Lecture 14: General Problem-Solving Methods
|
|
- Derick Day
- 5 years ago
- Views:
Transcription
1 Lecture 14: General Problem-Solving Methods
2 Problem Solving Methods Greedy Method Divide-and-Conquer Backtracking Dynamic Programming Branch-and-Bound
3 Greedy Method The greedy method consists of an iteration of the following computations: selection procedure-a selection procedure is created to choose the next item to add to a list of locally optimalsolutions to sub problems feasibility check-a test is made to see if the current set of choices satisfies some locally optimal criterion. solution check -when a complete set is obtained it is checked to verify that it constitutes a solution for the original problem. Aquestionthatshouldcometomindis:Whatismeantbylocallyoptimal? This term refers to the amount of work necessary to determine a solution or to measure the level to which a criterion is met. If the computation leading to an optimal solution or the evaluation of a criterion does not involve an exhaustive search then that activity may be considered local.
4 Divide-and-Conquer As its name implies this method involves dividing a problem into smaller problems that can be more easily solved. While the specifics can vary from one application to another, divide-and-conquer always includes the following three steps in some form: Divide-Typically this steps involves splitting one problem into two problems of approximately 1/2 the size of the original problem. Conquer-The divide step is repeated (usually recursively) until individual problem sizes are small enough to be solved (conquered) directly. Recombine-The solution to the original problem is obtained by combining all the solutions to the sub-problems. Divide and Conquer is not applicable to every problem class. Even when D&C works it may not produce an efficient solution.
5 Backtracking Backtracking is used to solve problems in which a feasible solution is needed rather than an optimal one, such as the solution to a maze or the arrangement of squares in the 15-puzzle. Typically, the solution to a backtracking problem is a sequence of items(or objects) chosen from a set of alternatives that satisfy some criterion. A backtracking algorithm is a scheme for solving a series of sub-problems each of which may have multiple possible solutions and where the solution chosen for one sub-problem can affect the possible solutions of later sub-problems. To solve the overall problem, we find a solution to the first sub-problem and then attempt to recursively solve the other sub-problems based on this first solution. If wecannot,orwewantallpossiblesolutions,webacktrackandtrythenextpossible solution to the first sub-problem and so on. Backtracking terminates when there are no more solutions to the first sub-problem orasolutiontotheoverallproblemisfound.
6 Dynamic Programming In mathematics and computer science, dynamic programming is a method of solving complex problems by breaking them down into simpler steps. It is applicable to problems that exhibit the properties of overlapping sub problems and optimal substructure. Overlapping sub problems means that the space of sub problems must be small, that is, any recursive algorithm solving the problem will solve the same sub problems over and over, rather than generating new sub problems. Dynamic programming takes account of this fact and solves each sub problem only once. Optimal substructure means that the solution to a given optimization problem can be obtained by the combination of optimal solutions to its sub problems. Consequently, the first step towards devising a dynamic programming solution is to check whether the problem exhibits an optimal substructure.
7 Branch-and-Bound Graph traversal refers to the problem of visiting all the nodes in a graph in a particular manner. Graph traversal can be used as a problem-solving method when a problem state can be represented as a graph and its solution can be represented as a path in the graph. When the graph is a tree it can represent the problem space for a wide variety of combinatorial problems. In these cases the solution is usually at one of the leaf-nodes of the tree or is the path to a particular leaf-node. To make graph traversal efficient we need to avoid searching paths that can be determined will not result in good (or optimal) solutions. Techniques such a branch-and-bound can be used to reduce the number of operations required to search the graph or tree problem space by eliminating infeasible or unpromising branches.
8 Coin Changing An optimal solution to the coin changing problem is the minimum number of coins whose total value equals a specified amount. For example what is the minimum number of coins (current U.S. mint) needed to total 83 cents = = = = = = = 0 A Greedy Algorithm for Coin Changing 1. Set remval=initial_value 2. Choose largest coin that is less than remval. 3. Add coin to set of coins and set remval:=revamal-coin_value 4. repeat Steps 2 and 3 until remval = 0;
9 Coin Changing - Another Example The greedy method works for the U.S. minted coin set, but will it work for any coin set? Consider the coin set below and a change value of 82 cents = = = = = = = 0 By the coin-changing algorithm we obtain 3 26 cent pieces and 4 pennies, but we can use 2 26 cent pieces and 3 dimes to total 82 cents. Hence the greedy approach does not work for this coin set.
