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Advanced
Programming and
Algorithms
Dr. Baldassano
KX·V (OLPH (GXŃMPLRQ
About Me
XWent to college at Princeton
for Electrical Engineering
XPhD at Stanford
in Computer Science
XNow a research fellow at the
Princeton Neuroscience Institute
Goals of the class
XLearn about the most useful algorithms that power modern computing XLearn how to apply algorithms to solve new problems
XLearn how to develop and analyze new algorithms
Course website
XGo to www.chrisbaldassano.com, click on Teaching, POHQ ´$GYMQŃHG 3URJUMPPLQJ MQG $OJRULPOPVµ XHas my email address
, schedule and assignments Programming languages
X0RVP RI POLV ŃOMVV RLOO ÓXVP XVH ´pseudocodeµ MQG PMON about algorithms at a conceptual level XFor homework assignments you can use any
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XI will be using Python for solutions and demos, but the ŃRGH VORXOG NH XQGHUVPMQGMNOH HYHQ LI \RX GRQ·P NQRR Python
What are algorithms and data
structures? XAlgorithm: A procedure for solving a problem
XWe are especially interested in efficientalgorithms, that solve problems using as little time and/or resources as possible XData structure: A way of organizing information
XIf we know the types of operations we want to do on the data, we can organize it in a way that makes these operations fast and/or easy Simple examples
XHow to find where a particular term is defined in a book? XAlgorithm 1: Open to random pages to find the definition XValid algorithm, will work eventually!
XBut very inefficient ²could revisit pages multiple times XAlgorithm 2: Start from beginning, go one page at a time to find definition XClose to the best we can do for finding a single word XAlgorithm 3: Go through entire book, create an index of the page number where every word occurs, then use this index to find term XSilly to do for one lookup, but this index makes all future lookups very fast Data structures
XAll algorithms make use of data structures to keep track of computations in an efficient way XDifferent data structures make different types of operations fast XExample: lists of numbers
XArray ²fast to read out number at any position, slow to insert new number X´ILQNHG OLVPµ ²fast to insert a new number, slow to read out number at any position XOften there is a tradeoff between memory and time XHI RH QHYHU POURR MQ\ LQIRUPMPLRQ MRM\ POHQ RH RRQ·P have to recomputeit, but it might take up lots of memory Why study algorithms?
XAll datasets are getting bigger and bigger:
XInternet ²RHN VHMUŃO SMŃNHP URXPLQJ"
XScience ²JHQHPLŃV NUMLQ LPMJLQJ ŃOLPMPH PRGHOLQJ" XComputers ²ŃLUŃXLP OM\RXP ILOH V\VPHPV"
XComputer graphics ²PRYLHV YLGHR JMPHV YLUPXMO UHMOLP\" XSecurity ²cell phones, e-ŃRPPHUŃH YRPLQJ PMŃOLQHV" XSocial networks ²UHŃRPPHQGMPLRQV QHRV IHHGV" XWe need efficient algorithms to design almost any modern computer system Why study algorithms?
XTo become a more proficient programmer:
X´H RLOO LQ IMŃP ŃOMLP POMP POH GLIIHUHQŃH NHPRHHQ M NMG programmer and a good one is whether he considers his code or his data structures more important. Bad programmers worry about the code. Good programmers RRUU\ MNRXP GMPM VPUXŃPXUHV MQG POHLU UHOMPLRQVOLSVBµ ³ LinusTorvalds(creator of Linux)
X%HŃMXVH POH\·UH LQPHUHVPLQJ
X´)RU PH JUHMP MOJRULPOPV MUH POH SRHPU\ RI ŃRPSXPMPLRQB Just like verse, they can be terse, allusive, dense, and even mysterious. But once unlocked, they cast a brilliant QHR OLJOP RQ VRPH MVSHŃP RI ŃRPSXPLQJBµ ³Francis Sullivan
Why study algorithms?
Why study algorithms?
XTo unlock the secrets of life and the universe:
X´FRPSXPHU PRGHOV PLUURULQJ UHMO OLIH OMYH NHŃRPH ŃUXŃLMO IRU PRVP MGYMQŃHV PMGH LQ ŃOHPLVPU\ PRGM\"B 7RGM\ POH computer is just as important a tool for chemists as the PHVP PXNHBµ ³Royal Swedish Academy of Sciences XTo enable us to solve complex problems:
History of Algorithms
History of Algorithms
Algorithm examples
XGuessing game:
game XRoute finding:
XGenerating app names:
XGenetic algorithm:
http://rednuht.org/genetic_walkers/ What makes an algorithm
good? XWant efficiency in time²produce an answer as quickly as possible XWant efficiency in memory²use as little RAM as possible XWant efficiency in implementation²the less complex the better XWant this to work on any dataset without hand-tuned conditions XWant algorithms that scale well with size of data XIf data gets 2x bigger, does algorithm require more than 2x as much time/space? Measuring how an algorithm
scales X´%LJ-2 QRPMPLRQµ
XO(log N) ²algorithm scales logarithmically with dataset size XO(N) ²algorithm scales linearly with dataset size (good) XO(N * log N) ²algorithm scales slightly worse that linearly XO(N2) ²algorithm scales quadraticallywith dataset size XO(2N) ²algorithm scales exponentially with dataset size Measuring how an algorithm
scales Example: Binary Search
XGiven a sorted list of numbers, find where a specific number appears 1 5 1012 14 19 20
XAt every step we can eliminate half the numbers
1 5 10 12 14 19 20
XSo a list twice as big takes only oneadditional step! XRunning time is O(log N)
Example: Sum-3
XGiven a list of numbers, are there three that sum to 0? -10 5 -2 3 -9 -8 20 XEasy algorithm: try every possible combination of three numbers XRunning time: O(N3)
XCan we do better?
Sum-3 Algorithm
XFirst sort numbers
-10 -9 -8 -2 3 5 20 X$VVXPH RH·OO XVH ILUVP QXPNHU
XTry pairing with first and last remaining numbers -10-9 -8 -2 3 5 20 XMove in from left and right, depending on whether sum is above or below zero -10-9 -8 -2 3 520 XIf the green numbers hit each other, try again with assuming that the second number is used -10 -9 -8 -2 3 5 20 Sum-3 Algorithm
XHQ POH RRUVP ŃMVH RH·OO OMYH PR PU\ MOO SRVVLNOH ´ILUVP ŃORLŃHµ UHG QXPNHUV
XFor each of these, we might have to look at every other number XRunning time: O(N2)
XIf there are 1000 numbers, this is 1000 times faster! XOne trick: we assumed sorting was fast! Turns out we can sort faster than O(N2), so we can ignore this for now Sieve of Eratosthenes
sieve WarmupIRU QH[P RHHN·V
class: sorting XPutting a list in order is a classic problem in computer science X6LPSOHVP MOJRULPOP ´%XNNOHµ VRUP
XCompare every pair of adjacent elements
XIf they are out of order, swap them
XKeep making passes over the list until it is sorted Bubble sort
Assignment
XImplement bubble sort in any language
XHow long does it take to sort 1,000 numbers? What about 10,000?
XEmail your code and answers to these two questions to me at chrisb@princeton.edu XDue before next class
X[FYI: Assignments are also posted at chrisbaldassano.com] Re-scheduling December 10th
class XI will be away on December 10th
XWe can reschedule the class for December 7th(Mon), or 11th(Fri)
XPart of your assignment: Email me which of these days you would be availablequotesdbs_dbs8.pdfusesText_14
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