intro to Programming, Section 4.4 http://www.cs.princeton.edu/introalgsds/43bst 1

Elementary implementations: summary

implementation

worst case search insert N N N N

average case search N/2 lg N N/2 N/2 insert N/2 N/2 N N/2

ordered iteration? no yes no yes

operations on keys equals() compareTo() equals() compareTo()

unordered array ordered array unordered list ordered list

N lg N N N

Challenge: Efficient implementations of get() and put() and ordered iteration.
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basic implementations randomized BSTs deletion in BSTs

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Binary Search Trees (BSTs) Def. A BINARY SEARCH TREE is a binary tree in symmetric order. it A binary tree is either: empty a key-value pair and two binary trees [neither of which contain that key]

• •

best of

the

was times

equal keys ruled out to facilitate associative array implementations

Symmetric order means that: every node has a key every node’s key is larger than all keys in its left subtree smaller than all keys in its right subtree

• •

node

x subtrees smaller

larger
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BST representation A BST is a reference to a Node. A Node is comprised of four fields: A key and a value. A reference to the left and right subtree.

• •

smaller keys

larger keys

root private class Node { Key key; Value val; Node left, right; }
Key and Value are generic types; Key is Comparable

it

2

best

1

was

2

the

1

of

1

times

1
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BST implementation (skeleton)

public class BST implements Iterable { instance variable private Node root; private class Node { Key key; Value val; Node left, right; Node(Key key, Value val) { this.key = key; this.val = val; } } inner class

public void put(Key key, Value val) // see next slides public Val get(Key key) // see next slides }
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BST implementation (search)

public Value