Understanding Algorithms: Sequential, Conditional, and Iterative Construction

1. Lecture 2 Introduction to Computer Science (continued) CS 100 - Lecture 2

2. Ways Algorithms can be Constructed • Sequential construction • Conditional construction • Iterative construction CS 100 - Lecture 2

3. first do this then do this Sequential Construction CS 100 - Lecture 2

4. testsomething either do this or do this continue Conditional Construction CS 100 - Lecture 2

5. do something if not, repeat test if done if done, continue Iterative Construction CS 100 - Lecture 2

6. Developing an Algorithm • Often good to begin by investigating how a person would do it • Control structures: • Shows how to order the steps • Reveals what different conditions may occur • Data structures: • Shows how to organize information • Reveals what additional information is required CS 100 - Lecture 2

7. carry 1 1 1 0 12 14 04 1 15 2 4 4 5 1 Developing Decimal Addition Algorithm: Example 8 1 4 7 7 2 9 5 CS 100 - Lecture 2

8. c c c c cc0 cc1 cc2 c4 cc3 c0 c1 c2 c3 c4 Developing Decimal Addition Algorithm: More General Case carry 0 a3a2a1a0 b3b2b1b0 CS 100 - Lecture 2

9. Algorithm for AddingTwo m-Digit Numbers CS 100 - Lecture 2

10. Algorithm • Set value of c (carry) to 0. • Set value of i (column number) to 0. • Repeat steps (a) – (d) until i > m–1. • Set ci to c + ai + bi. • If ci < 10, then set c to 0, • otherwise set c to 1 and reset ci to ci – 10. • Add 1 to i. • Set cm to value of c. • Print answer cmcm–1…c1c0. CS 100 - Lecture 2

11. Importance of Algorithms If you can specify an algorithm to solve a problem, then you can automate its solution CS 100 - Lecture 2

12. Requirements forAutomated Computation • Ability to make device to do basic operations • Ability to make control device for sequencing and conditional tests • Technology not available until early 20th century CS 100 - Lecture 2

13. Algorithmic Problem Solving • Are there algorithmic solutions for all problems? • No! Gödel discovered algorithmically unsolvable problems in 1930s • Can algorithmically solvable problems be solved efficiently? • No! They are inherently hard problems • Even for problems that are efficiently algorithmically solvable, efficient algorithms may be difficult to find • These are some of the issues addressed by computer scientists CS 100 - Lecture 2

14. Non-AlgorithmicInformation Processing • “Cognitive inversion”: many things that are easy for people are hard for computers, and vice versa • e.g., face recognition vs.calculating • Suggests that computers & brains work in very different ways • Much research in non-algorithmic information processing in neural networks CS 100 - Lecture 2

15. Definition of “Algorithm” An algorithm is a well-ordered collection of unambiguous and effectively computable operations that produces a result and halts in a finite amount of time • …a well-ordered collection… • …of unambiguous and effectively computable operations… • …that produces a result… • …and halts in a finite amount of time CS 100 - Lecture 2

16. Definition of CS Reconsidered Computer Science is the study of algorithms, including: • Their formal and mathematical properties • Their hardware realizations • Their linguistic realizations • Their applications CS 100 - Lecture 2

17. Organization of Text fig. from Schneider & Gersting CS 100 - Lecture 2

18. Reading • Read one chapter of S&G per week unless I say otherwise • Read ch. 2 for the next class CS 100 - Lecture 2