Module 7- Solving Complex Problems Solving Complex Problems The Towers Of Hanoi.

Slides:

Advertisements

Similar presentations

CSED101 INTRODUCTION TO COMPUTING GREEDY APPROACH, DIVIDE AND CONQUER Hwanjo Yu.

Advertisements

1a. Outline how the main memory of a computer can be partitioned b. What are the benefits of partitioning the main memory? It allows more than 1 program.

Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved Chapter 20 Recursion.

Problem Solving Strategies

Chapter 10 Recursion. Copyright © 2005 Pearson Addison-Wesley. All rights reserved Chapter Objectives Explain the underlying concepts of recursion.

Module 12 Computation and Configurations Formal Definition Examples.

Software design and development Marcus Hunt. Application and limits of procedural programming Procedural programming is a powerful language, typically.

Section 8.3 – Systems of Linear Equations - Determinants Using Determinants to Solve Systems of Equations A determinant is a value that is obtained from.

WHAT IS THIS? OBJECTIVE AND OUTCOMES Candidates should be able to: Describe and explain the CPU as fetching, decoding and executing of instructions and.

Recursion Chapter 7 Copyright ©2012 by Pearson Education, Inc. All rights reserved.

Computer Science: A Structured Programming Approach Using C1 6-9 Recursion In general, programmers use two approaches to writing repetitive algorithms.

Chapter 15: Advanced Topics: Introducing Data Structures and Recursion Visual Basic.NET Programming: From Problem Analysis to Program Design.

Operation Frequency No. of Clock cycles ALU ops % 1 Loads 25% 2

Chapter 8 Recursion Modified.

Chapter 4 Recursion. Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-2 Chapter Objectives Explain the underlying concepts of recursion.

C2: Solving Equations with Logarithms Learning Objective: to be able to solve equations of the form a x = b.

Informal Analysis of Merge Sort  suppose the running time (the number of operations) of merge sort is a function of the number of elements to sort  let.

Learning Objective The students should be able to: a. state the definition of software b. state the usage of software c. list different types of software.

Chapter 10 Algorithm Analysis.  Introduction  Generalizing Running Time  Doing a Timing Analysis  Big-Oh Notation  Analyzing Some Simple Programs.

Chapter 6.1: Recurrence Relations Discrete Mathematical Structures: Theory and Applications.

MA.912.A.3.1: Solve linear equations in one variable that include simplifying algebraic expressions. What is the value of x in the equation below? 3(x.

Petals Around the Rose. The name of the game is Petals Around the Rose. The name of the game is important. The computer will roll five dice and ask you.

22C:19 Discrete Math Advanced Counting Fall 2010 Sukumar Ghosh.

1 Recursion Recursion is a powerful programming technique that provides elegant solutions to certain problems. Chapter 11 focuses on explaining the underlying.

Pre-Calculus: Graphs and Limits By: Bryan Price. Contents and Standards Pennsylvania Mathematics Standards: Trigonometry – Use graphing calculators.

COMP 170 L2 L11: Recursion, Recurrence, and Induction l Objective n Recursion  A problem solving technique that reduces big problems into smaller ones.

Linear and Binary Search Algorithms

Today you will explore mathematical ways of sliding, turning, and flipping an object without changing its size or shape. These types of movements are called.

UNIT 17 Recursion: Towers of Hanoi.

CMPF144 FUNDAMENTALS OF COMPUTING THEORY Module 9: The Tower of Hanoi.

Class 17, October 29, 2015 Lesson 3.2.  By the end of this lesson, you should understand that: ◦ Units can be used in dimensional analysis to set up.

Concepts of Algorithms CSC-244 Unit 3 and 4 Algorithm Growth Rates Shahid Iqbal Lone Computer College Qassim University K.S.A.

Entry Task You are a passenger in a car. You are using a cell phone that connects with the tower shown. The tower has an effective range of 6 miles. If.

Advanced Algorithms Analysis and Design By Dr. Nazir Ahmad Zafar Dr Nazir A. Zafar Advanced Algorithms Analysis and Design.

Learning and remembering.

1 ADT Implementation: Recursion, Algorithm Analysis Chapter 10.

Section 1: Problem solving AQA Computing A2 © Nelson Thornes 2009 Examples of problems with different time complexities Section 1.2: Comparing algorithms.

Tower of Hanoi problem: Move the pile of rings from one peg to another

Solving Complex Problems

Big O notation Big O notation is used in Computer Science to describe the performance or complexity of an algorithm. Big O specifically describes the worst-case.

Complexity In examining algorithm efficiency we must understand the idea of complexity Space complexity Time Complexity.

ALGORITHMS & FLOWCHARTING II

Computing Year 7 - Unit 2 Programming Basics Types of Software.

Recursive Thinking Chapter 9 introduces the technique of recursive programming. As you have seen, recursive programming involves spotting smaller occurrences.

Java Software Structures: John Lewis & Joseph Chase

GCSE Maths Solving Jo Wright.

Loops in C C has three loop statements: the while, the for, and the do…while. The first two are pretest loops, and the the third is a post-test loop. We.

Recursive Thinking Chapter 9 introduces the technique of recursive programming. As you have seen, recursive programming involves spotting smaller occurrences.

Section 11.2: Solving Linear Systems by Substitution

Recursive Definitions

Hook was a famous year for what…..?

Algorithm An algorithm is a finite set of steps required to solve a problem. An algorithm must have following properties: Input: An algorithm must have.

Answers to pg: Start with 2 and multiply the output by 3 to get the next output 2. A B. 3 C A B. 3 C A B. 9 C.

المدخل إلى تكنولوجيا التعليم في ضوء الاتجاهات الحديثة

Quick Graphs of Linear Equations

Tower of Hanoi problem: Move the pile of rings from one peg to another

complex numbers: Review 1

Calculate the value of ‘

Learning Objectives To be able to describe the purpose of the CPU

17 – Exponential Modeling – Creating an Equation Calculator Required

How would you use your calculator to solve 52?

Learning Objective Solving equations with single brackets

Tower of Hanoi problem: Move the pile of rings from one peg to another

 Is a machine that is able to take information (input), do some work on (process), and to make new information (output) COMPUTER.

Solving a System of Linear Equations

The steps of scientific computation

Presentation transcript:

Module 7- Solving Complex Problems Solving Complex Problems The Towers Of Hanoi

Linear Complexity  Mowing the lawn is a problem that demonstrates linear complexity.  If you double the size of the area that you want to mow, it will take twice as long to complete the task.

More Complex Problems  Many problems will increase in complexity very quickly each time an extra input is added.  We will explore the Towers Of Hanoi Puzzle

How many moves does it take? Did you know you should be able to complete the puzzle in (2 n -1) moves where n is the number of disks. For 3 disks 2 n -1= (2 3 – 1) = (8-1) =7 moves

Number of Disks Number of Moves Required to Solve the Problem , ,554, ,099,511,627, ,223,372,036,854,775,808 How many moves does it take? Remember it takes (2 n -1) moves where n=number of disks

Number of Disks Time Taken to Solve the Problem seconds seconds seconds seconds days , 471 years How much time does it take? These calculations are based on a computer being able to execute 1 million instructions per second