10 Quicksort Example i j pivot value items being swapped new sublists for next pass of quicksort
11 N-Queens Problem A classic backtracking algorithm is the solution to the N-Queens problem. In this problem you are to place queens (chess pieces) on an NxN chessboard in such a way that no two queens are directly attacking one another. That is no two queens share the same row, column or diagonal on the board. Backtracking Approach -Version 1: Until all queens are placed, choose the first available location and put the next queen in this position. If queens remain to be placed and no space is left, backtrack (by removing the last queens placed and placing it in the next available position).
12 N-Queens Problem Backtracking Approach - Version 2: A more efficient backtracking approach is to note that each queen must be in its own column and row. This reduces the search from (N 2 )! to N!.
13 The Binomial Coefficient (a+b) 0 = 1 (a+b) 1 = a+b (a+b) 2 = a 2 +2ab+b 2 The binomial theorem gives a closed-form expression for the coefficient of any term in the expansion of a binomial raised to the nth power. (a+b) 3 = a 3 +3a 2 b+3ab 2 +b 3 (a+b) 4 = a 4 +4a 3 b+6a 2 b 2 +4ab 3 +b 4 ( a + b) n n! n = k= 0 k! ( n k )! a k b n k The binomial coefficient is also the number of combinations of n items taken k at a time, sometimes called n-choose-k n 1 n 1 n + = k 1 k k 1 for 0 < k k = 0 or < n k = n
14 Traveling Salesperson with Branch-and-Bound In the most general case the distances between each pair of cities is a positive value with dist(a,b) dist(b,a). In the matrix representation, the main diagonal values are omitted (i.e. dist(a,a) 0). A B C D E F G H A B A H C B C D G D E F F E G H
15 The live-node list is ordered by bounding value and then by level of completion. That is, if two nodes have the same bounding value we place the one that is closer to completion ahead of the other node. This is because the bounding value of the of the nodeclosertocompletionismorelikelytobeclosertotheactualtourlength.
16 An Example Branch-and-Bound TSP The initial tour is A-F-E-D-B-C-A with a total length of 32. The sum of the minimum costs of leaving every node is 29 so we know that a minimal tour cannot have length less than 29.
17 The node shown in red were expanded from an active node (F 3 ) with a possible tour length of 29. However the completed tours turned out to be significantly larger.
18 Expanding D 3 we find an actual tour that is shorter than our initial tour. We do not yet know if this is a minimal tour but we can remove nodes from our live-node list that have a bounding value of >= 31. Now we expand D 2 to find that it leads to tours oflength>=33.
19 Expansion of E 2 eliminates this path as a candidate for a minimal tour.
20 When the live-node list is empty we are finished. In this example a minmal tour is A-C-E-D-B-F-Awithalengthof31wehavefoundatourthatisshorterthantheoriginal candidate tour.
Algorithm classification
Types of Algorithms Algorithm classification Algorithms that use a similar problem-solving approach can be grouped together We ll talk about a classification scheme for algorithms This classification scheme
More informationCSC 8301 Design and Analysis of Algorithms: Exhaustive Search
CSC 8301 Design and Analysis of Algorithms: Exhaustive Search Professor Henry Carter Fall 2016 Recap Brute force is the use of iterative checking or solving a problem by its definition The straightforward
More informationCS 440 Theory of Algorithms /
CS 440 Theory of Algorithms / CS 468 Algorithms in Bioinformaticsi Brute Force. Design and Analysis of Algorithms - Chapter 3 3-0 Brute Force A straightforward approach usually based on problem statement
More informationGreedy Algorithms and Huffman Coding
Greedy Algorithms and Huffman Coding Henry Z. Lo June 10, 2014 1 Greedy Algorithms 1.1 Change making problem Problem 1. You have quarters, dimes, nickels, and pennies. amount, n, provide the least number
More informationAlgorithmic patterns
Algorithmic patterns Data structures and algorithms in Java Anastas Misev Parts used by kind permission: Bruno Preiss, Data Structures and Algorithms with Object-Oriented Design Patterns in Java David
