# Ppt on asymptotic notation of algorithms and flow

##### Algorithms: Design and Analysis Summer School 2013 at VIASM: Random Structures and Algorithms Lecture 1: Introduction Phan Th ị Hà D ươ ng 1.

37 III. Growth of Functions Asymptotic notation – The order of growth of the running time of an algorithm gives a simple characterization of the algorithms efficiency. – For input sizes large enough, we make only the order of growth of the running time relevant, so we study the asymptotic efficiency of algorithms. 38 g(n) is an asymptotically tight bound for f(n): Θ(g(n)) = {f(n) : there exist positive constants c1, c2, and N such that/

##### Complexity Analysis: Asymptotic Analysis. Recall What is the measurement of algorithm? How to compare two algorithms? Definition of Asymptotic Notation.

What is the measurement of algorithm? How to compare two algorithms? Definition of Asymptotic Notation Today Topic WAIT… Did we miss something? The resource function! Resource Function Time Function of an algorithm A Time Function of an algorithm A Space Function of an algorithm A Space Function of an algorithm A Size of input Time used Space used We don’t know, yet And this one From Experiment We count the number of instructions executed Only count/

##### CSC401 – Analysis of Algorithms Lecture Notes 1 Introduction

The asymptotic analysis of an algorithm determines the running time in big-Oh notation To perform the asymptotic analysis We find the worst-case number of primitive operations executed as a function of the input size We express this function with big-Oh notation Example: We determine that algorithm arrayMax executes at most 7n  2 primitive operations We say that algorithm arrayMax “runs in O(n) time” Since constant factors and/

##### Slide 5-1 交大資工 蔡文能 計概 J. Glenn Brookshear C H A P T E R 3 Chapter 5 Algorithms J. Glenn Brookshear 蔡 文 能.

f (n) be a function. f (n) is the maximum number of basic operations performed by the algorithm on any input size n. notation for efficiency classes – O( ? ) –  ( ? ) –  ( ? ) Best case, worst case, and average case Time Complexity vs. Space Complexity How shall we measure the amount of work done by an algorithm? Slide 5-81 交大資工 蔡文能 計概 Asymptotic Upper Bound (Big O) f(n)f(n) c g(n/

##### Analysis of Algorithms1 Estimate the running time Estimate the memory space required. Time and space depend on the input size.

asymptotic analysis of an algorithm determines the running time in big-Oh notation To perform the asymptotic analysis We find the worst-case number of primitive operations executed as a function of the input size We express this function with big-Oh notation Example: We determine that algorithm arrayMax executes at most 6 n  1 primitive operations We say that algorithm arrayMax “runs in O(n) time” Since constant factors and/

##### Analysis of Algorithms1 CS5302 Data Structures and Algorithms Lecturer: Lusheng Wang Office: Y6416 Phone: 2788 9820

asymptotic analysis of an algorithm determines the running time in big-Oh notation To perform the asymptotic analysis We find the worst-case number of primitive operations executed as a function of the input size We express this function with big-Oh notation Example: We determine that algorithm arrayMax executes at most 6 n  1 primitive operations We say that algorithm arrayMax “runs in O(n) time” Since constant factors and/

##### Λλ Fernando Magno Quintão Pereira P ROGRAMMING L ANGUAGES L ABORATORY Universidade Federal de Minas Gerais - Department of Computer Science P ROGRAM A.

of language and notation. (N. Wirth) The purpose of this class is to provide a proper notation to deal with these two questions. To achieve this goal, we shall look into algebraic bodies called lattices. – But before, we shall provide some intuition on why the dataflow algorithms are correct. How do we know that liveness terminates? Given a control flow/p ∈ pred(B) OUT[P] 7: OUT[B] = f b (IN[B]) The Asymptotic Complexity of the Solver 1.The IN/OUT set associated with a block can change at most H times; hence/

##### 1 Online Scheduling With Precedence Constraints Yumei Huo Department of Computer Science College.

be the c max produced by Delay-Coffman-Graham algorithm and S* be the c max of optimal schedule, then S ≤(S*+p). The asymptotic competitive ratio is 1 since S*>>p. 55 Outline Introduction: –Background and Notations –Three basic scheduling algorithms Online Scheduling of Precedence Constrained Tasks –Four nonpreemptive scheduling problems –Three preemptive scheduling problems Approximation Algorithms for Online Scheduling of Equal Processing Time Task System Future Work 56/

