This document provides an introduction to algorithms and their analysis. It discusses algorithm design techniques like insertion sort and asymptotic analysis using big O notation to describe an algorithm's running time. Insertion sort is analyzed as an example, with its best, average, and worst case times shown to be O(n), O(n^2), and O(n^2) respectively, where n is the input size. Common functions and standard asymptotic notations are also introduced.
This document provides an introduction to algorithms and their analysis. It discusses algorithm design techniques like insertion sort and asymptotic analysis using big O notation to describe an algorithm's running time. Insertion sort is analyzed as an example, with its best, average, and worst case times shown to be O(n), O(n^2), and O(n^2) respectively, ignoring constant factors. The key concepts of asymptotic notation like big O, Ω, and Θ are also introduced to formally analyze an algorithm's growth rate.
This document introduces algorithms and their basics. It defines an algorithm as a step-by-step procedure to solve a problem and get the desired output. Algorithms can be implemented in different programming languages. Common algorithm categories include search, sort, insert, update, and delete operations on data structures. An algorithm must be unambiguous, have well-defined inputs and outputs, terminate in a finite number of steps, and be feasible with available resources. The document also discusses how to write algorithms, analyze their complexity, and commonly used asymptotic notations like Big-O, Omega, and Theta.
Algorithm in Computer, Sorting and NotationsAbid Kohistani
The document discusses algorithms and their analysis. It begins by introducing algorithms and their importance in computer science. The problem of sorting is used as an example to introduce algorithms. Insertion sort is presented as a basic sorting algorithm, with examples of how it works. The analysis of algorithms is then discussed, including analyzing insertion sort's worst case running time, which grows quadratically as Θ(n^2). Asymptotic notation such as O, Ω, Θ is also introduced to analyze long term algorithm running times independent of machine details.
This document provides an overview of algorithms and their analysis. It defines an algorithm as a finite sequence of unambiguous instructions that will terminate in a finite amount of time. Key aspects that algorithms must have are being input-defined, having output, being definite, finite, and effective. The document then discusses steps for designing algorithms like understanding the problem, selecting data structures, and verifying correctness. It also covers analyzing algorithms through evaluating their time complexity, which can be worst-case, best-case, or average-case, and space complexity. Common asymptotic notations like Big-O, Omega, and Theta notation are explained for describing an algorithm's efficiency. Finally, basic complexity classes and their properties are summarized.
This document discusses data structures and algorithms. It provides course objectives which include imparting concepts of data structures and algorithms, introducing searching and sorting techniques, and developing applications using suitable data structures. Course outcomes include understanding algorithm performance analysis, concepts of data structures, linear data structures, and identifying efficient data structure implementations. The document also covers algorithm basics, specifications, expressions, analysis techniques and asymptotic notations for analyzing algorithms.
An algorithm is a set of steps to solve a problem. Algorithm efficiency describes how fast an algorithm solves problems of different sizes. Time complexity is the most important measure of efficiency, measuring the number of steps an algorithm takes based on the size of the input. Common techniques to analyze time complexity include calculating the number of operations in loops and recursions. Asymptotic notation like Big-O describes the long-term growth rate of an algorithm's running time as the input size increases.
This document provides an introduction to algorithm analysis and design. It defines what an algorithm is and lists some key properties it should have like being unambiguous, having a finite number of steps, and terminating. It discusses different ways to specify algorithms using natural language, flowcharts, or pseudocode. It also covers analyzing algorithm efficiency in terms of time and space complexity and introduces common asymptotic notations used like Big O, Big Omega, and Big Theta notation.
This document provides an introduction to algorithms and their analysis. It discusses algorithm design techniques like insertion sort and asymptotic analysis using big O notation to describe an algorithm's running time. Insertion sort is analyzed as an example, with its best, average, and worst case times shown to be O(n), O(n^2), and O(n^2) respectively, where n is the input size. Common functions and standard asymptotic notations are also introduced.
This document provides an introduction to algorithms and their analysis. It discusses algorithm design techniques like insertion sort and asymptotic analysis using big O notation to describe an algorithm's running time. Insertion sort is analyzed as an example, with its best, average, and worst case times shown to be O(n), O(n^2), and O(n^2) respectively, ignoring constant factors. The key concepts of asymptotic notation like big O, Ω, and Θ are also introduced to formally analyze an algorithm's growth rate.
