Advanced Data Structures 2006

Advanced Data Structures, JIIT Sanjay Goel, 2006

ADS: Lecture Notes
Even Sem: 2005-06

1. 10.01.06
1. Learning Outcomes, relationship with DS, DBMS, and OOPS.
2. Concept map (DS) Concept map (DBMS) ER Diagram
Class Diagram
3. Assignment: Suggest a solution of converting file format in any domain. Identify
the problems and issues.

2. 17.01.06
1. Review of Key issues:
- Computational problem solving process.
- Design as story telling.
2. Some options for identifying your first paper for your literature survey:
i. Select paper(s) that use one or more of the of the Data Structure
already studied by you (e.g. Table, Stack, Binary Tree, BST, Queue,
Dequeue and so on) in the first course.
ii. Select paper(s) on ADT specification and design.
iii. Select paper(s) that describe the ADTs or classes used for designing a
complete software system of your choice.
iv. Select paper(s) that discuss recursive solution for some algorithmic
problem.
v. Select paper(s) that recursion removal techniques.
vi. Select Paper(s) that discuss simulation models using queues.
vii. Select papers that analyze the performance of some DS.
viii. Select papers that discuss some file format.

3. 18.01.06
1. Review and Enhancement Concept mapping Notation
- Identify data tanks as
i. IN Data Tanks
ii. OUT Data Tanks
iii. IN & OUT Data Tanks
iv. Buffer Data Tanks
- All IN and IN & OUT data Tanks are part of INITIAL STATE (IS)
- All OUT and IN & OUT data Tanks are part of FINAL STATE (FS)
- Develop Initial State Diagram (ISD) as a collection of IN and IN & OUT
Data tanks.
- Develop Final State Diagram (FSD) as a collection of OUT and IN &
OUT Data tanks.
- Develop Concept map (CM) as a network of all Data tanks and
Processing Units.


- Put the following symbols on the center of the top line of the Rectangular
box of Tank.
i. IN Data Tanks :

ii. OUT data tanks :

iii. IN & OUT Data tanks:

iv. Temporary buffer type data tanks: No symbol.

2. Storing a Graph as a Table.
3. Storing a Binary Tree in a Table.
4. Traversing (pre-order) of Binary tree stored as a table.
5. Assignment: When you have learnt SQL in DBMS, use it to do traversal over
binary tree stores as a table.
6. Assignment (Group of 2) (3 marks each): Export the Table(s) created by you or
by your group partner as your DBMS assignment to a text file. Write any three
query functions (already executed by you using ACCESS) to process this text file
using C language.

4. 24.01.06
1. Big O, small o, Big Omega, small omega, Big Theta notations.
2. Worst case, Best case, Average Case complexity analysis.
3. Assignment: Perform the average case complexity analysis for following
algorithms:
- Linear Search in unordered array, Linear search in Ordered array, Binary
search.
- Insertion sort, Bubble sort, Selection sort.

5. 25.01.06
1. Average Case Complexity analysis: Linear search, Binary search, Insertion sort.
2. Impact of hardware speedup on the data size that can be processed by an
algorithm of known complexity f (n).
3. Assignment: In the three research papers that have to be studied by you, at least
one should be on complexity analysis. Write program to experimentally
validate the theoretical/experimental results on complexity analysis reported
in the paper studied by you. Include your results in the literature survey report
and presentation. Keep reporting your Lab instructors about the progress on
literature survey.

6. 31.01.06
1. Insertion sort Selection sort. Comparison of algorithmic process.
2. Merge sort Transform the process Quick Sort.


3. Comparison less sorting Radix sort
4. Assignment: Analyze the Best case, Worst case, and average case complexity for
sorting a linked list using selection sort and insertion sort, Your algorithm
should have a space complexity of O(1).
5. Assignment (5 marks): WAP for Radix sort, non-recursive Merge sort, and Quick
sort algorithms. Experimentally test the performance for varying data size and
distribution. Design the test cases for this experiment. Graphically plot the results
of your experiment.

7. 01.02.06
1. Best case and Worst case analysis of Merge Sort.
2. Algorithmic performance improvement by mixing different algorithms Binary
insertion sort.
3. Algorithmic performance improvement by identifying the weakness and
removing them for large n Shell sort.
4. Assignment (Group of two, 3 marks each): In the three research papers that have
to be studied by you, one can be on sorting techniques. Write program to
experimentally find out the best initial step size for shell sort for sorting an
array of 10,000 integers.