More informationBacktracking and Branch-and-Bound
Backtracking and Branch-and-Bound Usually for problems with high complexity Exhaustive Search is too time consuming Cut down on some search using special methods Idea: Construct partial solutions and extend
More informationCoping with the Limitations of Algorithm Power Exact Solution Strategies Backtracking Backtracking : A Scenario
Coping with the Limitations of Algorithm Power Tackling Difficult Combinatorial Problems There are two principal approaches to tackling difficult combinatorial problems (NP-hard problems): Use a strategy
More informationUCSD CSE 21, Spring 2014 [Section B00] Mathematics for Algorithm and System Analysis
UCSD CSE 21, Spring 2014 [Section B00] Mathematics for Algorithm and System Analysis Lecture 11 Class URL: http://vlsicad.ucsd.edu/courses/cse21-s14/ Lecture 11 Notes Goals for this week (Tuesday) Linearity
More informationData Structures, Algorithms & Data Science Platforms
Indian Institute of Science Bangalore, India भ रत य व ज ञ न स स थ न ब गल र, भ रत Department of Computational and Data Sciences DS221 19 Sep 19 Oct, 2017 Data Structures, Algorithms & Data Science Platforms
More informationSearch and Optimization
Search and Optimization Search, Optimization and Game-Playing The goal is to find one or more optimal or sub-optimal solutions in a given search space. We can either be interested in finding any one solution
More informationwww.thestudycampus.com Recursion Recursion is a process for solving problems by subdividing a larger problem into smaller cases of the problem itself and then solving the smaller, more trivial parts. Recursion
More informationChapter-6 Backtracking
Chapter-6 Backtracking 6.1 Background Suppose, if you have to make a series of decisions, among various choices, where you don t have enough information to know what to choose. Each decision leads to a
More informationCMSC Introduction to Algorithms Spring 2012 Lecture 16
CMSC 351 - Introduction to Algorithms Spring 2012 Lecture 16 Instructor: MohammadTaghi Hajiaghayi Scribe: Rajesh Chitnis 1 Introduction In this lecture we will look at Greedy Algorithms and Dynamic Programming.
More informationL.J. Institute of Engineering & Technology Semester: VIII (2016)
Subject Name: Design & Analysis of Algorithm Subject Code:1810 Faculties: Mitesh Thakkar Sr. UNIT-1 Basics of Algorithms and Mathematics No 1 What is an algorithm? What do you mean by correct algorithm?
More information5105 BHARATHIDASAN ENGINEERING COLLEGE
CS 6402 DESIGN AND ANALYSIS OF ALGORITHMS II CSE/IT /IV SEMESTER UNIT I PART A 1. Design an algorithm to compute the area and circumference of a circle?(dec 2016) 2. Define recurrence relation? (Dec 2016)
More informationSankalchand Patel College of Engineering - Visnagar Department of Computer Engineering and Information Technology. Assignment
Class: V - CE Sankalchand Patel College of Engineering - Visnagar Department of Computer Engineering and Information Technology Sub: Design and Analysis of Algorithms Analysis of Algorithm: Assignment
More informationLecture 3. Brute Force
Lecture 3 Brute Force 1 Lecture Contents 1. Selection Sort and Bubble Sort 2. Sequential Search and Brute-Force String Matching 3. Closest-Pair and Convex-Hull Problems by Brute Force 4. Exhaustive Search
More informationBacktracking. See Section 7.7 p of Weiss
Backtracking See Section 7.7 p 333-336 of Weiss So far we have looked at recursion in general, looked at Dynamic Programming as a way to make redundant recursions less inefficient, and noticed that recursion
More informationRecursion as a Problem-Solving Technique. Chapter 5
Recursion as a Problem-Solving Technique Chapter 5 Overview Ass2: TimeSpan Ass3: Maze "Quiz Ch02 + Ch05" - due before Wednesday class Not all in-class quizzes will be announced ahead of time Week-5: Sample
More informationDESIGN AND ANALYSIS OF ALGORITHMS
DESIGN AND ANALYSIS OF ALGORITHMS QUESTION BANK Module 1 OBJECTIVE: Algorithms play the central role in both the science and the practice of computing. There are compelling reasons to study algorithms.