This document introduces algorithms and their basics. It defines an algorithm as a step-by-step procedure to solve a problem and get the desired output. Algorithms can be implemented in different programming languages. Common algorithm categories include search, sort, insert, update, and delete operations on data structures. An algorithm must be unambiguous, have well-defined inputs and outputs, terminate in a finite number of steps, and be feasible with available resources. The document also discusses how to write algorithms, analyze their complexity, and commonly used asymptotic notations like Big-O, Omega, and Theta.
Algorithm in Computer, Sorting and NotationsAbid Kohistani
The document discusses algorithms and their analysis. It begins by introducing algorithms and their importance in computer science. The problem of sorting is used as an example to introduce algorithms. Insertion sort is presented as a basic sorting algorithm, with examples of how it works. The analysis of algorithms is then discussed, including analyzing insertion sort's worst case running time, which grows quadratically as Θ(n^2). Asymptotic notation such as O, Ω, Θ is also introduced to analyze long term algorithm running times independent of machine details.
This document provides an overview of algorithms and their analysis. It defines an algorithm as a finite sequence of unambiguous instructions that will terminate in a finite amount of time. Key aspects that algorithms must have are being input-defined, having output, being definite, finite, and effective. The document then discusses steps for designing algorithms like understanding the problem, selecting data structures, and verifying correctness. It also covers analyzing algorithms through evaluating their time complexity, which can be worst-case, best-case, or average-case, and space complexity. Common asymptotic notations like Big-O, Omega, and Theta notation are explained for describing an algorithm's efficiency. Finally, basic complexity classes and their properties are summarized.
This document discusses data structures and algorithms. It provides course objectives which include imparting concepts of data structures and algorithms, introducing searching and sorting techniques, and developing applications using suitable data structures. Course outcomes include understanding algorithm performance analysis, concepts of data structures, linear data structures, and identifying efficient data structure implementations. The document also covers algorithm basics, specifications, expressions, analysis techniques and asymptotic notations for analyzing algorithms.
An algorithm is a set of steps to solve a problem. Algorithm efficiency describes how fast an algorithm solves problems of different sizes. Time complexity is the most important measure of efficiency, measuring the number of steps an algorithm takes based on the size of the input. Common techniques to analyze time complexity include calculating the number of operations in loops and recursions. Asymptotic notation like Big-O describes the long-term growth rate of an algorithm's running time as the input size increases.
This document provides an introduction to algorithm analysis and design. It defines what an algorithm is and lists some key properties it should have like being unambiguous, having a finite number of steps, and terminating. It discusses different ways to specify algorithms using natural language, flowcharts, or pseudocode. It also covers analyzing algorithm efficiency in terms of time and space complexity and introduces common asymptotic notations used like Big O, Big Omega, and Big Theta notation.
The document defines algorithms and describes their characteristics and design techniques. It states that an algorithm is a step-by-step procedure to solve a problem and get the desired output. It discusses algorithm development using pseudocode and flowcharts. Various algorithm design techniques like top-down, bottom-up, incremental, divide and conquer are explained. The document also covers algorithm analysis in terms of time and space complexity and asymptotic notations like Big-O, Omega and Theta to analyze best, average and worst case running times. Common time complexities like constant, linear, quadratic, and exponential are provided with examples.
This document provides an overview of algorithms including definitions, characteristics, design, and analysis. It defines an algorithm as a finite step-by-step procedure to solve a problem and discusses their key characteristics like input, definiteness, effectiveness, finiteness, and output. The document outlines the design of algorithms using pseudo-code and their analysis in terms of time and space complexity using asymptotic notations like Big O, Big Omega, and Big Theta. Examples are provided to illustrate linear search time complexity and the use of different notations to determine algorithm efficiency.
The document provides an introduction and overview of the Design and Analysis of Algorithms course. It covers key topics like asymptotic notations and their properties, analyzing recursive and non-recursive algorithms, divide-and-conquer algorithms like quicksort and mergesort, and sorting algorithms like heap sort. Examples of insertion sort and analysis of its worst-case running time of O(n2) are provided. Asymptotic notation like Big-O, Ω, and Θ are introduced to analyze algorithms' time complexities as the problem size n approaches infinity.