##### Analysis of Algorithms (Chapter 4)

big-Oh notation To perform the asymptotic analysis We find the worst-case number of basic operations as a function of the input size We express this function with big-Oh notation Example: We determine that algorithm arrayMax executes at most 8n  2 primitive operations We say that algorithm arrayMax “runs in O(n) time” Example: Sequential Search Algorithm SequentialSearch(A, x): Input: An array A and a target/

##### Performance Analysis: Theory and Practice Chris Mueller Tech Tuesday Talk July 10, 2007.

Web  Workloads Data mining Databases Statistical analysis and modeling Graph problems Information visualization  Key: data size Theory Big-O Notation Big-O notation is a method for describing the time or space requirements of an algorithm. f(x) = O(g(x)) Example/of communication to computation ratio is based on the sequence lengths, size of the DNA alphabet, and number of matches: |∑ DNA | n + m +  nm nm  is the percentage of dots that are recorded as matches and is the asymptotic limit of the algorithm/

##### The Seven Functions. Analysis of Algorithms. Simple Justification Techniques. 2 CPSC 3200 University of Tennessee at Chattanooga – Summer 2013 2010 Goodrich,

n  n 0 this is true for c = 8 and n 0 = 2 CPSC 3200 University of Tennessee at Chattanooga – Summer 2013 26 2010 Goodrich, Tamassia The asymptotic analysis of an algorithm determines the running time in big-Oh notation. To perform the asymptotic analysis We find the worst-case number of primitive operations executed as a function of the input size. We express this function with big-Oh/

##### 9/26/2002CSE 202 - Intro CSE 202 - Algorithms Fall 2002 Instructor: Larry Carter Office hours (4101 AP&M) Tu & Th 3:30 – 5:00 (or whenever)

whenever) TA: John-Paul Fryckman jfryckm@cs.ucsd.edu CSE 202 - Intro2 What we’ll study General Techniques Divide and Conquer, Dynamic Programming, Hashing, Greedy Algorithms, Reduction to other problems,... Specific Problems Sorting, sorting, shortest paths, max flow, sorting,... Various Paradigms Probabilistic algorithms Alternate models of computation NP Completeness CSE 202 - Intro3 Sounds like my undergrad course... Going over same material twice is good! We/

##### Describing Data The canonical descriptive strategy is to describe the data in terms of their underlying distribution As usual, we have a p-dimensional.

and sets X, Y, and Z returns either yes or no Goal: d-sep(X; Y | Z, G) = yes iff I(X;Y|Z) follows from Markov(G) Paths Intuition: dependency must “flow” along paths in the graph A path is a sequence of/a small induced width, there are algorithms that find it in polynomial time /notation Y[1]Y[2] Y[M] Y[M+1]  Y|X XX m X[m] Y[m] Query Bayesian Networks and/of the form N (x i,pa i ) –Parameter estimation Bayesian methods also require choice of priors Both MLE and Bayesian are asymptotically equivalent and/

##### Kinetics and Statistical Methods for Complex Particle Systems

, Simulations of granular flows from UT Austin and CalTech groups Goals: Understanding of analytical properties: large energy tails Long time asymptotics and characterization of asymptotics states A unified approach for Maxwell type interactions and generalizations. / matter phenomena Remark: The numerical algorithm is based on the evolution of the continuous spectrum of the solution as in Greengard-Lin’00 spectral calculation of the free space heat kernel, i.e. self-similar of the heat equation in all space/

##### Data Structures Richard Anderson University of Washington 7/2/20081IUCEE: Data Structures.

Data Structures (4) Abstract data types and their implementations as data structures. Efficient of algorithms employing these data structures; asymptotic analyses. Dictionaries: balanced search trees, hashing. Priority queues: heaps. Disjoint sets with union, find. Graph algorithms: shortest path, minimum spanning tree, /of Order Notation Upper bound:T(n) = O(f(n))Big-O Exist positive constants c and n’ such that T(n)  c f(n)for all n  n’ Lower bound:T(n) =  (g(n))Omega Exist positive constants c and/

