1. CS223 Advanced Data Structures and Algorithms 1 Review for Midterm Neil Tang 03/06/2008

2. CS223 Advanced Data Structures and Algorithms 2 Algorithm Analysis  Asymptotic notations (O, ,  ): definition, properties  Important functions: polynomial, logN, 2 N  Rules  Time complexities of major sorting algorithms  Recursion and the master method  Sum calculation: double-sum and sum of an arithmetic- geometric sequence

3. CS223 Advanced Data Structures and Algorithms 3 Trees  Basic concepts  Tree traversals  Binary search tree: insert, remove and time complexities  AVL tree: rotation methods  Red-black tree: definition, rotation and color fix methods, delete

4. CS223 Advanced Data Structures and Algorithms 4 Heap  Binary heap: insert, deleteMin, percolateUp/Down, buildHeap and time complexities.  Heapsort  An application: find kth largest/smallest element.  D-heap: definition and tradeoff

5. CS223 Advanced Data Structures and Algorithms 5 Hashing  Hash functions  Separate chaining  Open addressing: linear probing, quadratic probing, double- hashing  Load factor, primary/secondary clustering problems  Rehashing: conditions

6. CS223 Advanced Data Structures and Algorithms 6 Disjoint Set  Implementations: Linked-list and array  Union: basic, union-by-size, union-by-rank  Find: basic, path compression, time complexities  Time complexity of a sequence of find/union operations