Analysis and Algorithms: basic Introductionssuseraf8b2f
This document discusses analyzing algorithms and their time and space complexity. It introduces various metrics for analyzing algorithms such as correctness, time complexity, space complexity, and optimality. Time complexity, which is the main focus, refers to the amount of time an algorithm takes to complete as a function of the input size. Various algorithm examples are provided and different approaches for calculating time complexity like worst-case, best-case, average-case and asymptotic analysis are explained. Asymptotic notations like Big-O, Big-Omega and Theta notation are introduced to describe the asymptotic behavior of algorithms.
This document discusses algorithmic efficiency and complexity. It begins by defining an algorithm as a step-by-step procedure for solving a problem in a finite amount of time. It then discusses estimating the complexity of algorithms, including asymptotic notations like Big O, Big Omega, and Theta that are used to describe an algorithm's time and space complexity. The document provides examples of time and space complexity for common algorithms like searching and sorting. It concludes by emphasizing the importance of analyzing algorithms to minimize their cost and maximize efficiency.
The document provides an overview of algorithms, including definitions, types, characteristics, and analysis. It begins with step-by-step algorithms to add two numbers and describes the difference between algorithms and pseudocode. It then covers algorithm design approaches, characteristics, classification based on implementation and logic, and analysis methods like a priori and posteriori. The document emphasizes that algorithm analysis estimates resource needs like time and space complexity based on input size.
Design Analysis of Alogorithm 1 ppt 2024.pptxrajesshs31r
This document discusses algorithms and their analysis. It begins by defining an algorithm as a sequence of unambiguous instructions to solve a problem in a finite amount of time. It then provides examples of Euclid's algorithm for computing the greatest common divisor. The document goes on to discuss the fundamentals of algorithmic problem solving, including understanding the problem, choosing exact or approximate solutions, and algorithm design techniques. It also covers analyzing algorithms by measuring time and space complexity using asymptotic notations.
Analysis of Algorithm full version 2024.pptxrajesshs31r
This document discusses algorithms and their analysis. It begins by defining an algorithm as a sequence of unambiguous instructions to solve a problem in a finite amount of time. Euclid's algorithm for computing the greatest common divisor is provided as an example. The document then covers fundamentals of algorithmic problem solving, including understanding the problem, choosing exact or approximate solutions, and algorithm design techniques. It also discusses analyzing algorithms based on time and space complexity, as well as worst-case, best-case, and average-case efficiencies. Common problem types like sorting, searching, and graph problems are briefly outlined.
Data Structure & Algorithms - Introductionbabuk110
This document introduces key concepts in data structures and algorithms including algorithms, programs, data structures, objects, and relations between data structures and objects. It discusses analyzing algorithms through measuring running time experimentally and theoretically using asymptotic analysis. Examples are provided of insertion sort and prefix averages algorithms, analyzing their best, worst, and average cases, and calculating their asymptotic running times as O(n) and O(n^2) respectively. The document outlines criteria for good algorithms and techniques for asymptotic analysis including Big-O notation.
This document discusses algorithms and their analysis. It defines an algorithm as a well-defined computational procedure that takes inputs and produces outputs. Examples of algorithms include procedures for returning web pages with keywords and various sorting algorithms. The document emphasizes the importance of analyzing algorithms for correctness and efficiency. It introduces pseudocode as a way to describe algorithms at a high level. The analysis focuses on determining the worst-case number of primitive operations like assignments and comparisons as a function of the input size using the random access machine model of computation. Counting the operations provides a way to evaluate an algorithm's speed independently of hardware.
The document discusses algorithms and their analysis. It defines an algorithm as a sequence of unambiguous steps to solve a problem within a finite time. Characteristics of algorithms include being unambiguous, having inputs/outputs, and terminating in finite time. Algorithm analysis involves determining theoretical and empirical time and space complexity as input size increases. Time complexity is analyzed by counting basic operations, while space complexity considers fixed and variable memory usage. Worst, best, and average cases analyze how efficiency varies with different inputs. Asymptotic analysis focuses on long-term growth rates to compare algorithms.
An algorithm is a well-defined set of steps to solve a problem in a finite amount of time. The complexity of an algorithm measures the time and space required for inputs of different sizes. Time complexity indicates the running time, while space complexity measures storage usage. These complexities can be analyzed before and after implementation using asymptotic notations like Big-O, Omega, and Theta to determine worst-case, best-case, and average-case efficiencies. Proper algorithm design considers factors like understandability, efficiency, and resource usage.