##### Writing for Computer Science 7. Algorithms 8. Editing 2008. 05. 23 Cho, Ho-Gi GNU OSLab.

by choice of algorithm but also by changing the way disk is used and memory is accessed.  Disk and network traffic Because of the sophistication of current disk drives and the complexity of their interaction with CPU and OS, exact mathematical descriptions of algorithm behavior are unattainable; broad approximations are often the only manageable way of describing disk performance. 7. Algorithms GNU OSLabWriting for Computer Science 5 Asymptotic complexity  Define : Big-O notation a function/

##### Introduction to Optimization 1. Optimization … is a branch of mathematics and computational science that studies methods and techniques specially designed.

and space complexity Time is the number of steps required to solve a problem of size n. We are looking for the worst-case asymptotic bound on the step count (not an exact count). Asymptotic behavior is the limiting behavior as n tends to a large number. 21 Complexity of Algorithms An algorithm/– a quadratic polynomial. Other examples are minimum spanning tree, max flow network etc. The solutions for the above problems are tractable 22 Complexity of Algorithms Exponential time O(c n ) where is c is a positive/

##### Evolution of statistical models of non-conservative particle interactions Irene M. Gamba Department of Mathematics and ICES The University of Texas at.

analytical properties: large energy tails Long time asymptotics and characterization of asymptotics states Long time asymptotics and characterization of asymptotics states A unified approach for Maxwell type interactions and generalizations. A unified approach for Maxwell type interactions and generalizations. Spectral-Lagrangian solvers for dissipative interactionsSpectral-Lagrangian solvers for dissipative interactions Simulations of granular flows from UT Austin and CalTech groupsUT Austin CalTech Part I/

must specify the requirements of the software system Must be based on accurate information Various techniques: – discussions and negotiations with the client – modeling the problem structure and data flow – observation of client activities – analysis of existing solutions and systems Copyright © 2005/ of the algorithm We often use Big-Oh notation to specify the order, such as O(n 2 ) Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 1-30 FIGURE 1.11 Some growth functions and their asymptotic /

##### Coursenotes A Practical Introduction to Data Structures and Algorithm Analysis Second Edition Clifford A. Shaffer Department of Computer Science Virginia.

algorithm that makes efficient use of the computer’s resources. Algorithm Efficiency (cont) Goal (1) is the concern of Software Engineering. Goal (2) is the concern of data structures and algorithm analysis. When goal (2) is important, how do we measure an algorithm’s cost? How to Measure Efficiency? 1.Empirical comparison (run programs) 2.Asymptotic Algorithm/LIFO: Last In, First Out. Restricted form of list: Insert and remove only at front of list. Notation: Insert: PUSH Remove: POP The accessible element /

##### Advanced Membrane Based Water Treatment Technologies Sohail Murad, Chemical Engineering Department Prime Grant Support: US Department of Energy Problem.

metrics of the larger unchanged chip beyond pre-set bounds (e.g., <= 10% increase in wire-length) Use of a new network-flow /and need expertise to use. This project aims to develop techniques to profit from both types of languages. Transformation based approach Design an algorithmic approach to transform UML diagrams systematically into a formal notation/. Extend the analysis to large random networks. Derive low-complexity asymptotically-optimal Network & Channel code pairs. Extend to interference networks, /

##### ENEE759K/CMSC751: Parallel Algorithmics, Spring 2012 Time and Location MW 2:00-3:15. JMP 2202 Instructor: Dr. U. Vishkin Office.

-flow example? As advanced any irregular fine-grained parallel algorithms dared on any parallel architecture - Horizons of a computer architecture cannot only be studied using elementary algorithms [Performance, efficiency and effectiveness of a car not tested only in low gear or limited road conditions] - Stress test for important architecture capabilities not often discussed: 1.Strong scaling : Increase #processors, not problem size 2.Rewarding even little amounts of algorithm/

##### Coursenotes A Practical Introduction to Data Structures and Algorithm Analysis Second Edition Clifford A. Shaffer Department of Computer Science Virginia.

algorithm that makes efficient use of the computer’s resources. Algorithm Efficiency (cont) Goal (1) is the concern of Software Engineering. Goal (2) is the concern of data structures and algorithm analysis. When goal (2) is important, how do we measure an algorithm’s cost? How to Measure Efficiency? 1.Empirical comparison (run programs) 2.Asymptotic Algorithm/LIFO: Last In, First Out. Restricted form of list: Insert and remove only at front of list. Notation: Insert: PUSH Remove: POP The accessible element /

##### WIRELESS MESH NETWORKS Ian F. AKYILDIZ* and Xudong WANG** * Georgia Institute of Technology BWN (Broadband Wireless Networking) Lab & ** TeraNovi Technologies.