More informationGraph Applications, Class Notes, CS 3137 1 Traveling Salesperson Problem Web References: http://www.tsp.gatech.edu/index.html http://www-e.uni-magdeburg.de/mertens/tsp/tsp.html TSP applets A Hamiltonian
More informationAlgorithms for Integer Programming
Algorithms for Integer Programming Laura Galli November 9, 2016 Unlike linear programming problems, integer programming problems are very difficult to solve. In fact, no efficient general algorithm is
More informationCSCE 321/3201 Analysis and Design of Algorithms. Prof. Amr Goneid. Fall 2016
CSCE 321/3201 Analysis and Design of Algorithms Prof. Amr Goneid Fall 2016 CSCE 321/3201 Analysis and Design of Algorithms Prof. Amr Goneid Course Resources Instructor: Prof. Amr Goneid E-mail: goneid@aucegypt.edu
More informationCLASS: II YEAR / IV SEMESTER CSE CS 6402-DESIGN AND ANALYSIS OF ALGORITHM UNIT I INTRODUCTION
CLASS: II YEAR / IV SEMESTER CSE CS 6402-DESIGN AND ANALYSIS OF ALGORITHM UNIT I INTRODUCTION 1. What is performance measurement? 2. What is an algorithm? 3. How the algorithm is good? 4. What are the
More informationCSE373: Data Structure & Algorithms Lecture 23: More Sorting and Other Classes of Algorithms. Catie Baker Spring 2015
CSE373: Data Structure & Algorithms Lecture 23: More Sorting and Other Classes of Algorithms Catie Baker Spring 2015 Admin No class on Monday Extra time for homework 5 2 Sorting: The Big Picture Surprising
More information6. Algorithm Design Techniques
6. Algorithm Design Techniques 6. Algorithm Design Techniques 6.1 Greedy algorithms 6.2 Divide and conquer 6.3 Dynamic Programming 6.4 Randomized Algorithms 6.5 Backtracking Algorithms Malek Mouhoub, CS340
More informationBacktracking. Chapter 5
1 Backtracking Chapter 5 2 Objectives Describe the backtrack programming technique Determine when the backtracking technique is an appropriate approach to solving a problem Define a state space tree for
More informationDEPARTMENT OF COMPUTER SCIENCE & ENGINEERING Question Bank Subject Name: CS6402- Design & Analysis of Algorithm Year/Sem : II/IV UNIT-I INTRODUCTION
Chendu College of Engineering & Technology (Approved by AICTE, New Delhi and Affiliated to Anna University) Zamin Endathur, Madurantakam, Kancheepuram District 603311 +91-44-27540091/92 www.ccet.org.in
More informationUNIVERSITY OF WATERLOO DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING ECE 250 ALGORITHMS AND DATA STRUCTURES
UNIVERSITY OF WATERLOO DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING ECE 250 ALGORITHMS AND DATA STRUCTURES Final Examination Instructor: R.E.Seviora 9-12 AM, Dec 14, 2002 Name (last, first) Student
More informationThe problem: given N, find all solutions of queen sets and return either the number of solutions and/or the patterned boards.
N-ueens Background Problem surfaced in 1848 by chess player Ma Bezzel as 8 queens (regulation board size) Premise is to place N queens on N N board so that they are non-attacking A queen is one of si different
More informationAPCS-AB: Java. Recursion in Java December 12, week14 1
APCS-AB: Java Recursion in Java December 12, 2005 week14 1 Check point Double Linked List - extra project grade Must turn in today MBCS - Chapter 1 Installation Exercises Analysis Questions week14 2 Scheme
More informationContents. 1 Introduction. 2 Searching and Traversal Techniques. Preface... (vii) Acknowledgements... (ix)
Contents Preface... (vii) Acknowledgements... (ix) 1 Introduction 1.1 Algorithm 1 1.2 Life Cycle of Design and Analysis of Algorithm 2 1.3 Pseudo-Code for Expressing Algorithms 5 1.4 Recursive Algorithms
More informationCSC 427: Data Structures and Algorithm Analysis. Fall 2006
CSC 427: Data Structures and Algorithm Analysis Fall 2006 Problem-solving approaches divide & conquer greedy backtracking examples: N-queens, Boggle, 2-D gels hw6: Sudoku solver 1 Divide & Conquer RECALL:
More informationPractice Problems for the Final
ECE-250 Algorithms and Data Structures (Winter 2012) Practice Problems for the Final Disclaimer: Please do keep in mind that this problem set does not reflect the exact topics or the fractions of each
More informationAn algorithm is a sequence of instructions that one must perform in order to solve a wellformulated
1 An algorithm is a sequence of instructions that one must perform in order to solve a wellformulated problem. input algorithm problem output Problem: Complexity Algorithm: Correctness Complexity 2 Algorithm
