Can we do better than BST if we do not need ordered operations ?

(No compare methods, use equals method)

Idea: save items in an array.
Hash function: method for calclulating the array index of a key.


  • computing hash function
  • equality tests
  • collision resolution

Classic space-time tradeoff.

1. Hash …


1. 1d Range Search

Goal: intersections of geometric objects.

Solution: BST

operations required:

  • insert
  • search
  • delete
  • range search: all keys between k1 and k2
  • range count: how many keys are between k1 and k2

→ find points on an interval

implementation by BST

range count
using the …


goal: lgN for insert/search/delete operations (not necessarily binary trees..)
3 algo: 2-3 tree, (left leaning) red-black tree, B-tree

1. 2-3 Search Trees

def. 2-3 tree

  • allow 1 or 2 keys per node, & 2 or 3 children per node:
    • 2-node: one key, 2 children (ordinary BST node)
    • 3-node …



1. Binary Search Trees

def. BST
A binary tree where each node has a key:
for every node, the key is larger than all nodes in left subtree, smaller than all nodes in right subtree.

Fields: key, val, left, right


An inner class of BST nodes:

private …


1. Symbol Table API

key-value pair abstraction

  • insert a value with a key
  • given a key, search for its value

Association array abstraction

Associate a value to a key — generalized array: a[key]=val.

public class ST<Key, Value>{   
    void put(Key k, Value v);//remove key if value …


1. API and elementary implementations

Collection: data struct for inserting and deleting items (ex. stack and queue).
Priority queue: a special kind of collection — remove largest/smallest element.


public class Max<Kye implements Comparable<Key>>{   
    public MaxPQ();    
    public void insert(Key k);   
    public Key delMax();    
    public boolean isEmpty …


(maybe best algorithm for sorting.)

1. Quicksort


  1. shuffle the array
  2. Partition the array into two subarrays to left and right of pivot (*now pivot is *in its final position)

no larger entry to the left of pivot
no smaller entry to the right of pivot

  1. sort each subarray …


Two classical sorting algorithms: mergesort, quicksort.

1. Mergesort

Divide and conquer: top 10 algorithms of the 20th century, invented by von Neumann.


  • divide array into 2 halves
  • recursively sort each half
  • merge two sorted halves


Goal: a[lo] to a[mid] and a[mid+1] to …


1. Introduction

rearanging array of size N into ascending order
test client code: Insertion.sort(a);

sort any datatype


callback = reference to executable code
i.e. passing functions as argument to sort() method
sort() function calls object's compareTo() method

→ implement the Comparable interface:

    public class XX implements Comparable …


fundamental data types: stacks and queues operations: insert, remove, test empy, iterate,...

module programming: seperate interface and implementation

1. Stacks

ex. a stack of strings

  • API:

    public interface StackoOfStrings{ void push(String item); String pop(); boolean isEmpty(); //int size(); }

implementation 1: using a linkedlist

insert/remove from the top …