-hop wireless networks. Next we will focus on the asymptotic analysis of network capacity of multi-hop wireless networks. Major results in this research area are presented based on concise explanations about how they are derived. Major results in this research area are presented based on concise explanations about how they are derived. 14 15 Notations and Terms O(·): A Landau symbol. Given f = O/

##### 1-1 Software Development Objectives: Discuss the goals of software development Identify various aspects of software quality Examine two development life.

and debugging – maintenance and evolution 1-6 Problem Specification We must specify the requirements of the software system Must be based on accurate information Various techniques: – discussions and negotiations with the client – modeling the problem structure and data flow – observation of client activities – analysis of existing solutions and/the order of the algorithm We often use Big-Oh notation to specify the order, such as O(n 2 ) 1-25 FIGURE 1.11 Some growth functions and their asymptotic complexity /

##### On Priority Queues with Impatient Customers: Exact and Asymptotic Analysis Seminar in Operations Research 01/01/2007 Luba Rozenshmidt Advisor: Prof. Avishai.

Avishai Mandelbaum 2 Flow of the Talk Environments with heterogeneous customers Call Centers: Overview Background – exact and asymptotic results Erlang-C with priorities Erlang-A with priorities Asymptotic results: the lowest priority Asymptotic results: other priorities Additional results and future research 3 /1 1 L L 1 + Non-Preemptive Priority: Transition-Rate Diagram 18 Non-Preemptive Priority: K Types The Algorithm Step 1: Step 2: ”Merge” the first k types to a single type with Step 3: 19 Towards/

##### Algorithms and Data Structures

often an implementation of an ADT Algorithm Analysis Problem Solving Space Complexity Time Complexity Classifying Functions by Their Asymptotic Growth 1. Problem Definition What is the task to be accomplished? Calculate the average of the grades for /year to run to completion Algorithms running time is an important issue Pseudo Code and Flow Charts Basic elements of Pseudo code Basic operations of Pseudo code Flow Chart Symbols used in flow charts Examples Pseudo Code and Flow Charts There are two commonly/

##### Winter 2014Parallel Processing, Fundamental ConceptsSlide 1 3 Parallel Algorithm Complexity Review algorithm complexity and various complexity classes:

, Fundamental ConceptsSlide 4 Some Commonly Encountered Growth Rates Notation Class nameNotes O(1) ConstantRarely practical O(log log/asymptotic analysis.  A question of interest is whether or not the algorithm at hand is the best algorithm for solving the problem? 3.2. Algorithm Optimality And Efficiency Winter 2014Parallel Processing, Fundamental ConceptsSlide 7 3.2. Algorithm Optimality And Efficiency What is the running timeƒ(n) of the fastest algorithm for solving this problem? Of course, algorithm/

##### An Integrated Theory of Type-Based Static and Dynamic Verification Taro Sekiyama Dept. of Communications and Computer Engineering Graduate School of Informatics.

All value flows between typed and untyped parts have to be monitored by casts Paraphrase of Type /if (x : Dyn bool ) then “true” else “false” Blame calculus Notation typed code untyped code cast let x = Dyn if…then succ Dyn else / Data structures Data structures are crucial to design algorithms Efficient, correct algorithms need fine- grained specifications on data structures E/of both worlds E.g., tails of sorted lists are merely lists Checking specs at run time can worsen asymptotic time complexity Pros and/

##### Problemas Analíticos para la Ecuación de Boltzmann Analytical issues from the Boltzmann Transport Equation Irene M. Gamba The University of Texas at Austin.

