The document discusses algorithms, including their definition, characteristics, and complexity analysis. An algorithm is a finite set of steps to solve a problem. It has inputs, outputs, definiteness, finiteness, and effectiveness. The time and space complexity of algorithms depends on factors like the input size and memory requirements. Complexity is commonly expressed using Big O notation to categorize algorithms and compare their efficiency. Analysis considers best, worst, and average case time complexities.

1. ALGORITHM
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2. Introduction to Algorithm
● An algorithm is finite set of steps defining the
solution of a particular problem.
● It can be expressed in English like language,
called pseudocode, in programming language
or in the form of flowchart.
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3. Characteristics
● Input – There are zero or more values which are
externally supplied.
● Output – At least one value is produced
● Definiteness – Each step must be clear and
unambiguous
● Finiteness – If we trace the steps of an
algorithm, then for all cases, the algorithm must
terminate after a finite number of steps
● Effectiveness – Each step must be sufficiently
basic that it can in principal be carried out by a
person using only paper and pencil
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4. Algorithm Complexity
● There are basically two aspects of computer
programming.
○ Data Organization (i.e Data & structure)
○ Algorithm
● The choice of a particular algorithm depends
on the following consideration :
○ Time Complexity (Performance Requirements)
○ Space Complexity (Memory Requirements)
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5. Space Complexity
● It means the amount of memory, algorithm or
program needs to run to completion.
● Some of the reasons for studying space
complexity are
○ If a multi user system
○ Sufficient memory is available to run the
program
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6. Space Complexity (Cont.)
● The space needed by a program consists of
the following components.
○ Instruction Space : Space needed to store the
executable version of the program
○ Data Space : Space needed to store all
constants, variable values and has further
following components
■ Constants, variables, structured variables like
array and structure
■ Dynamically allocated space
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7. Space Complexity (Cont.)
● Environmental Stack Space : Space needed
to store the information needed to resume the
suspended functions.
○ Return Address
○ Values of all local variables and the values of
formal parameters in the function being
involved.
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8. Time Complexity
● It means the amount of time it needs to run to
completion
● Reasons for studying time complexity
○ Interested to know in advance that whether a
program will provide a satisfactory real time
response
○ There may be several possible solutions with
different time requirements
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9. Expressing Space and Time
Complexity
● The space and/or time complexity is usually
expressed in form of the function f(n)
○ Where n is the input size for a given instance of the
problem being solved.
● Expressing space and/ or time complexity as a
function has following reasons
○ We may be interested to predict the rate of growth
of complexity as the size of problem increases.
○ To Compare the complexities of two or more
algorithm
○ Since in modern computers, the memory is not a
sence constraint, therefore, our analysis of
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algorithms will be on the basis of time complexity.

10. Big ‘O’ Notation
● Big O is a characterization scheme that
allows to measure properties of algorithms
such time and space complexity.
● It is useful to set the prerequisites of
algorithms and to develop and design efficient
algorithms in terms of time and space
complexity.
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11. Categories of Algorithm
● Based on Big O notation, the algorithm can
be categorized as follows
○ Constant time O(1)
○ Logarithmic time O(log n)
○ Linear time O(n)
○ Polynomial time O(nk) (for k > 1)
○ Exponentail time O(kn) for k > 1
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12. Algorithm Analysis
● Different ways or algorithms to solve a
problem.
● Hence, some of the algorithm may be more
efficient than the others
● There are different types of time complexities
which can be analyzed for an algorithm
○ Best Case Time Analysis
○ Average Case Time Analysis
○ Worst Case Time Analysis
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13. Best Case Time Complexity
● It is a measure of the minimum time that the
algorithm will require for an input of size ‘n’.
● The running time of many algorithms varies
not only for the inputs of different sizes but
also for the different inputs of same size
○ Example : Sorting or Searching
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14. Worst Case Time Complexity
● The worst case time complexity of an
algorithm is a measure of the maximum time
that the algorithm will require for an input of
size ‘n’.
● Example : If ‘n’ input data items are supplied in
reverse order for any sorting algorithm, the
algorithm will require n2 operations to perform the
sort.
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15. Average Case Time Complexity
● The time that an algorithm will require to
execute a typical input data of size ‘n’ is
known as average case time complexity.
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