More informationCS1 Lecture 31 Apr. 3, 2019
CS Lecture 3 Apr. 3, 209 HW6 due Fri. Q3: think carefully about overlaps draw pictures Think dimension by dimension three D problems if they don t overlap in x, they don t overlap» Express this in terms
More informationRecursion. Recursion is: Recursion splits a problem:
Recursion Recursion Recursion is: A problem solving approach, that can... Generate simple solutions to... Certain kinds of problems that... Would be difficult to solve in other ways Recursion splits a
More informationGraph Algorithms. Tours in Graphs. Graph Algorithms
Graph Algorithms Tours in Graphs Graph Algorithms Special Paths and Cycles in Graphs Euler Path: A path that traverses all the edges of the graph exactly once. Euler Cycle: A cycle that traverses all the
More informationCS6402 DESIGN AND ANALYSIS OF ALGORITHMS QUESTION BANK UNIT I
CS6402 DESIGN AND ANALYSIS OF ALGORITHMS QUESTION BANK UNIT I PART A(2MARKS) 1. What is an algorithm? 2. What is meant by open hashing? 3. Define Ω-notation 4.Define order of an algorithm. 5. Define O-notation
More informationDr. Mustafa Jarrar. Chapter 4 Informed Searching. Artificial Intelligence. Sina Institute, University of Birzeit
Lecture Notes on Informed Searching University of Birzeit, Palestine 1 st Semester, 2014 Artificial Intelligence Chapter 4 Informed Searching Dr. Mustafa Jarrar Sina Institute, University of Birzeit mjarrar@birzeit.edu
More informationPSD1A. DESIGN AND ANALYSIS OF ALGORITHMS Unit : I-V
PSD1A DESIGN AND ANALYSIS OF ALGORITHMS Unit : I-V UNIT I -- Introduction -- Definition of Algorithm -- Pseudocode conventions -- Recursive algorithms -- Time and space complexity -- Big- o notation --
More informationUnit-2 Divide and conquer 2016
2 Divide and conquer Overview, Structure of divide-and-conquer algorithms, binary search, quick sort, Strassen multiplication. 13% 05 Divide-and- conquer The Divide and Conquer Paradigm, is a method of
More informationProbabilistic (Randomized) algorithms
Probabilistic (Randomized) algorithms Idea: Build algorithms using a random element so as gain improved performance. For some cases, improved performance is very dramatic, moving from intractable to tractable.
More informationComputer Science 385 Design and Analysis of Algorithms Siena College Spring Topic Notes: Dynamic Programming
Computer Science 385 Design and Analysis of Algorithms Siena College Spring 29 Topic Notes: Dynamic Programming We next consider dynamic programming, a technique for designing algorithms to solve problems
More informationUnit-5 Dynamic Programming 2016
5 Dynamic programming Overview, Applications - shortest path in graph, matrix multiplication, travelling salesman problem, Fibonacci Series. 20% 12 Origin: Richard Bellman, 1957 Programming referred to
More informationPartha Sarathi Mandal
MA 515: Introduction to Algorithms & MA353 : Design and Analysis of Algorithms [3-0-0-6] Lecture 39 http://www.iitg.ernet.in/psm/indexing_ma353/y09/index.html Partha Sarathi Mandal psm@iitg.ernet.in Dept.
More informationINSTITUTE OF AERONAUTICAL ENGINEERING
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad -500 043 INFORMATION TECHNOLOGY TUTORIAL QUESTION BANK Course Name : DESIGN AND ANALYSIS OF ALGORITHMS Course Code : AIT001 Class
More informationAlgorithm Design Techniques (III)
Algorithm Design Techniques (III) Minimax. Alpha-Beta Pruning. Search Tree Strategies (backtracking revisited, branch and bound). Local Search. DSA - lecture 10 - T.U.Cluj-Napoca - M. Joldos 1 Tic-Tac-Toe
More informationLecture 3, Review of Algorithms. What is Algorithm?
BINF 336, Introduction to Computational Biology Lecture 3, Review of Algorithms Young-Rae Cho Associate Professor Department of Computer Science Baylor University What is Algorithm? Definition A process
More informationD.K.M.COLLEGE FOR WOMEN (AUTONOMOUS), VELLORE-1.
D.K.M.COLLEGE FOR WOMEN (AUTONOMOUS), VELLORE-1. DESIGN AND ANALYSIS OF ALGORITHM UNIT- I SECTION-A 2 MARKS 1. Define an algorithm? 2. Specify the criteria of algorithm? 3. What is Computational Procedure?
More informationArtificial Intelligence (part 4a) Problem Solving Using Search: Structures and Strategies for State Space Search
Artificial Intelligence (part 4a) Problem Solving Using Search: Structures and Strategies for State Space Search Course Contents Again..Selected topics for our course. Covering all of AI is impossible!
