What is Computer Science
About?
Part 1: Computational Thinking
Main Points
• There is more to computer science than just
programming.
• Computer science is about computational
thinking and algorithms.
• We try to formalize activities into repeatable
procedures and concrete decisions.
• Generalizing a procedure into an abstract
algorithm helps us recognize if there are known
solutions, and how complex the problem is.
• Programming is just translating an algorithm into
a specific syntax.
Some definitions...
• Computational thinking
– translating processes/procedures into step-by-step activities with
well-defined choice points and decision criteria
• Design and analysis of algorithms
– expression of a procedure in terms of operations on abstract
data structures like graphs, lists, strings, and trees
– finite number of steps (clear termination conditions; it has to halt)
– is the algorithm correct?
– are all cases handled, or might it fail on certain inputs?
– how much time will it take? how much space (memory)?
• Programming
– translating algorithms into a specific language
• Software engineering
– managing the development and life-cycle of a system, including
design/specification, documentation, testing, use of
components/libraries, release of new/updated versions
– usually a team effort
Computational Thinking
• CT has infused into all kinds of fields from cooking
and sports, to transportation, medical diagnosis,
and particle physics
• many intelligent activities are often ill-defined, and
CT is about formalizing them into concrete
decisions and repeatable procedures
– think about how to find a good place to eat in a new
town
• ask a friend? desired type of food? consult Zagat’s? look for
restaurant with many cars in the parking lot?
– think about how choose a book to read
• interest? availability? recommendations? reviews?
– “finding Waldo” (how do you search for shapes in
images?)
Google’s ideas on Computational Thinking
http://www.google.com/edu/computational-thinking/what-is-ct.html
Four components:
Example: baking a cake Computationally:
DECOMPOSION
breaking a problem into
(decoupled) sub-problems
mixing dry ingredients,
then wet ingredients
divide-and-conquer
PATTERN RECOGNITION
identifying repeatable
operations
crack egg1,
crack egg2,
crack egg3...
for/while-loops,
sub-routines
GENERALIZATION and
ABSTRACTION
baking chocolate cake or
carrot cake or pound cake
is similar, except
add/substitute a few
different ingredients
adding parameters to
code; also, can we apply
the same procedure to
other data like vectors,
arrays, lists, trees, graphs?
ALGORITHM DESIGN
formalize procedure into
recipe others can use;
define things like how you
know when it is done (bake
30 min at 350 or until
crust is “golden”...)
step-by-step procedure
with clear initialization,
decision and termination
conditions
• mechanical analogies
– think about how a thermostat does
temperature control
• mechanical analogies
– think about how a thermostat does
temperature control
• what are the actions that can be taken?
• what are the conditions under which these actions
are triggered?
• what parameters affect these decisions?
• mechanical analogies
– think about how a thermostat does
temperature control
• what are the actions that can be taken?
• what are the conditions under which these actions
are triggered?
• what parameters affect these decisions?
let T be the desired or “control” temperature
if temp>T, turn on AirConditioner
if temp<T, turn on Heater
• mechanical analogies
– think about how a thermostat does
temperature control
• what are the actions that can be taken?
• what are the conditions under which these actions
are triggered?
• what parameters affect these decisions?
let D be the acceptable range of temp. variation
if temp>T+D, turn on AirConditioner
if temp<T-D, turn on Heater
• mechanical analogies
– think about how a thermostat does
temperature control
• what are the actions that can be taken?
• what are the conditions under which these actions
are triggered?
• what parameters affect these decisions?
if
if
if
if
temp>T, turn on AirConditioner
temp<T, turn on Heater
AC on and temp<T, turn AC off
HE on and temp>T, turn HE off
• mechanical analogies
– think about how a thermostat does
temperature control
• what are the actions that can be taken?
• what are the conditions under which these actions
are triggered?
• what parameters affect these decisions?
– think about how a soda machine works
• keep accepting coins till enough for item
• dispense item (if avail.), then make change
– think about the decision policy for an elevator
– think about the pattern of traffic signals at an
intersection (with sensors)
• how do lights depend on cars waiting? pedestrians?
• ultimately, we formalize these things into:
– flowcharts and pseudocode
– abstractions like finite-state machines
procedure bubbleSort( list A )
repeat
swapped = false
for i = 1 to length(A)-1 do:
if A[i] > A[i+1] then
swap( A[i], A[i+1] )
swapped = true
until not swapped
finite-state machine
representing a
turnstile
1 1
3 3
7 7
9 2
2 9
11 11
13 13
17 17
these play a big role in
compilers, network
protocols, etc.
The “earliest” known algorithm
• Euclid’s algorithm for determining the GCD
(greatest common denominator) – also known
as the Chinese Remainder Theorem
• problem: given two integers m and n, find the
largest integer d that divides each of them
• example: 4 divides 112 and 40; is it the GCD?