solutions Space inhomogeneous problems Time splitting algorithms Simulations of boundary value – layers problems Benchmark simulations Part III A general form statistical transport : The space-homogenous BTE with external heating sources Important examples from mathematical physics and social sciences: The term models external heating sources: background thermostat (linear collisions), thermal bath (diffusion) shear flow (friction), dynamically scaled long time limits (self-similar solutions). Inelastic/

##### Jan. 20151 Welcome to the Course of Advanced Algorithm Design (ACS-7101/3)

Hill, 2002. Lecture slides online Other reference: The Design and Analysis of Computer Algorithms, A.V. Aho, J.E. Hopcroft and J.D. Ullman Jan. 20156 Course Roadmap Algorithmics Basics Divide and Conquer Sorting and Selection Search Trees Graph Algorithms Dynamic Programming Greedy Algorithms Selected Topics Randomized Algorithms Jan. 20157 Algorithmics Basics Introduction to algorithms, complexity, and proof of correctness. (Chapters 1 & 2) Asymptotic Notation. (Chapter 3.1) Goals –Know how to write formal/

##### Topics Will be covered Important Programming Concepts Types, Recursion/Induction, Asymptotic Complexity The Toolbox (Data Structures) Arrays, Linked Lists,

Lectures 24 and above Java Virtual Machine Distributed Systems and Cloud Computing Balancing Trees (e.g.: AVL trees) But do know what a balanced and unbalanced tree is Recurrences Network Flow Primitive Types boolean, int, double, etc… Test equality with == and != Compare with, and >= Typing void/2 + n + 2: 2n 3 is the dominant term Asymptotic Complexity Meaning of c Cannot get a precise measurement Famous election recounts (Bush/Gore, Coleman/Franken) Algorithm’s speed on a 2 GHz versus a 1 GHz processor /

##### Lecture 5 Advanced (= Modern) Regression Analysis NUMERICAL ANALYSIS OF BIOLOGICAL AND ENVIRONMENTAL DATA John Birks.

of distributions into their underlying components. Maximum likelihood solution based on assumption of two univariate normal distributions with unequal variances. Expectation – maximisation (EM) algorithm to estimate means  1 and  2 and variances  1 and  2 of/ area and forest plus agriculture area), animal density (ANI), average annual precipitation (PRE) and flow (FLO). Concentration of total phosphorus (CTP), concentration of ortho-phosphorus (COP), export of total phosphorus (ETP) and export of ortho-/

##### Fall 2010Parallel Processing, Fundamental ConceptsSlide 2 3.1 Asymptotic Complexity Fig. 3.1 Graphical representation of the notions of asymptotic complexity.

Algorithmic Graph Theory and Perfect Graphs [GOLU04]: Complexity of determining whether an n-vertex graph is planar ExponentialKuratowski1930 O(n 3 )Auslander and Porter1961 Goldstein1963 Shirey1969 O(n 2 )Lempel, Even, and Cederbaum1967 O(n log n)Hopcroft and Tarjan1972 O(n)Hopcroft and Tarjan1974 Booth and Leuker1976 A second, more complex example: Max network flow/Given f(n) = a f(n/b) + h(n); a, b constant, h arbitrary function the asymptotic solution to the recurrence is (c = log b a) f(n) =  (n c )if /

##### Graph-based Algorithms for Information Retrieval and Natural Language Processing Rada Mihalcea University of North Texas RANLP 2005.

l Part 1: Elements of graph-theory: –Terminology, notations, algorithms on graphs l Part 2: Graph-based algorithms for IR –Web search –Text clustering and classification l Part 3: Graph-based algorithms for NLP –Word Sense Disambiguation –Clustering of entities (names/numbers)/-flow algorithms, with polynomial asymptotic running times l Use the min-cut / max-flow algorithm RANLP 2005 134 Cut-based Algorithm (cont.) Notice that without the structural information we would be undecided about the assignment of /

##### 0 Course Outline n Introduction and Algorithm Analysis (Ch. 2) n Hash Tables: dictionary data structure (Ch. 5, CLRS) n Heaps: priority queue data structures.

operations. Crude but valuable measure of algorithm ’ s performance as a function of input size. 44 Average, Best, and Worst-Case On which input instances should the algorithm ’ s performance be judged? n Average case:  Real world distributions difficult to predict n Best case:  Seems unrealistic n Worst case:  Gives an absolute guarantee  We will use the worst-case measure. 45 Asymptotic Notation Review Big-O, “ bounded/