More informationmywbut.com Informed Search Strategies-II
Informed Search Strategies-II 1 3.3 Iterative-Deepening A* 3.3.1 IDA* Algorithm Iterative deepening A* or IDA* is similar to iterative-deepening depth-first, but with the following modifications: The depth
More informationNP Completeness. Andreas Klappenecker [partially based on slides by Jennifer Welch]
NP Completeness Andreas Klappenecker [partially based on slides by Jennifer Welch] Dealing with NP-Complete Problems Dealing with NP-Completeness Suppose the problem you need to solve is NP-complete. What
More informationCMPSCI 250: Introduction to Computation. Lecture #24: General Search, DFS, and BFS David Mix Barrington 24 March 2014
CMPSCI 250: Introduction to Computation Lecture #24: General Search, DFS, and BFS David Mix Barrington 24 March 2014 General Search, DFS, and BFS Four Examples of Search Problems State Spaces, Search,
More informationCS 151. Recursion (Review!) Wednesday, September 19, 12
CS 151 Recursion (Review!) 1 Announcements no class on Friday, and no office hours either (Alexa out of town) unfortunately, Alexa will also just be incommunicado, even via email, from Wednesday night
More informationCS Data Structures and Algorithm Analysis
CS 483 - Data Structures and Algorithm Analysis Lecture VI: Chapter 5, part 2; Chapter 6, part 1 R. Paul Wiegand George Mason University, Department of Computer Science March 8, 2006 Outline 1 Topological
More informationTOTAL CREDIT UNITS L T P/ S SW/F W. Course Title: Analysis & Design of Algorithm. Course Level: UG Course Code: CSE303 Credit Units: 5
Course Title: Analysis & Design of Algorithm Course Level: UG Course Code: CSE303 Credit Units: 5 L T P/ S SW/F W TOTAL CREDIT UNITS 3 1 2-5 Course Objectives: The designing of algorithm is an important
More informationDESIGN AND ANALYSIS OF ALGORITHMS
QUESTION BANK DESIGN AND ANALYSIS OF ALGORITHMS UNIT1: INTRODUCTION OBJECTIVE: Algorithms play the central role in both the science and the practice of computing. There are compelling reasons to study
More informationMath 414 Lecture 30. The greedy algorithm provides the initial transportation matrix.
Math Lecture The greedy algorithm provides the initial transportation matrix. matrix P P Demand W ª «2 ª2 «W ª «W ª «ª «ª «Supply The circled x ij s are the initial basic variables. Erase all other values
More informationDr. Mustafa Jarrar. Chapter 4 Informed Searching. Sina Institute, University of Birzeit
Lecture Notes, Advanced Artificial Intelligence (SCOM7341) Sina Institute, University of Birzeit 2 nd Semester, 2012 Advanced Artificial Intelligence (SCOM7341) Chapter 4 Informed Searching Dr. Mustafa
More informationCAD Algorithms. Categorizing Algorithms
CAD Algorithms Categorizing Algorithms Mohammad Tehranipoor ECE Department 2 September 2008 1 Categorizing Algorithms Greedy Algorithms Prim s Algorithm (Minimum Spanning Tree) A subgraph that is a tree
More informationCS 206 Introduction to Computer Science II
CS 206 Introduction to Computer Science II 03 / 25 / 2013 Instructor: Michael Eckmann Today s Topics Comments/Questions? More on Recursion Including Dynamic Programming technique Divide and Conquer techniques
More informationR13 SET - 1. ''' '' ''' ' blog: anilkumarprathipati.wordpress.com. Code No: RT32054
R13 SET - 1 III B. Tech II Semester Regular Examinations, April - 2016 1 a) Distinguish between Algorithm and Psuedocode. [3M] b) Describe the Algorithm Analysis of Binary Search. [4M] c) State the Job
More informationIn this chapter we will very briefly review the most common algorithmic techniques which are used in bioinformatics.
Algorithm Techniques In this chapter we will very briefly review the most common algorithmic techniques which are used in bioinformatics. Bioinfo I (Institut Pasteur de Montevideo) Algorithm Techniques
More informationAnalysis of Algorithms. Unit 4 - Analysis of well known Algorithms
Analysis of Algorithms Unit 4 - Analysis of well known Algorithms 1 Analysis of well known Algorithms Brute Force Algorithms Greedy Algorithms Divide and Conquer Algorithms Decrease and Conquer Algorithms
More informationChapter 3. A problem-solving agent is a kind of goal-based agent. It decide what to do by finding sequences of actions that lead to desirable states.
Chapter 3 A problem-solving agent is a kind of goal-based agent. It decide what to do by finding sequences of actions that lead to desirable states. A problem can be defined by four components : 1. The
More informationLecture 6: Combinatorics Steven Skiena. skiena
Lecture 6: Combinatorics Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.sunysb.edu/ skiena Learning to Count Combinatorics problems are
More informationAssignment No 2 (Group B)
Assignment No 2 (Group B) 1 Problem Statement : Concurrent Implementation of Travelling Salesman Problem. 2 Objective : To develop problem solving abilities using Mathematical Modeling. To apply algorithmic
More informationSearch means finding a path or traversal between a start node and one of a set of goal nodes. Search is a study of states and their transitions.
