1. Apoorva Vadi M.S Information Systems New York University
Gyan from the Geek
Apoorva Vadi
M.S Information Systems
New York University

3. What is computer Science?

4. Lets talk about M&M? The Math Monster

5. BAD MATH !!!!

7. Algorithms…
What are those things?

8. An algorithm…is like a recipe
Problem solving as an analogy to cooking: 1. Inputs 2. Recipe/Set of defined rules (or an Algorithm) 3. Outputs

9. Now lets use algorithms…
To solve Puzzles!
Towers of Hanoi
Dining Philosophers
Travelling salesman
Eight queens

10. Towers of Hanoi
You have a stack of discs, from largest to smallest, that slide on to the first peg of a three peg board. Your goal is to move the entire stack of discs from the first peg to the third peg. However, you can only move the topmost disc of any peg, and smaller discs must always be placed on larger discs. How many moves will it take? 

12. Now lets write a recipe for this…
Alternating between the smallest and the next-smallest disks, follow the steps for the appropriate case:
For an even number of disks:
make the legal move between pegs A and B
make the legal move between pegs A and C
make the legal move between pegs B and C
repeat until complete
For an odd number of disks:
In each case, a total of 2n-1 moves are made.

13. But that was too long… lets try recursion…
Step 1: Move N−1 discs from A to B. This leaves Nth disc alone on peg A. Step 2: Move Nth disc from A to C Step 3: Move N−1 discs from B to C so they sit on disc N.

14. Dining Philosophers Problem
Lets try something ‘non-arkymalarky’: Five philosophers sit around a circular table. In front of each philosopher is a large plate of rice. The philosophers alternate their time between eating and thinking. There is one chopstick between each philosopher, to their immediate right and left. In order to eat, a given philosopher needs to use both chopsticks. How can you ensure all the philosophers can eat reliably without starving to death?

15. So this is a classic example of a common computing problem in concurrency…
Issues:
Deadlock - cycle of unwarranted requests. Every philosopher picked up a left fork and waits for a right fork (forever).
Resource Starvation – one philosopher might have to wait extended amounts of time.
Mutual exclusion – multiple processes accessing sets of data.

17. Welcome to the world of Data Structures
Stacks
Queues
Linked Lists
Trees
Have Fun

18. Applications of Stacks
Direct applications
Page-visited history in a Web brows
Undo sequence in a text editor
Indirect applications
Component of other data structures

19. Applications of Queues
Direct application
Waiting lines
Access to shared resources (e.g., printer)
Multiprogramming
Indirect applications
Component of other data structures

20. List A singly linked list is a concrete data structure
consisting of a sequence of nodes
-Each node stores element
-link to the next node

21. Queue with a Singly Linked List
We can implement a queue with a singly linked list -The front element is stored at the first node -The rear element is stored at the last node

22. Doubly Linked List
A doubly linked list provides a natural implementation of the List ADT
Nodes implement Position and store:
-element
-link to the previous node
-link to the next node
Special trailer and header nodes

23. Doubly Linked List

24. Trees
In computer science, a tree is an abstract model of a hierarchical
structure
-A tree consists of nodes with a parent-child
relation
Applications:
-Organization charts
-File systems
-Programming environments

25. Binary Trees A binary tree is a tree with the following properties:
-Each internal node has two children
-The children of a node are an ordered pair
- We call the children of an internal
node left child and right child
- Alternative recursive definition: a
binary tree is either
-a tree consisting of a single node, or
- a tree whose root has an ordered pair of children, each of which is a binary tree
Applications:
-arithmetic expressions
-decision processes
-searching

26. Binary Tree

27. Tree Traversals (power of recursion)
Depth First Search
Pre-order(NLR): Root Node- Left child- Right child
A-B-D-E-H-I-C-F-G
In-order(LNR): Left child - Root Node - Right child
D-B-H-E-I-A-F-C-G
Post-order(LRN): Left child - Right child – Root Node
D-H-I-E-B-F-G-C-A
Breadth First Traversal
Level order Traversal: Traverse each node level by level
A-B-C-D-E-F-G-H-I

28. Links http://www.youtube.com/watch?v=jq_EcstLlfE&feature=related

29. That’s all folks !