An algorithm is a well-defined set of steps to solve a problem in a finite amount of time. The complexity of an algorithm measures the time and space required for inputs of different sizes. Time complexity indicates the running time, while space complexity measures storage usage. Analyzing algorithms involves determining their asymptotic worst-case, best-case, and average-case time complexities using notations like Big-O, Omega, and Theta. This provides insights into an algorithm's efficiency under different conditions.
This document discusses algorithms and their analysis. It defines an algorithm as a set of unambiguous instructions to solve a problem with inputs and outputs. Good algorithms have well-defined steps, inputs, outputs, and terminate in a finite number of steps. Common algorithm analysis methods include calculating time and space complexity using asymptotic notations like Big-O. Pseudocode and flowcharts are commonly used to represent algorithms. Asymptotic analysis determines an algorithm's best, average, and worst case running times.
Introduction to design and analysis of algorithmDevaKumari Vijay
This document defines algorithms and describes how to analyze their efficiency. It states that an algorithm is a set of unambiguous instructions that accepts input and produces output within a finite number of steps. The document outlines criteria algorithms must satisfy like being definite, finite, and effective. It also describes different representations of algorithms like pseudocode and flowcharts. The document then discusses analyzing algorithms' time and space efficiency using asymptotic notations like Big-O, Big-Omega, and Big-Theta. It defines these notations and provides examples to classify algorithms' order of growth.
Advanced Datastructures and algorithms CP4151unit1b.pdfSheba41
Insertion sort has a running time of O(n^2) in the worst case. It works by iterating through the array (n times) and inserting each element into its sorted position (taking up to n steps). This results in a total worst case time of n(n) = O(n^2) operations.
This document provides an overview of algorithms. It begins by discussing the origins and evolution of the term "algorithm" from its Arabic roots in the 9th century to its modern meaning of a well-defined computational procedure. The document then defines algorithms and their key characteristics such as being precise, unambiguous, and terminating after a finite number of steps. Common algorithm design techniques like divide-and-conquer, greedy algorithms, and dynamic programming are introduced. Examples of merge sort and finding the maximum element in a list are used to illustrate algorithm concepts.
asymptotic analysis and insertion sort analysisAnindita Kundu
This document discusses asymptotic analysis of algorithms. It introduces key concepts like algorithms, data structures, best/average/worst case running times, and asymptotic notations like Big-O, Big-Omega, and Big-Theta. These notations are used to describe the long-term growth rates of functions and provide upper/lower/tight bounds on the running time of algorithms as the input size increases. Examples show how to analyze the asymptotic running time of algorithms like insertion sort, which is O(n^2) in the worst case but O(n) in the best case.
Data structures and algorithms involve organizing data to solve problems efficiently. An algorithm describes computational steps, while a program implements an algorithm. Key aspects of algorithms include efficiency as input size increases. Experimental studies measure running time but have limitations. Pseudocode describes algorithms at a high level. Analysis counts primitive operations to determine asymptotic running time, ignoring constant factors. The best, worst, and average cases analyze efficiency. Asymptotic notation like Big-O simplifies analysis by focusing on how time increases with input size.
Improving the viability of probiotics by encapsulation methods for developmen...Open Access Research Paper
The popularity of functional foods among scientists and common people has been increasing day by day. Awareness and modernization make the consumer think better regarding food and nutrition. Now a day’s individual knows very well about the relation between food consumption and disease prevalence. Humans have a diversity of microbes in the gut that together form the gut microflora. Probiotics are the health-promoting live microbial cells improve host health through gut and brain connection and fighting against harmful bacteria. Bifidobacterium and Lactobacillus are the two bacterial genera which are considered to be probiotic. These good bacteria are facing challenges of viability. There are so many factors such as sensitivity to heat, pH, acidity, osmotic effect, mechanical shear, chemical components, freezing and storage time as well which affects the viability of probiotics in the dairy food matrix as well as in the gut. Multiple efforts have been done in the past and ongoing in present for these beneficial microbial population stability until their destination in the gut. One of a useful technique known as microencapsulation makes the probiotic effective in the diversified conditions and maintain these microbe’s community to the optimum level for achieving targeted benefits. Dairy products are found to be an ideal vehicle for probiotic incorporation. It has been seen that the encapsulated microbial cells show higher viability than the free cells in different processing and storage conditions as well as against bile salts in the gut. They make the food functional when incorporated, without affecting the product sensory characteristics.