UNIT 3 BASIC TRAVERSAL AND SEARCH TECHNIQUES Search means finding a path or traversal between a start node and one of a set of goal nodes. Search is a study of states and their transitions. Search involves
More informationChapter 6 Backtracking Algorithms. Backtracking algorithms Branch-and-bound algorithms
Chapter 6 Backtracking Algorithms Backtracking algorithms Branch-and-bound algorithms 1 Backtracking Algorithm The task is to determine algorithm for finding solutions to specific problems not by following
More informationCS6402 Design and Analysis of Algorithm. 2 Marks Question & Answer UNIT I INTRODUCTION
CS6402 Design and Analysis of Algorithm 2 Marks Question & Answer UNIT I INTRODUCTION 1. What is performance measurement? Performance measurement is concerned with obtaining the space and the time requirements
More informationCS159. Nathan Sprague. November 9, 2015
CS159 Nathan Sprague November 9, 2015 Recursive Definitions Merriam Websters definition of Ancestor: Ancestor One from whom a person is descended [...] Here is a recursive version: Ancestor One s parent.
More informationCSE 417 Branch & Bound (pt 4) Branch & Bound
CSE 417 Branch & Bound (pt 4) Branch & Bound Reminders > HW8 due today > HW9 will be posted tomorrow start early program will be slow, so debugging will be slow... Review of previous lectures > Complexity
More informationInternational Journal of Modern Engineering and Research Technology
ABSTRACT The N queen problems is an intractable problem and for a large value of 'n' the problem cannot be solved in polynomial time and thus is placed in 'NP' class. Various computational approaches are
More informationProblem solving paradigms
Problem solving paradigms Bjarki Ágúst Guðmundsson Tómas Ken Magnússon Árangursrík forritun og lausn verkefna School of Computer Science Reykjavík University Today we re going to cover Problem solving
More informationDepartment of Computer Applications. MCA 312: Design and Analysis of Algorithms. [Part I : Medium Answer Type Questions] UNIT I
MCA 312: Design and Analysis of Algorithms [Part I : Medium Answer Type Questions] UNIT I 1) What is an Algorithm? What is the need to study Algorithms? 2) Define: a) Time Efficiency b) Space Efficiency
More informationSubset sum problem and dynamic programming
Lecture Notes: Dynamic programming We will discuss the subset sum problem (introduced last time), and introduce the main idea of dynamic programming. We illustrate it further using a variant of the so-called
More informationCMSC 132: Object-Oriented Programming II. Recursive Algorithms. Department of Computer Science University of Maryland, College Park
CMSC 132: Object-Oriented Programming II Recursive Algorithms Department of Computer Science University of Maryland, College Park Recursion Recursion is a strategy for solving problems A procedure that
More informationCS6402-DESIGN AND ANALYSIS OF ALGORITHM. TWO MARK QUESTION WITH ANSWERS Unit-I. Introduction
CS6402-DESIGN AND ANALYSIS OF ALGORITHM TWO MARK QUESTION WITH ANSWERS Unit-I Introduction Why is the need of studying algorithms? From a practical standpoint, a standard set of algorithms from different
More informationLecture 6: Recursion RECURSION
Lecture 6: Recursion RECURSION You are now Java experts! 2 This was almost all the Java that we will teach you in this course Will see a few last things in the remainder of class Now will begin focusing
More information12/30/2013 S. NALINI,AP/CSE
12/30/2013 S. NALINI,AP/CSE 1 UNIT I ITERATIVE AND RECURSIVE ALGORITHMS Iterative Algorithms: Measures of Progress and Loop Invariants-Paradigm Shift: Sequence of Actions versus Sequence of Assertions-
More information3 INTEGER LINEAR PROGRAMMING
3 INTEGER LINEAR PROGRAMMING PROBLEM DEFINITION Integer linear programming problem (ILP) of the decision variables x 1,..,x n : (ILP) subject to minimize c x j j n j= 1 a ij x j x j 0 x j integer n j=
More informationCS61BL. Lecture 5: Graphs Sorting
CS61BL Lecture 5: Graphs Sorting Graphs Graphs Edge Vertex Graphs (Undirected) Graphs (Directed) Graphs (Multigraph) Graphs (Acyclic) Graphs (Cyclic) Graphs (Connected) Graphs (Disconnected) Graphs (Unweighted)
More informationLecture Chapter 6 Recursion as a Problem Solving Technique
Lecture Chapter 6 Recursion as a Problem Solving Technique Backtracking 1. Select, i.e., guess, a path of steps that could possibly lead to a solution 2. If the path leads to a dead end then retrace steps
More informationFramework for Design of Dynamic Programming Algorithms