8. 07.02.06
1. Best case and Worst case Complexity Analysis of Quick sort.
2. Algorithmic visualization techniques.
3. Assignment (bonus: only for those who have submitted earlier assignments on
sorting program before 10.02.04: 3 marks): Write a function for array
visualization to graphically display its sorted-ness. Insert this function in sorting
programs to demonstrate algorithms’ progress.

9. 08.02.06
1. Tree Sort algorithm: Using BST.
2. Top down Vs Bottom up growth of tree.
3. Construction of expression tree.
4. Huffman encoding algorithm.
5. Assignment (2 marks): Using your existing functions, WAP and experimentally
evaluate the performance of Tree sort algorithm.

10. 14.02.06
1. Review of key ideas.
2. Dynamic programming: e.g. Merge sort.
3. Greedy Algorithms: Huffman encoding.
4. Heap: Priority Queue: insertion and deletion operations. Number of comparison
during insertion and deletion.

11. 15.02.06
1. Heap: element insertion, deletion.
2. Heapsort.


12. 02.03.06
1. Review of Algorithmic Design techniques:
a. Brute Force Method: Instead of creative logic, computational speed is
used for solving the problem e.g. Linear Search, Selection sort, Bubble
sort.
b. Decrease and Conquer: Instead of solving the problem with n elements,
the problem is solved for n-k elements and then n-2k and so on. The
solution for n elements is derived from the solution of smaller size data
set e.g. Insertion sort.
c. Divide and conquer: The problem size is decreased by a ratio rather than
a constant e.g. Binary search, Quick sort, Hanoi, Maze, recursive Merge,
and so on.
d. Greedy: Rather than trying to take best alternative a locally best solution
is picked us and short sighted decisions are taken to solve problems e.g.
Huffman encoding, Traveling salesman, Activity scheduling, Map
coloring, and so on.
2. Assignment (4 marks): All should allow a user inputted data for processing.
B1, B2: Huffman encoding (variable number of n symbols)
B2, B3: Activity scheduling, (variable number of n activities and
variable number of m venues).
B4, B5: Traveling Salesman (variable number of n cities)
Others: Map coloring (variable number of n regions)

13. 03.03.06
1. Greedy Algorithms:
- Coin exchange
- Graph: Dominant set of graph
- Graph: MST: Kruskal, Prim
2 Assignment (4 marks): All should allow a user inputted data for processing.
B1 : Dominant set (variable number of n nodes and m links using
Adjacency matrix based storage of Graph)
B2: Dominant set (variable number of n nodes and m links using
Adjacency list based storage of Graph)
B3: Dominant set (variable number of n nodes and m links using
linked storage of Graph)
B4: Kruskal’s Algorithm, (variable number of n nodes and m links
using Adjacency matrix based storage of Graph).
using Adjacency list based storage of Graph).
using linked storage of Graph).
B7: Prim’s Algorithm, (variable number of n nodes and m links
using Adjacency matrix based storage of Graph).
using Adjacency list based storage of Graph).


using linked storage of Graph).

13-14. 7.3.06 and 8.3.06

More on Greedy Algorithms

Cases of Greedy Algorithms: MST Algorithms

Kruskal’s Algo

Examine arcs one-by-one in the sorted order and add them to OUTPUT if their
addition does not create a cycle.

10
2 4
35

25
1 20 30

40
3 5
15
Minimum cost, No cycle, select

10
2 4
35

25
1 20 30

40
3 5
15
Selected Link count < 4 so continue
Next Minimum cost, No cycle, select


10
2 4
35

25
1 20 30

40
3 5
15
Next Minimum cost, No cycle, select

10
2 4
35

25
1 20 30

40
3 5
15
Next Minimum cost, will create a cycle so reject
10
2 4
35

25
1 20 30

40
3 5
15
Next Minimum cost, will create a cycle so reject


10
2 4
35

25
1 20 30

40
3 5
15
Next Minimum cost, No cycle, so select

10
2 4
35

25
1 20 30

40
3 5
15
Selected Link count = 4, so stop.
Prim’s Algo
Start with a vertex and grow the tree by gradually adding the cheapest unselected edge
connected to any node in the selected subset.

10
2 4
35

25
1 20 30

40
3 5
15
Start with any node say 1.


