1. Lecture 2 Introduction to Computer Science (continued)
11/15/2018
Lecture 2
Introduction to Computer Science
(continued)
11/15/2018
CS Lecture 2
CS 100

2. Ways Algorithms can be Constructed
Lecture 2
11/15/2018
Ways Algorithms can be Constructed
Sequential construction
Conditional construction
Iterative construction
11/15/2018
CS Lecture 2
CS 100

3. Sequential Construction
Lecture 2
11/15/2018
Sequential Construction
first do this
then do this
After showing this observe:
If we have two or more operations, we can either do:
ALL of them (AND), or
ONE of them (OR)
If we do ALL of them, we can either:
do them one at a time (as above)
do them all at once (parallel execution, which we won’t discuss)
If we are only going to do ONE of them, we must decide which…
11/15/2018
CS Lecture 2
CS 100

4. Conditional Construction
Lecture 2
11/15/2018
Conditional Construction
test something
either do this
or do this
It is also possible to have choices between more than two alternatives
Also, if one alternate is “do nothing” then in effect we have the choice of whether to do something or not
(We could pick which to do by tossing a coin, but that sort of non-decision can be reduced to this form)
continue
11/15/2018
CS Lecture 2
CS 100

5. Iterative Construction
Lecture 2
11/15/2018
Iterative Construction
do something
if not, repeat
test if done
This is a sort of combination of the previous two:
we do something
AND then we decide to do it again OR not
Note that this is not the only kind of iterative operation
This form does the operation at least once
if done, continue
11/15/2018
CS Lecture 2
CS 100

6. Developing an Algorithm
Lecture 2
11/15/2018
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
11/15/2018
CS Lecture 2
CS 100

7. Developing Decimal Addition Algorithm: Example
Lecture 2
11/15/2018
Developing Decimal Addition Algorithm: Example 1
carry 15 5 1 04 4 4 1 1
We could have two cases, carry or no-carry, but it’s simpler to always add in the carry and make it either 1 or 0. 14 12 2
11/15/2018
CS Lecture 2
CS 100

8. Developing Decimal Addition Algorithm: More General Case
Lecture 2
11/15/2018
Developing Decimal Addition Algorithm: More General Case
carry
cc3 c3 c
cc2 c2 c c1 c c0 c c4
a3 a2 a1 a0
b3 b2 b1 b0
Note that we make the first column like the others by setting the initial carry to 0
cc1
cc0
11/15/2018
CS Lecture 2
CS 100

9. Algorithm for Adding Two m-Digit Numbers
Lecture 2
11/15/2018
Algorithm for Adding Two m-Digit Numbers
Note, we always must be clear about what inputs our algorithm should work on.
Numbers of at least one digit? AT least 2? Is there a maximum?
11/15/2018
CS Lecture 2
CS 100

10. Algorithm Set value of c (carry) to 0.
Lecture 2
11/15/2018
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.
Note that this is very slightly different from the book (p. 7) for greater clarity.
11/15/2018
CS Lecture 2
CS 100

11. Importance of Algorithms
Lecture 2
11/15/2018
Importance of Algorithms
If you can specify an algorithm to solve a problem, then you can automate its solution
11/15/2018
CS Lecture 2
CS 100

12. Requirements for Automated Computation
Lecture 2
11/15/2018
Requirements for Automated 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
11/15/2018
CS Lecture 2
CS 100

13. Algorithmic Problem Solving
Lecture 2
11/15/2018
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
11/15/2018
CS Lecture 2
CS 100

14. Non-Algorithmic Information Processing
Lecture 2
11/15/2018
Non-Algorithmic Information 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
Note it took several days to get the Mars Rover past the blocked ramp.
11/15/2018
CS Lecture 2
CS 100

15. Definition of “Algorithm”
Lecture 2
11/15/2018
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
well-ordered collection:
we know the order in which the operations should be performed
of unambiguous and effectively computable operations:
unambiguous: we have to know what we are supposed to do
depends on computing agent (context)
the most basic operations are called primitive operations
effectively computable: an operation performable by a computing agent
that produces a result: generally algorithms are used to get answers
in some cases, algorithms control devices, etc., so “result” must be taken broadly
and halts in a finite amount of time: we can’t wait forever
some algorithms are designed to run forever (or indefinitely),
but they must do their work along the way in finite time
11/15/2018
CS Lecture 2
CS 100

16. Definition of CS Reconsidered
Lecture 2
11/15/2018
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
11/15/2018
CS Lecture 2
CS 100

17. Organization of Text fig. from Schneider & Gersting 11/15/2018
Lecture 2
11/15/2018
Organization of Text
fig. from Schneider
& Gersting
11/15/2018
CS Lecture 2
CS 100

18. Reading Read one chapter of S&G per week unless I say otherwise
Lecture 2
11/15/2018
Reading
Read one chapter of S&G per week unless I say otherwise
Read ch. 2 for the next class
11/15/2018
CS Lecture 2
CS 100