(no, 8 is)
• Euclid’s algorithm: repeatedly divide the smaller into
the larger number and replace with the remainder
GCD(a,b):
if a<b, swap a and b
while b>0:
let r be the remainder
of a/b
a←b, b←r
return a
1.
2.
3.
4.
a=112, b=40, a/b=2 with rem. 32
a=40, b=32, a/b=1 with rem. 8
a=32, b=8, a/b=4 with rem. 0
a=8, b=0, return 8
• questions a Computer Scientist would ask:
– Does it halt? (note how a always shrinks with each pass).
– Is it correct?
– Is there a more efficient way to do it (that uses fewer
steps)?
– Relationship to factoring and testing for prime numbers.
...UCLA 92 Stanford 80 – OklaSt 55 Iowa 61 – Indiana 83 MichSt 82 ...
• while monitoring a stream of basketball
scores, keep track of the 3 highest scores
– impractical to just save them all and sort
– how would you do it?
...UCLA 92 Stanford 80 – OklaSt 55 Iowa 61 – Indiana 83 MichSt 82 ...
• algorithm design often starts with representation
– imagine keeping 3 slots, A B C for the highest
scores seen so far
– define the “semantics” or an “invariant” to maintain:
• A > B > C > all other scores
...UCLA 92 Stanford 80 – OklaSt 55 Iowa 61 – Indiana 83 MichSt 82 ...
• algorithm design often starts with representation
– imagine keeping 3 slots, A B C for the highest
scores seen so far
– define the “semantics” or an “invariant” to maintain:
• A > B > C > all other scores
– with each new game score (p,q) (e.g. Aggies 118, Longhorns 90)
if p>A then C=B, B=A, A=p
else if p>B, then C=B, B=p
else if p>C, then C=p
repeat this “shifting” with q
p A B
A p B
A B p
...UCLA 92 Stanford 80 – OklaSt 55 Iowa 61 – Indiana 83 MichSt 82 ...
• algorithm design often starts with representation
– imagine keeping 3 slots, A B C for the highest
scores seen so far
– define the “semantics” or an “invariant” to maintain:
• A > B > C > all other scores
– with each new game score (p,q) (e.g. Aggies 118, Longhorns 90)
if p>A then C=B, B=A, A=p
else if p>B, then C=B, B=p
else if p>C, then C=p
repeat this “shifting” with q
– questions to consider:
p A B
A p B
A B p
• what happens on first pass, before A, B, and C are defined?
• what happens with ties?
• should A, B, and C represent distinct games, or could 2 of them
come from the same game?
Spell-checking
• given a document as a list of words, wi,
identify misspelled words and suggest
corrections
– simple approach: use a dictionary
• for each wi, scan dictionary in sorted order
– can you do it faster? (doc size N x dict size D)
• suppose we sort both lists
• sorting algs usually take N log2 N time
– example: if doc has ~10,000 words, sort in ~132,000 steps
– assume you can call a sort sub-routine (reuse of code)
– note: you will learn about different sorting algorithms (and
related data structures like trees and hash tables) and
analyze their computational efficiency in CSCE 211
• can scan both lists in parallel (takes D steps)
– D + N log N < ND
Words in a document like the US
Declaration of Independence:
• abdicated
• abolish
• abolishing
• absolute
• absolved
• abuses
• accommodation
• accordingly
• accustomed
• acquiesce
• act
• acts
• administration
• affected
• after
• against
• ages
• all
• allegiance
• alliances
• alone
• ...
Words in the English Dictionary:
• ...
• achieve
• achromatic
• acid
• acidic
note that this
• acknowledge
list is “denser”
• acorn
• acoustic
• acquaint
• acquaintance
• acquiesce
• acquiescent
• acquire
• acquisition
• acquisitive
• acquit
• acquittal
• acquitting
• acre
• acreage
• acrid
• acrimonious
• ...
• a harder problem: suggesting
spelling corrections
– requires defining “closest match”
• fewest different letters? same length?
– occupashun  occupation
– occurence  occurrence
occupashun
||||||***| d=3
occupation
occupashun
||||****** d=6
occurrence
occupashun
|||***|**| d=5
occl-usion
• “edit distance”:
– formal defn: # diff letters + # gap spaces
– minimal dist over all possible gap placements
calculated by Dynamic Programming
• how to efficiently find all words in dictionary
with minimal distance?
– does context matter?
• used as noun or verb (affect vs. effect)
• compliment vs. complement
• principle vs. principal
Summary about Computational Thinking
• CT is about transforming (often ill-defined)
activities into concrete, well-defined procedures.
– a finite sequence of steps anybody could follow, with
well-defined decision criteria and termination
conditions
• take-home message: the following components
are important to computational thinking:
1.
2.
3.
4.
5.
decomposition
identifying patterns and repetition
abstraction and generalization
choosing a representation for the data
defining all decision criteria