##### OverviewKindergartenEvidence:First GradeEvidence:Second GradeEvidence: Counting and Cardinality Know number names and the count sequence. (K.CC.A) 1.Count.

the capacity to produce populations of infinite size, but environments and resources are finite. The distribution and abundance of organisms and populations in ecosystems are limited by the availability of matter and energy and the ability of the ecosystem to recycle materials. Principles that Underlie the Concept and/or Skill: Matter and energy flow and conservation Living systems require continuous energy input. Matter and energy are conserved as they flow through and between organisms. Some energy/

##### 0 CS 130 A: Data Structures and Algorithms n Course webpage: n

operations. Crude but valuable measure of algorithm ’ s performance as a function of input size. 64 Average, Best, and Worst-Case On which input instances should the algorithm ’ s performance be judged? n Average case:  Real world distributions difficult to predict n Best case:  Seems unrealistic n Worst case:  Gives an absolute guarantee  We will use the worst-case measure. 65 Asymptotic Notation Review Big-O, “ bounded/

#####  FUNDAMENTALS OF ALGORITHMS.  FUNDAMENTALS OF DATA STRUCTURES.  TREES.  GRAPHS AND THEIR APPLICATIONS.  STORAGE MANAGEMENT.

1) Primitive data structure. int, char, float. 2) Non-Primitive data structure. arrays, structure and files. TOPICS COVERED: 1)Algorithms. 2)Analysis of algorithm. 3) Analysis of algorithms using data structures. 4) Performance Analysis 4.1) Time Complexity. 4.2) Space Complexity. 4.3) Amortized time Complexity. 5) Asymptotic notation.  1.1 Definition:  An algorithm consists of a set of explicit and unambiguous, finite steps when carrying out for a given set/

##### Process Mining An index to the state of the art and an outline of open research challenges at DIIAG Claudio Di Ciccio, Massimo Mecella Seminars in Software.

(responded existence) Whenever B is performed, C must be performed afterwards and B can not be repeated until C is done (alternate response) The notation here is based on [AalstEtAl06, MaggiEtAl11] (DecSerFlow, Declare)AalstEtAl06 MaggiEtAl11/and global statistics on the mutual order of appearance of events for further fast querying Performances: the algorithm is proven to be fast (over 12m events processed in less than 170 secs.) Asymptotically: linear in the number of the traces quadratic in the number of/

##### Review for IST 441 exam. Exam structure Closed book and notes Graduate students will answer more questions Extra credit for undergraduates.

..... Why Use Big-O Notation Used when we only know the asymptotic upper bound. –What does asymptotic mean? –What does upper bound mean? If you are not guaranteed certain input, then it is a valid upper bound that even the worst-case input will be below. Why worst-case? May often be determined by inspection of an algorithm. Two Categories of Algorithms 2 4 8 16 32/

##### 1 Jeff Edmonds York University COSC 2011 Abstract Data Types Positions and Pointers Loop Invariants System Invariants Time Complexity Classifying Functions.

random coin flips R are independent of the input. Actually my algorithm always gives the right answer. And for EVERY input I, the expected running time (over choice of R) is great. There are/ e d f g hC2C2 Last Update: Dec 4, 2014 Properties Notation nnumber of vertices mnumber of edges deg(v)degree of vertex v Property 1  v deg(v) = 2m Proof: /256 Primal-Dual Hill Climbing No Gap Flow alg witness that network has this flow. Cut alg witness that network has no bigger flow. Prove: For every location to stand/

##### Brief Introduction of Algorithm. What is Algorithm A method with several definite steps to effectively complete a task. In general, it starts from the.

Example of Algorithm Sorting some disordered data  Bubble sort  Quick sort Example – Bubble Sort A step-by-step example Example – Quick Sort A step-by-step example Example – Comparison In general, quick sort can be much more faster than bubble sort. However, there are some issues when making comparison  A quantitative comparison?  Is there a worst case? Computational Complexity Big O notation (infinite asymptotics/

##### CS 361 – Chapter 1 What is this class about? –Data structures, useful algorithm techniques –Programming needs to address both –You already have done some.

