1. CSE 326: Data Structures: Midterm Review
Lecture 15: Monday, Feb 10, 2003

2. The Midterm Mechanics Wednesday, 2/12/2003, 1:30-2:20 (50’)
We may start a few minutes early so you have > 50’
Chapters 1-6 in the textbook
Closed book, closed notes, except:
You may bring one 8 ½” x 11” sheet of handwritten notes
Bring pens and/or pencils

3. The Midterm
Practice:
Read the book, the lecture notes, review the homeworks
Practice midterm and solutions are on the website
Our midterm will be a bit more challenging
Make sure you sleep well the night before
Enjoy it ! We have fun questions

4. Midterm Review: Math Background
Big-Oh, big-omega, and theta notations:
T(n) = O(f(n)) if there exists c, n0 s.t. forall n > n0, T(n) < c f(n)
Should we have n  n0, and T(n)  c f(n) instead ?
O(f(n)) means “less than or equal to” f(n)
(f(n)) means “greater than or equal to” f(n)
(f(n)) means “same as” f(n)

5. Summations Summations are easy... for (i=1; i<=n; i++)
for (j=1; j<=i; j++)
print “hello”
Summations are easy...

6. Recurrences f(n) = f(n-1) + n f(n) = f(n-1) + 1 f(n) = 2f(n-1)+1
 O(n2)
f(n) = f(n-1) + 1
 O(n)
f(n) = 2f(n-1)+1
 O(2n)
f(n) = 2f(n/2) + 1
 O(n)
f(n) = 2f(n/2) + n
...recurrences are hard !
 O(n log n)
f(n) = f(n/2) + 1
 O(log n)
f(n) = f(n/5) + f(3n/5) + n
 O(n)
f(n) = f(n-1) + f(n-2)
 O(n)

7. Algorithm Analysis T(n) = running time for inputs of “size” n
The “size” does not tell us everything about the input; hence:
Worst case T(n)
Average case T(n)
Best case T(n)
Analyze the algorithm:
Find f(n) s.t. T(n) = O(f(n))
Find f(n) s.t. T(n) = (f(n))
Need to pick f(n) to be a simple function
Amortized analysis !

8. List, Stacks, Queues Lists: insert, find, delete Stacks: push, pop
Singly-linked lists with header node
Doubly-linked lists and circular lists
Runtime and space needed for array-based v.s. pointer based
Stacks: push, pop
Pointer v.s. array implementations
Use of stacks in balancing symbols (recall the homework)
Queues: equene, dequeue
Array-based v.s. list based implementations

9. Trees Terminology: Preorder, postorder, inorder traversal of a tree
Root, children, parent, path, height, depth, ...
Preorder, postorder, inorder traversal of a tree
Can do recursively, or with a stack, or with pointers to parents

10. Search Trees BST AVL trees Splay trees B-trees Definition
Find, insert, delete
AVL trees
Definition, running times
Know the rotation cases (we wont ask you to write the code, but may ask you to show on an example)
Splay trees
B-trees

11. Priority queues: binary heaps
Definition, implementation
Main operations:
findMin, insert, deleteMin
Other operations:
decreaseKey, increaseKey
Binomial heaps: merge
No need to know details of leftist or skew heaps

12. Hashing Know how hash functions work: Collisions:
Hash(k) = k mod TableSize
TableSize is chosen to be a prime, when the keys are integers
Collisions:
Chaining: colliding values  linked list
Open addressing: works when table is not very full. Linear probing, quadratic probing, double hashing
Extensible hash tables
That’s all, folks !
See you on Wednesday