10
2 4
35

25
1 20 30

40
3 5
15
Selected links <4 so continue
Check the minimum cost link (amongst the dotted blue),
Does not create a cycle so select

10
2 4
35

25
1 20 30

40
3 5
15
Check the minimum cost link from the already selected nodes,

10
2 4
35

25
1 20 30

40
3 5
15


10
2 4
35

25
1 20 30

40
3 5
15

10
2 4
35

25
1 20 30

40
3 5
15
Selected links =4 so stop

Sollin’s Algorithm

1. Proceeds by adding the least cost arc emanating from each tree.
2. Each iteration reduces the number of components by a factor of at least 2.
10
2 4
35

25
1 20 30

40
3 5
15
Selected link count <4 so continue
Choose a node, check its cheapest link, No cycle so select


10
2 4
35

25
1 20 30

40
3 5
15
Choose next node, check its cheapest link, No cycle or duplication, so select

10
2 4
35

25
1 20 30

40
3 5
15
Choose next node, check its cheapest link, No cycle or duplication, so select

10
2 4
35

25
1 20 30

40
3 5
15
Choose next node, check its cheapest link, No cycle but duplication, so no new selection

No New adge is added for node 4 as the cheapest edge from node 4 is already
selected.


10
2 4
35

25
1 20 30

40
3 5
15
Choose next node, check its cheapest link, No cycle but duplication, so no new selection

No New adge is added for node 5 as the cheapest edge from node 5 is already
selected.

10 10
2 4 2 4
35 35

25
1 20 30 1

40
3 5 3 5
15 15

Ist iteration over we get some connected components

(2nd Iteration starts to link these connected components)

10
2 4
35

25
1 20 30

40
3 5
15
Choose a tree (connected component) , check its cheapest link, No cycle no duplication,
so select.


10
2 4
35

25
1 20 30

40
3 5
15
Selected link count = 4 so stop

15. 21.3.06
1. Dijkastra’s shortest path Algorithm for un-weighted graph and weighted graph.
2. Programming Assignments: (5 marks)
B1: Dijkastra’s Algorithm for weighted graph using Adj matrix for Graph and
linked structure for priority queue.
B2: Dijkastra’s Algorithm for weighted graph using Adj matrix for graph and
array based structure for priority queue.
B3: Dijkastra’s Algorithm for weighted graph using Adj List for graph and array
based structure for priority queue.
B4: Dijkastra’s Algorithm for weighted graph using Adj List and linked structure
for priority queue.
B5: Dijkastra’s Algorithm for weighted graph using Linked Structure for graph
and array based structure for priority queue
B6: Dijkastra’s Algorithm for weighted graph using Linked Structure for graph
and linked structure for priority queue.
B7: Dijkastra’s Algorithm for weighted graph using Simulated pointer based
Structure for graph and array based structure for priority queue
B8: Dijkastra’s Algorithm for weighted graph using Simulated pointer based
Structure for graph and linked structure for priority queue.
B9: Sollin’s Algorithm using Adj Matrix for Graph.

16. 22.3.06
1. Map Colouring.
2. Limitations of Greedy Algorithm: Optimality is an issue.
3. Dynamic Programming: overlapping sub-problems, recursion removal:
Fibonacci, Binomial Coefficients, Coin.
4. Assignment: If your choice of three research papers is not over, include one
paper or Dynamic Programming.

17-18. 4.4.06 and 5.4.06
1. Decision Tree for classification
2. Puzzle solving:
i. Problem space States: goal, initial, others, states are defined by
problem


ii. Operators for state transition depend upon the problem.
iii. Goal test.
iv. Data Structure for State representation (generally using flags).
1. 8-puzzle
2. River Problem
3. 8-Queen possible 3d extension
4. Robot path finding
5. Robot block world
6. Water jug problem
7. Rat in the maze
8. Tower of Hanoi
9. Rubic Cube
v. Generating choice depending upon the available operators:
generating decision tree.
vi. Searching the goal state and path to reach goal state in decision
tree: Depth first Vs Breadth First Search.
vii. Search strategy properties: completeness (yes/no), optimality
(yes/no), and Time and Space complexity of algorithm.

3. Assignment: (group of 2 students, 5 marks each)
B1: WAP for placing maximum number of queen on chess like board of 5x5 cells
following the rules of chess. Analyze the complexities of your algorithm.
B2: WAP for placing maximum number of Knights on chess like board of 5x5
cells following the rules of chess. Analyze the complexities of your
algorithm.
B3: WAP for placing maximum number of rooks (n1) and bishops (n2) on a
chess like board of 5x5 cells following the rules of chess such that ABS (n1-
n2) <=1. Analyze the complexities of your algorithm.
B4: WAP for solving 4x4 puzzle (one hole) (re-arrange any user inputted initial
pattern of letters into a desired user inputted given pattern). Analyze the
complexities of your algorithm.
B5: WAP for solving Water jug problem for any user inputted amount with 4
jugs of capacity of 10, 9, 5, and 2. Analyze the complexities of your
algorithm.
jugs of capacity of 7, 4, and 3. Analyze the complexities of your algorithm.
jugs of capacity of 7 and 6. Analyze the complexities of your algorithm.
B8: WAP for solving 4x4 puzzle (two holes) (re-arrange any user inputted initial
pattern of letters into a desired user inputted given pattern). Analyze the
complexities of your algorithm.
B9: WAP for solving 4x4 puzzle (three holes) (re-arrange any user inputted
initial pattern of letters into a desired user inputted given pattern). Analyze
the complexities of your algorithm.