1 step = 1 ns Algorithm analysis 2 ways –Exact: “count” exact number of operations –Asymptotic: find asymptotic or upper bound Amortization –Technique to simplify calculation –E.g. consider effect of occasional time penalties Exact analysis Not done often, only for small parts of code We want # assembly /to show that f(n) is O(g(n)) How do we show this is true using the definition? –We need to specify values of c and n 0. –We want to show that 7n 2 + 8n + 11 <= c n 2 for sufficiently large n. –Note that 7n/

##### DATA STRUCTURES Prepared by, K.ABINAYA L/IT. Aim: To present the concepts of arrays, structures, stack, queue, linked list, graphs, trees and storage.

, 2004. 5. Tanaenbaum A. S. Langram, Y. Augestein M.J, “Data Structures using C”,Pearson Education, 2004. INTRODUCTION UNIT-1 Fundamentals of Algorithm  Analysis of Algorithm  Performance Analysis Time complexity Space complexity  Asymptotic Notations UNIT-2 Fundamentals of Data Structure  Arrays  Structures  Stacks and its Application  Queue and its Representation  Linked List STACKSQUEUES UNIT-3 Trees  Binary Search Trees  Binary Tree Traversal Post-Order Pre-Order In-Order  Sorting/

##### 1 Chapter 7 Performance analysis of failure- prone production lines Learning objectives : Understanding the mathematical models of production lines Understanding.

are the curves increasing?Why do there reach an asymptote? What is TH when N= 0? What is the limit of TH as N tends to infinity? Why are/of the most efficient ones and can be extended to other systems such as assembly lines. Focus on Continuous flow model but all results can be extended to discrete flow models M1 B1 M2 B2 M3 B3 M4 75 Notation/ d (i) E(i), ps(i), pb(i) are functions of u (i),  u (i), d (i),  d (i) Decomposition method Decomposition 87 DDX Algorithm: Step 1: Initialisation u (i) = i,  u (i)/

##### EECC756 - Shaaban #1 Exam Review Spring2001 5-10-2001 Parallel Computer Architecture A parallel computer is a collection of processing elements that cooperate.

efficiency E(s, n) = 1 for all algorithms with any number of processors and any size problem s. Scalability Definition (more formal): The scalability  (s, n) of a machine for a given algorithm is defined as the ratio of the asymptotic speedup S(s,n) on the real machine to the asymptotic speedup S I (s, n) On the ideal realization of an EREW PRAM EECC756 - Shaaban #78 Exam/

##### UMass Lowell Computer Science 91.503 Analysis of Algorithms Prof. Karen Daniels Fall, 2001 Lecture 4 Tuesday, 10/2/01 Graph Algorithms: Part 2 Network.

a flow in G. Then: ä Implicit summation notation: source: 91.503 textbook Cormen et al. Exercise: show source: Sedgewick, Graph Algorithms Flow Properties (continued) Flow Equilibrium A = amount of flow into left set from outside right set B = amount of flow out of left set (and not into right set) C = amount of flow into right set from outside left set D = amount of flow out of right set (and not into left set) y = amount of flow into/

##### 1 Essential Computing for Bioinformatics Bienvenido Vélez UPR Mayaguez Lecture 4 High-level Programming with Python Part I: Controlling the flow of your.

Programming with Python Part I: Controlling the flow of your program Reference: How to Think Like/No need to retype your functions Keep a single group of related functions and declarations in each file 8 Why Functions? Powerful mechanism for/algorithms independently from a specific implementation, software or hardware? 21 Runtime Complexity Big O Notation Big Idea Measure the number of steps taken by the algorithm as a asymptotic function of the size of its input What is a step? How can we measure the size of/

##### Review Algorithm Analysis Problem Solving Space Complexity

Asymptotic Growth Pseudo Code and Flow Charts Basic elements of Pseudo code Basic operations of Pseudo code Flow Chart Symbols used in flow charts Examples Pseudo Code and Flow Charts There are two commonly used tools to help to document program logic (the algorithm/notion of an ordered sequence of operations Furthermore we introduce a dot notation (e.g. 3.1 come after 3 but before 4) to number subordinate operations for conditional and iterative operations Each instruction should be unambiguous and /