Thinking in Data Structures

1. Thinking in Data Structures
Tushar B Kute
http://www.tusharkute.com

2. Data Structure
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What is the "Data Structure" ?
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Ways to represent data.
In a general sense, any data representation is a data structure.
Example: An integer more typically, a data structure is meant to be
an organization for a collection of data items.
Why data structure ?
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Have proven correct algorithms
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To design and implement large-scale computer system
The art of programming
How to master in data structure ?
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practice, discuss, and think
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3. Need of data structures
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Data structures organize data
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More powerful computers
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More efficient programs.
More complex applications.
More complex applications demand more calculations.
Complex computing tasks are unlike our everyday
experience.
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4. List of data structures
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Static
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Stack
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Array
Queue
Dynamic
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Linked list
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Tree
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Graph
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5. Choosing a data structure
int p[10], i=0;
int *p, i=0;
while(1)
while(1)
{
{
scanf(“%d”, &p[i]);
i++;
}
scanf(“%d”, &p[i]);
i++;
}
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6. System life cycle
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Summary
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Requirements
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RADRCV
What inputs, functions, and outputs.
Analysis
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Break the problem down into manageable pieces.
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Top-down approach.
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Bottom-up approach.
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7. System life cycle
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Design
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Refinement and Coding
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Create abstract data types and the algorithm
specifications, language independent.
Determining data structures and algorithms.
Verification
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Developing correctness proofs, testing the program,
and removing errors.
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8. Efficiency
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A solution is said to be efficient if it solves the problem
within its resource constraints.
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Space
Time
The cost of a solution is the amount of resources that the
solution consumes.
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9. Data Structure philosophy
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Each data structure has costs and benefits.
Rarely is one data structure better than another in all
situations.
A data structure requires:
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space for each data item it stores,
time to perform each basic operation,
Programming effort.
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10. Data structure philosophy
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Each problem has constraints on available space and
time.
Only after a careful analysis of problem characteristics
can we know the best data structure for the task.
Bank example:
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Start account: a few minutes
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Transactions: a few seconds
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Close account: overnight
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11. Example.
for(a=0; a>10; a++)
//loop-1
{
printf(“Hello World...”);
}
for(a=0; a<10; a++)
//loop-2
{
printf(“Hello World...”);
}
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12. Example.
for(a=0; a<=10; a++)
//loop-3
{
printf(“Hello World...”);
}
for(a=0; a!=10; a++)
//loop-4
{
printf(“Hello World...”);
}
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13. Example: check for prime number
flag=0;
for(a=2;a<num;a++)
{
if(num%a==0)
flag=1;
}
if(flag==1)
printf(“Number is not prime.”);
else
printf(“Number is prime.”);
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14. Refinement-1
flag=0;
for(a=2;a<num;a++)
{
if(num%a==0) {
flag=1;
break;
}
}
if(flag==1)
printf(“Number is not prime.”);
else
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printf(“Number is prime.”);
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15. Refinement-2
flag=0;
for(a=2;a<num/2;a++)
{
if(num%a==0) {
flag=1;
break;
}
}
if(flag==1)
printf(“Number is not prime.”);
else
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printf(“Number is prime.”);
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16. Refinement-3
for(a=2;a<num/2;a++)
{
if(num%a==0)
break;
}
if(a==(num/2))
printf(“Number is prime.”);
else
printf(“Number is not prime.”);
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17. Example: swapping of two numbers, Way-1
a=13, b=29;
temp = a;
a = b;
b = temp;
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18. Way-2
a=13, b=29;
a = a + b;
a = a – b;
b = a – b;
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19. Way-3
a=13, b=29;
a = a ^ b;
b = a ^ b;
a = a ^ b;
or
a^=b^=a^=b;
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20. Worst / Average / Best case
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Worst-case running time of an algorithm
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The longest running time for any input of size n
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An upper bound on the running time for any input
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Guarantee that the algorithm will never take longer
Example: Sort a set of numbers in increasing order; and the data is in
decreasing order
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The worst case can occur fairly often
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E.g. in searching a database for a particular piece of information
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Best-case running time
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Sort a set of numbers in increasing order; and the data is already in
increasing order
Average-case running time
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May be difficult to define what “average” means
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21. Example: searching in database
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Best case: O(1)
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Worst case: O(n)
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Average case: O(n/2)
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22. Running time of algorithms
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Bounds are for the algorithms, rather than programs
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Programs are just implementations of an algorithm,
and almost always the details of the program do not
affect the bounds
Bounds are for algorithms, rather than problems
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A problem can be solved with several algorithms,
some are more efficient than others
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23. Describing algorithms
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Natural language
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English, Chinese
Instructions must be definite and effectiveness.
Graphic representation
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Flowchart
Work well only if the algorithm is small and simple.
Pseudo language
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Readable
Instructions must be definite and effectiveness.
Combining English and C
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Simple and Tough task to do.
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24. Algorithm and programs
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Algorithm: a method or a process followed to solve a
problem.
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An algorithm takes the input to a problem (function) and
transforms it to the output.
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A recipe: The algorithm gives us a “recipe” for solving
the problem by performing a series of steps, where
each step is completely understood.
A mapping of input to output.
A problem can be solved by many algorithms.
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25. A problem can have many solutions
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For example, the problem of sorting can be solved by the
following algorithms:
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Insertion sort
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Bubble sort
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Selection sort
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Shell sort
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Merge sort
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Radix sort
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Merge sort
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Quick sort
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26. Algorithm properties
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An algorithm possesses the following properties:
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It must be composed of a series of concrete steps.
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There can be no ambiguity as to which step will be
performed next.
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It must be composed of a finite number of steps.
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It must be correct.
It must terminate.
A computer program is an instance, or concrete
representation, for an algorithm in some programming
language.
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27. Thank you
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