19. 11.04.06
1. Threaded BST

Assignment (Group of 2, 7.5 marks each):
B1: Create a graph of student records with following attributes:
i. Name
ii. Roll Number
iii. Department
The inter-node links represent close friendship between students. One student
can have at most 5 close friends.
A BST tree is used to index this database on student’s Name. WAP to store
this database and answer following queries and perform following operations:
i. List the Roll numbers of friends of a given name.
ii. List the Names of the friends of given roll number.
iii. insertion of new record.
iv. deletion of a record
v. insertion of a link
vi. deletion of a link
Use pointer based storage for graph and pointer-less storage for BST.

• Name
• Roll Number
• Department
List the Roll numbers of friends of a given name.
List the Names of the friends of given roll number.
insertion of new record.
deletion of a record
insertion of a link
deletion of a link
Use pointer based storage for graph and pointer based storage for BST.

• Name
• Roll Number
• Department


insertion of a link
deletion of a link
Use pointer-less storage for graph and pointer based storage for BST.

• Name
• Roll Number
• Department
insertion of a link
deletion of a link
Use pointer-less storage for graph and pointer-less storage for BST.

B5: Create a graph of employee records with following attributes:
• Name
• Employee Number
• Department
The inter-node links represent shared postings between employees. One
employee can have at most 4 shared postings with other employees.
A BST tree is used to index this database on employee number. WAP to store
this database and answer following queries and operations:
List the department of co-posted employees of a given name.
List the Names of the co-posted employees of given employee
number.
insertion of a link
deletion of a link

• Name
• Employee Number
• Department


number.
insertion of a link
deletion of a link
Use pointer-less storage for graph and pointer based storage for BST.

• Name
• Employee Number
• Department
number.
insertion of a link
deletion of a link
Use pointer based storage for graph and pointer-less storage for BST.

• Name
• Employee Number
• Department
number.
insertion of a link
deletion of a link
Use pointer based storage for graph and pointer based storage for
BST.


B9: Create a graph of Book records with following attributes:
• Title
• Author name
• ISBN Number
• Library Acquisition Number
• Publisher
The inter-node links represent cross referencing between books. One book can
refer to at most 5 other employees.
A BST tree is used to index this database on ISBN number. WAP to store this
database and answer following queries and operations:
List the publishers of books referred by of a given book given its
ISBN number.
List the publishers of books referring to of a given book given its
Title
Insertion of new record.
insertion of a link
deletion of a link

20. 18.04.06
1. Comparison of Linear Index and BST based Index.
2. Indexed BST.
3. ASSIGNMENT (Group of two or alone, 9 marks each) : Modify your
last assignment given on 11.04.05 as follows:
i. Replace ordinary BST with Threaded Indexed BST.
ii. Save and upload your database (graph as well as index) on (and
from) file(s).

21. 19.04.06
1. AVL Tree.
2. Bonus Assignment (single student, 5 marks, only for those who
scored a total of minimum 20 marks out of 60 in two minor tests and
all five lab tests, three tests conducted by seniors in the evenings as
well as two tests by faculty during lab time): Modify your last
assignment by replacing Threaded Indexed BST with Threaded Indexed
AVL search Tree.

22-23. 25-26.04.06
1. AVL Tree: Balancing after Insertion and Deletion. LL, RR, LR, RL, R0,
R1, R-1, L0, L1, L-1.
2. TRIE, Compact TRIE.


24-25. 02.5.06

1. Multi-way Search Trees for creating Index structure for large database:
B Tree, B+ Tree, B* Tree: Data structure, Search, Insertion, Deletion.

25. 03.05.06

1. Hashing: Hash function, Synonym, Collision, Collision resolution, Open
hashing, Bucket hashing, Closed hashing.

****************************************************************
Some relevant quotes:

1. I cannot teach anybody anything; I can only make them think. – Socrates

2. You cannot teach people anything.
You can only help them discover it within themselves. - Galileo

3. I do not teach anything. I create conditions for learning.
4. The only source of knowledge is experience. - Einstein

Advanced Data Structures 2006

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