The document outlines 16 design exercises for students to complete related to data structures. The exercises involve tasks like proposing computerization opportunities, designing general purpose modules, linearizing data storage, representing matrices and graphs, implementing common ADTs like stacks and queues, solving algorithm problems like maze traversal, and binary tree traversal and manipulation. The exercises are meant to be completed over the course of several weeks to give students hands-on practice with data structure and algorithm design.

1. Sanjay Goel, JIIT, 2002
Data Structures: Design Exercises
Design Exercise #1 (1st week)
- Make a group of Three.
- Pick any domain of your choice.
- Propose computerisation opportunities in your chosen domain.
Design Exercise #2 ( 2nd Week)
- Make Macro-Groups of six Groups
- Refine your Designs based on the Feedback
- Propose a set of General purpose Formative Modules with permitted Functions on each
to serve the needs of all the groups in a Macro-Group
- Each Group Submit the Refined Designs for their project
- Each Macro-Group submit specifications of General purpose Formative Modules
Design Exercise #3 ( 3rd Week)
- Each Batch divide yourself into two equal size Groups.
- Propose a set of General purpose Formative Modules (Data storage Building Blocks)
with permitted Functions on each to serve the needs of all the applications conceived
by the group members.
- Each Group submit specifications of General purpose Formative Modules .
- Propose a high level design for computer aided Analog electronic circuit design cum
analysis tool.
- Propose a high level design for Chess player. Think, how many patterns are legally
possible? What criteria should be adopted to take the decision for the next move by
the computer.
Design Exercise #4 ( 4th Week)
- Propose schemes for Linearising you data i.e. storing the data from your chosen
domain(s) in a Linear Array of Bytes.
Design Exercise #5 ( 5th Week)
- Conclude your Group Assignment.
- Propose a scheme to linearise 1D/2D/3D/…/nD arrays of
int/char/double/float/struct/union:
LOC(A[i,j]) = ?
LOC(A[i,j,k]) = ?
LOC(A[i1,i2,i3,…,ik]) = ?

2. Sanjay Goel, JIIT, 2002
- Propose a scheme to efficiently linearise 2D/3D/…/nD triangular/ k dimensional
tetrahedral matrices:
LOC(A[i,j]) = ?
LOC(A[i,j,k]) = ?
LOC(A[i1,i2,i3,…,ik]) = ?
i,j,k,i1,i2…..,ik = ?
- Propose a scheme to efficiently store a 2D/3D/…/nD sparse matrix in linear (1D)
memory ?
- Identify the Generic ADTs as a result of your group exercise. Design specifications
for these ADTs.
- Design an ADT to model the control flow in all your recursive programs.
- Design an ADT to model the Books of different types.
- Think how to implement C++ compiler in C. Propose some data structure to readily
offer OO features to the C++ user.
- Design the specifications for Basic ADTs (set, dictionary, linear list, array, stack,
queue, deque, tree, graph) in terms of :
- Permitted operations
- Pre and Post-conditions for each operation
Design Exercise #6 ( 7th Week)
1. Design Algorithms and Write programs for multi variable polynomial input,
output, addition, subtraction, multiplication, differentiation and integration using
linked list representation.
Design Exercise #7 ( 9th Week)
1. Write algorithms for Matrix addition, subtraction, multiplication and transpose of
sparse matrices using pointer less representation.
2. Represent the lists of contributors (with their enrollment number, address, hobbies,
past record of extra curricular activities, awards, previously held positions, current
responsibilities, personally known established hobbyists/professionals and so on) to
various activities of JYC under the three broad sections of literary, cultural and
sports.
Write algorithms to insert, delete, modify and inquire the records.

3. Sanjay Goel, JIIT, 2002
3. Design Algorithms for sparse matrix input, output, addition, subtraction,
transpose and multiplication for different linked list based representations.
Design Exercise #8 ( 10th Week)
1. Write the specifications for the following ADTs:
- Table
- String
2. Create Design options for Stack ADT in terms of List ADT.
Design Exercise #9 ( 11th Week)
1. Write a non-recursive program for Tower of Hanoi problem.
2. Design the specifications for ADT “video”.
3. Use a stack to convert the following function to non-recursive, iterative form:
function r(x:T)
if p(x) then
a(x)
else
b(x)
r(f(x))
c(x)
end if
end p
where T is an arbitrary type, p is an arbitrary predicate, a, b and c are arbitrary
procedures and f is an arbitrary function.
3. Write the algorithm for Rat in the maze problem.
Design Exercise #10 ( 12th Week)
1. Write the algorithm for Postfix evaluation.
2. Propose a design to store N stacks in one Array.
4. Propose the options to handle the growth of stacks within the limits of the array.
Design Exercise #11 ( 13th Week)
1. Write the pre and post conditions for the operations of Queue.
2. Define the ADT Queue in terms of List ADT.
3. Develop Queue from Scratch using the available features of programming language
4. Derive Queue from LinearList
5. Rewrite palindrome checker using one stack and one queue

4. Sanjay Goel, JIIT, 2002
Design Exercise #12 ( 14th Week)
1. Modify the algorithms for other design options for Array based implementation of
queue from scratch.
2. Develop a linked list based Queue from scratch to get better performance than
obtainable by deriving from Chain.
Design Exercise #13 ( 15th Week)
1. Write an algorithm for finding the shortest path between given points in a maze.
2. Write an algorithm for finding out the unreachable points from any given point in a
maze.
3. Choose different definitions for neighbours to design and analyse other maze
traversal schemes.
4. Write a generic maze traversal algorithm that works with neighbour definition as an
additional input.
Design Exercise #14 ( 16th Week)
1. Propose a design to store N queues in one Array.
2. Propose the options to handle the growth of queues within the limits of the array
3. Propose a design for creating a queue of stacks
4. Extend the car wash simulation discussed in the class (constant wash time and single
wash line ) to include multiple car washing lines as well as varying wash time
requirements.
5. Propose a design for creating a stack of queues headers. Supervisor I creates new
queues and pushes them onto this stack. It also randomly generates and enqueues job
requests in stacked queues. Supervisor II serves the queues in normally LIFO order
and dequeues the front of each queue on the stack in of each cycle. However, if the
queue count of any queue is more than 100, it is given one time priority over any
other queue.
Design Exercise #15 ( 17th Week)
1. Generate the design options for designing deque ADT.
2. Give the detailed descriptions of your design options.
3. Propose a design to store N deques in one Array.
4. Propose the options to handle the growth of deques within the limits of the array.
Design Exercise #16 ( 19th Week)
5. Write iterative algorithms for inorder, preorder and post order traversal of array base
as well as linked binary trees.

5. Sanjay Goel, JIIT, 2002
6. Write algorithms for transformation of k-ary tree into binary tree (left child, right
sibling) and vice versa.
7. Write algorithm for making a clone of a binary tree.
8. Write algorithm for checking the equality of two binary trees.