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algorithm_lec_1eregdsgdfgdgdfgdfgdfg.ppt
1. Design & Analysis of
Algorithms
Design the Algorithm
Analysis the Algorithm
2. Introduction
• Algorithm: Idea behind the Program
• Pseudo-Code: Natural Language + Flavour of
Programming Language (Even that can be used to
describe an algorithm)
• Program: Set of Instruction
• Process: Program in Execution
3. Algorithms
Finiteness: An algorithm must always terminate after a
finite number of steps.
Definiteness: Each step of an algorithm must be precisely
defined; the actions to be carried out must be rigorously
and unambiguously specified for each case.
Input: An algorithm has zero or more inputs, i.e, quantities
which are given to it initially before the algorithm begins.
Output: An algorithm has one or more outputs i.e,
quantities which have a specified relation to the inputs.
Effectiveness: An algorithm is also generally expected to
be effective. This means that all of the operations to be
performed in the algorithm must be sufficiently basic that
they can in principle be done exactly and in a finite length
of time.
17. Running Time
• The running time depends on the input: an already
sorted sequence is easier to sort.
• Parameterize the running time by the size of the
input, since short sequences are easier to sort than
long ones.
• Generally, we seek upper bounds on the running
time, because everybody likes a guarantee.
18. Kinds of analyses
Worst-case: (usually)
• T(n) = maximum time of algorithm on any input of
size n.
Average-case: (sometimes)
• T(n) = expected time of algorithm over all inputs of
size n.
• Need assumption of statistical distribution of inputs.
Best-case:
• Cheat with a slow algorithm that works fast on some
input.
19. Machine-Independent time
The RAM Model
Machine independent algorithm design depends on a
hypothetical computer called Random Acces Machine (RAM).
Assumptions:
• Each simple operation such as +, -, if ...etc takes exactly
one time step.
• Loops and subroutines are not considered simple
operations.
• Each memory acces takes exactly one time step.
20. Machine-independent time
What is insertion sort’s worst-case time?
• It depends on the speed of our computer,
• relative speed (on the same machine),
• absolute speed (on different machines).
BIG IDEA:
• Ignore machine-dependent constants.
• Look at growth of
“Asymptotic Analysis”
n
n
T as
)
(
21. Machine-independent time: An example
A pseudocode for insertion sort ( INSERTION SORT ).
INSERTION-SORT(A)
1 for j 2 to length [A]
2 do key A[ j]
3 Insert A[j] into the sortted sequence A[1,..., j-1].
4 i j – 1
5 while i > 0 and A[i] > key
6 do A[i+1] A[i]
7 i i – 1
8 A[i +1] key
24. Analysis of INSERTION-SORT(contd.)
The best case: The array is already sorted.
(tj =1 for j=2,3, ...,n)
)
1
(
)
1
(
)
1
(
)
1
(
)
( 8
5
4
2
1
n
c
n
c
n
c
n
c
n
c
n
T
).
(
)
( 8
5
4
2
8
5
4
2
1 c
c
c
c
n
c
c
c
c
c
25. Analysis of INSERTION-SORT(contd.)
•The worst case: The array is reverse sorted
(tj =j for j=2,3, ...,n).
)
1
2
/
)
1
(
(
)
1
(
)
( 5
2
1
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n
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T
)
1
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)
2
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1
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(
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2
/
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1
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( 8
7
6
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n
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c
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c )
2
/
2
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2
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(
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2
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7
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2
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1
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an
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26. Growth of Functions
Although we can sometimes determine the exact
running time of an algorithm, the extra precision is not
usually worth the effort of computing it.
For large inputs, the multiplicative constants and lower
order terms of an exact running time are dominated by
the effects of the input size itself.
27. Asymptotic Notation
The notation we use to describe the asymptotic running
time of an algorithm are defined in terms of functions
whose domains are the set of natural numbers.
Asymptotic notations are the
mathematical notations used to describe the running time
of an algorithm when the input tends towards a particular
value or a limiting value.
...
,
2
,
1
,
0
N
28. O-notation
• For a given function , we denote by the set
of functions
• We use O-notation to give an asymptotic upper bound of
a function, to within a constant factor.
• means that there existes some constant c
s.t. is always for large enough n.