CSE 441T/541T Advanced Algorithms September 22, 2010 Framework for Design of Dynamic Programming Algorithms Dynamic programming algorithms for combinatorial optimization generalize the strategy we studied
More informationComputer Science 385 Design and Analysis of Algorithms Siena College Spring Topic Notes: Brute-Force Algorithms
Computer Science 385 Design and Analysis of Algorithms Siena College Spring 2019 Topic Notes: Brute-Force Algorithms Our first category of algorithms are called brute-force algorithms. Levitin defines
More informationBacktracking is a refinement of the brute force approach, which systematically searches for a
Backtracking Backtracking is a refinement of the brute force approach, which systematically searches for a solution to a problem among all available options. It does so by assuming that the solutions are
More informationComputer Science 385 Analysis of Algorithms Siena College Spring Topic Notes: Divide and Conquer
Computer Science 385 Analysis of Algorithms Siena College Spring 2011 Topic Notes: Divide and Conquer Divide and-conquer is a very common and very powerful algorithm design technique. The general idea:
More informationAnany Levitin 3RD EDITION. Arup Kumar Bhattacharjee. mmmmm Analysis of Algorithms. Soumen Mukherjee. Introduction to TllG DCSISFI &
Introduction to TllG DCSISFI & mmmmm Analysis of Algorithms 3RD EDITION Anany Levitin Villa nova University International Edition contributions by Soumen Mukherjee RCC Institute of Information Technology
More informationAlgorithm Design and Analysis
Algorithm Design and Analysis LECTURE 16 Dynamic Programming (plus FFT Recap) Adam Smith 9/24/2008 A. Smith; based on slides by E. Demaine, C. Leiserson, S. Raskhodnikova, K. Wayne Discrete Fourier Transform
More informationOutline of the talk. Local search meta-heuristics for combinatorial problems. Constraint Satisfaction Problems. The n-queens problem
Università G. D Annunzio, maggio 00 Local search meta-heuristics for combinatorial problems Luca Di Gaspero Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica Università degli Studi di Udine
More informationAlgorithm Concepts. 1 Basic Algorithm Concepts. May 16, Computational Method
Algorithm Concepts David R. Musser Brian Osman May 16, 2003 This document contains Section 1 of Algorithm Concepts, a collection of algorithm concept descriptions in both Web page and print form under
More informationSPANNING TREES. Lecture 21 CS2110 Spring 2016
1 SPANNING TREES Lecture 1 CS110 Spring 016 Spanning trees What we do today: Calculating the shortest path in Dijkstra s algorithm Look at time complexity of shortest path Definitions Minimum spanning
More informationMathematical Tools for Engineering and Management
Mathematical Tools for Engineering and Management Lecture 8 8 Dec 0 Overview Models, Data and Algorithms Linear Optimization Mathematical Background: Polyhedra, Simplex-Algorithm Sensitivity Analysis;
More informationDesign and Analysis of Algorithms
CSE 101, Winter 018 D/Q Greed SP s DP LP, Flow B&B, Backtrack Metaheuristics P, NP Design and Analysis of Algorithms Lecture 8: Greed Class URL: http://vlsicad.ucsd.edu/courses/cse101-w18/ Optimization
More informationConstraint (Logic) Programming
Constraint (Logic) Programming Roman Barták Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic bartak@ktiml.mff.cuni.cz Sudoku Combinatorial puzzle, whose goal is to enter
More informationIntroduction to Operations Research Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras
Introduction to Operations Research Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Module - 05 Lecture - 24 Solving LPs with mixed type of constraints In the
More informationMath 98 - Introduction to MATLAB Programming. Fall Lecture 2
Reminders Instructor: Chris Policastro Login:!cmfmath98 (username) c a 1numerals (password) Class Website: https://math.berkeley.edu/~cpoli/math98/fall2016.html Assignment Submission: https://bcourses.berkeley.edu
More informationEE 368. Weeks 4 (Notes)
EE 368 Weeks 4 (Notes) 1 Read Chapter 3 Recursion and Backtracking Recursion - Recursive Definition - Some Examples - Pros and Cons A Class of Recursive Algorithms (steps or mechanics about performing
More informationHeuristic Optimisation
Heuristic Optimisation Revision Lecture Sándor Zoltán Németh http://web.mat.bham.ac.uk/s.z.nemeth s.nemeth@bham.ac.uk University of Birmingham S Z Németh (s.nemeth@bham.ac.uk) Heuristic Optimisation University
More information