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.

• 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

Some definitions...

• 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?)

Computational Thinking

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

Google’s ideas on Computational Thinkinghttp://www.google.com/edu/computational-thinking/what-is-ct.html

• 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?

if temp>T, turn on AirConditionerif temp<T, turn on Heater

let T be the desired or “control” temperature

• 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 temp>T+, turn on AirConditionerif temp<T-, turn on Heater

let be the acceptable range of temp. variation

• 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 temp>T, turn on AirConditionerif temp<T, turn on Heaterif AC on and temp<T, turn AC offif 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

13792

111317

finite-state machinerepresenting aturnstile

these play a big role in compilers, networkprotocols, etc.

13729

111317

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

• 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.

1. a=112, b=40, a/b=2 with rem. 322. a=40, b=32, a/b=1 with rem. 83. a=32, b=8, a/b=4 with rem. 04. a=8, b=0, return 8

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

• 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, for the highest scores

seen so far– define the “semantics” or an “invariant” to maintain:

• A > B > C > all other scores

A B C

...UCLA 92 Stanford 80 – OklaSt 55 Iowa 61 – Indiana 83 MichSt 82 ...

• algorithm design often starts with representation– imagine keeping 3 slots, 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=pelse if p>B, then C=B, B=pelse if p>C, then C=prepeat this “shifting” with q

A B C

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, 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=pelse if p>B, then C=B, B=pelse if p>C, then C=prepeat this “shifting” with q

– questions to consider: • 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?

A B C

p A B

A p B

A B p

...UCLA 92 Stanford 80 – OklaSt 55 Iowa 61 – Indiana 83 MichSt 82 ...

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 USDeclaration 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• acknowledge• acorn• acoustic• acquaint• acquaintance• acquiesce• acquiescent• acquire• acquisition• acquisitive• acquit• acquittal• acquitting• acre• acreage• acrid• acrimonious• ...

note that thislist is “denser”

• a harder problem: suggesting spelling corrections– requires defining “closest match”

• fewest different letters? same length?– occupashun occupation– occurence occurrence

• “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

occupashun||||||***|occupation

occupashun ||||******occurrence

occupashun |||***|**|occl-usion

d=3

d=6

d=5

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. decomposition

2. identifying patterns and repetition

3. abstraction and generalization

4. choosing a representation for the data

5. defining all decision criteria