)
(n
g ))
(
( n
g
O
0
0
all
for
)
(
)
(
0
s.t.
and
constants
positive
exist
there
:
)
(
))
(
(
n
n
n
cg
n
f
n
c
n
f
n
g
O
))
(
(
)
( n
g
O
n
f
)
(n
cg
)
(n
f
29. Ω-Omega notation
• For a given function , we denote by the
set of functions
• We use Ω-notation to give an asymptotic lower bound on
a function, to within a constant factor.
• means that there exists some constant c s.t.
is always for large enough n.
)
(n
g ))
(
( n
g
0
0
all
for
)
(
)
(
0
s.t.
and
constants
positive
exist
there
:
)
(
))
(
(
n
n
n
f
n
cg
n
c
n
f
n
g
))
(
(
)
( n
g
n
f
)
(n
f )
(n
cg
30. -Theta notation
• For a given function , we denote by the set
of functions
• A function belongs to the set if there exist
positive constants and such that it can be “sand-
wiched” between and or sufficienly large n.
• means that there exists some constant c1
and c2 s.t. for large enough n.
)
(n
g ))
(
( n
g
0
2
1
0
2
1
all
for
)
(
)
(
)
(
c
0
s.t.
and
,
,
constants
positive
exist
there
:
)
(
))
(
(
n
n
n
g
c
n
f
n
g
n
c
c
n
f
n
g
)
(n
f ))
(
( n
g
1
c 2
c
)
(
1 n
g
c )
(
2 n
g
c
Θ
))
(
(
)
( n
g
n
f
)
(
)
(
)
( 2
1 n
g
c
n
f
n
g
c
32. 2
2
2
2
1 3
2
1
n
c
n
n
n
c
2
1
3
2
1
c
n
c
Example 1.
Show that
We must find c1 and c2 such that
Dividing bothsides by n2 yields
For
)
(
3
2
1
)
( 2
2
n
n
n
n
f
)
(
3
2
1
,
7 2
2
0 n
n
n
n
33. Theorem
• For any two functions and , we have
if and only if
)
(n
g
))
(
(
)
( n
g
n
f
)
(n
f
)).
(
(
)
(
and
))
(
(
)
( n
g
n
f
n
g
O
n
f
44. Standard notations and common functions
• Floors and ceilings
1
1
x
x
x
x
x
45. Standard notations and common functions
• Logarithms:
)
lg(lg
lg
lg
)
(log
log
log
ln
log
lg 2
n
n
n
n
n
n
n
n
k
k
e
46. Standard notations and common functions
• Logarithms:
For all real a>0, b>0, c>0, and n
b
a
a
a
n
a
b
a
ab
b
a
c
c
b
b
n
b
c
c
c
a
b
log
log
log
log
log
log
log
)
(
log
log
47. Standard notations and common functions
• Logarithms:
b
a
c
a
a
a
a
b
a
c
b
b
b
b
log
1
log
log
)
/
1
(
log
log
log
48. Standard notations and common functions
• Factorials
For the Stirling approximation:
n
e
n
n
n
n
1
1
2
!
0
n
)
lg
(
)
!
lg(
)
2
(
!
)
(
!
n
n
n
n
n
o
n
n
n
49. Types of Functions
O(1) ------ Constant
Ex.: f(n)= 2 or 5 or 5000 (any constant) O(1)
O(logn) ------ logarithmic
Ex.: alogn+b O(logn)
O(n) Linear
Ex.: an+b =O(n)
O(n^2) Quadratic
Ex.: an^2+bn+c
O(n^3) Cubic
Ex.: an^3+bn^2+cn+d
O(a^n) like 2^n, 3^n, n^n Exponential
51. Machine Independent
• Time Complexity of an Algorithm:
Number of Primitive computations.
Relationship between the running time
of an algorithm and the size of its input
• Does not depend on Software and
Hardware
52. A Model of the Computer: RAM
• An informal model of the random-access machine (RAM)
• Basic types in the RAM model
• ◮ integer and floating-point numbers
• ◮ limited size of each “word” of data (e.g., 64 bits)
• Basic steps in the RAM model
• ◮ operations involving basic types
• ◮ load/store: assignment, use of a variable
• ◮ arithmetic operations: addition, multiplication, division,
etc.
• ◮ branch operations: conditional branch, jump
• ◮ subroutine call
A basic step in the RAM model takes a constant time