Thinking in algorithms

CS-503, WINTER 2020 ALGORITHMS
 AND
 DATA STRUCTURES KEVIN WAYNE http://www.princeton.edu/~cos226

CS-503 course overview What is CS-503? survey course.・Intermediate-level and problem solving, with applications.・Programming method for solving a problem.・Algorithm: structure: method to store information.・Data topic data structures and algorithms data types stack, queue, bag, union-find, priority queue sorting quicksort, mergesort, heapsort, radix sorts searching BST, red-black BST, hash table graphs BFS, DFS, Prim, Kruskal, Dijkstra strings KMP, regular expressions, tries, data compression advanced B-tree, k-d tree, suffix array, maxflow 2

Why study algorithms? Their impact is broad and far-reaching. Internet. Web search, packet routing, distributed file sharing, ... Biology. Human genome project, protein folding, …
 Computers. Circuit layout, file system, compilers, …
 Computer graphics. Movies, video games, virtual reality, …
 Security. Cell phones, e-commerce, voting machines, …
 Multimedia. MP3, JPG, DivX, HDTV, face recognition, …
 Social networks. Recommendations, news feeds, advertisements, …
 Physics. N-body simulation, particle collision simulation, …
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Why study algorithms? Their impact is broad and far-reaching. 4

Why study algorithms? Old roots, new opportunities. of algorithms dates at least to Euclid.・Study by Church and Turing in 1930s.・Formalized important algorithms were discovered
・Some by undergraduates in a course like this! BCE 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 300 5

Why study algorithms? For intellectual stimulation. F R O M T H E E D I T O R S THE JOY OF ALGORITHMS Francis Sullivan, Associate Editor-in-Chief HE THEME OF THIS FIRST-OF-THE-CENTURY ISSUE OF COMPUTING IN “ For me, great algorithms are the poetry of computation. Just SCIENCE & ENGINEERING IS ALGORITHMS. IN FACT, WE WERE BOLD T ENOUGH—AND PERHAPS FOOLISH ENOUGH—TO CALL THE 10 EXAMPLES WE’VE SE- LECTED “THE TOP 10 ALGORITHMS OF THE CENTURY.” Computational algorithms are probably as old as civilization. mysterious. But once unlocked, they cast a brilliant new light Sumerian cuneiform, one of the most ancient written records, on some aspect of computing. A colleague recently claimed consists partly of algorithm descriptions for reckoning in base that he’d done only 15 minutes of productive work in his 60. And I suppose we could claim that the Druid algorithm for whole life. He wasn’t joking, because he was referring to the estimating the start of summer is embodied in Stonehenge. 15 minutes during which he’d sketched out a fundamental op- timization algorithm. He regarded the previous years of really hard hardware!) thought and investigation as a sunk cost that might or might like verse, they can be terse, allusive, dense, and even mysterious. (That’sLike so many other things that technology affects, algo- rithms have advanced in startling and unexpected ways in the not have paid off. 20th century—at least it looks that way to us now. The algo- Researchers have cracked many hard problems since 1 Jan- rithms we chose for this issue have been essential for progress uary 1900, but we are passing some even harder ones on to the in communications, health care, manufacturing, economics, next century. In spite of a lot of good work, the question of weather prediction, defense, and fundamental science. Con- how to extract information from extremely large masses of versely, progress in these areas has stimulated the search for data is still almost untouched. There are still very big chal- ever-better algorithms. I recall one late-night bull session on lenges coming from more “traditional” tasks, too. For exam- the Maryland Shore when someone asked, “Who first ate a ple, we need efficient methods to tell when the result of a large crab? After all, they don’t look very appetizing.’’ After the usual floating-point calculation is likely to be correct. Think of the speculations about the observed behavior of sea gulls, someone way that check sums function. The added computational cost But once unlocked, they cast a brilliant new light on some gave what must be the right answer—namely, “A very hungry is very small, but the added confidence in the answer is large. person first ate a crab.” Is there an analog for things such as huge, multidisciplinary The flip side to “necessity is the mother of invention’’ is “in- optimizations? At an even deeper level is the issue of reason- vention creates its own necessity.’’ Our need for powerful ma- able methods for solving specific cases of “impossible’’ prob- chines always exceeds their availability. Each significant com- lems. Instances of NP-complete problems crop up in at- putation brings insights that suggest the next, usually much tempting to answer many practical questions. Are there larger, computation to be done. New algorithms are an attempt efficient ways to attack them? to bridge the gap between the demand for cycles and the avail- I suspect that in the 21st century, things will be ripe for an- able supply of them. We’ve become accustomed to gaining the other revolution in our understanding of the foundations of Moore’s Law factor of two every 18 months. In effect, Moore’s computational theory. Questions already arising from quan- Law changes the constant in front of the estimate of running tum computing and problems associated with the generation of random numbers seem to require that we somehow tie to- as a function of problem size. Important new algorithms gether theories of computing, logic, and the nature of the aspect of computing. ” — Francis Sullivan timedo not come along every 1.5 years, but when they do, they can change the exponent of the complexity! physical world. For me, great algorithms are the poetry of computation. The new century is not going to be very restful for us, but it Just like verse, they can be terse, allusive, dense, and even is not going to be dull either! 2 C O MPUTING IN SCIENCE & ENGINEERING “ An algorithm must be seen to be believed. ” — Donald Knuth 6

Why study algorithms? To become a proficient programmer. “ I will, in fact, claim that the difference between a bad 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 worry about data structures and their relationships. ” — Linus Torvalds (creator of Linux) “ Algorithms + Data Structures = Programs. ” — Niklaus Wirth 7

Why study algorithms? They may unlock the secrets of life and of the universe. “ Computer models mirroring real life have become crucial for most advances made in chemistry today…. Today the computer is just as important a tool for chemists as the test tube. ” — Royal Swedish Academy of Sciences (Nobel Prize in Chemistry 2013) Martin Karplus, Michael Levitt, and Arieh Warshel 8

Why study algorithms? To solve problems that could not otherwise be addressed. http://www.youtube.com/watch?v=ua7YlN4eL_w 9

Why study algorithms? For fun and profit. 10

Why study algorithms? impact is broad and far-reaching.・Their roots, new opportunities.・Old intellectual stimulation.・For become a proficient programmer.・To may unlock the secrets of life and of the universe.・They solve problems that could not otherwise be addressed.・To else is doing it.・Everybody fun and profit.・For Why study anything else? 11

Resources (textbook) Required reading. Algorithms 4th edition by R. Sedgewick and K. Wayne, Addison- Wesley Professional, 2011, ISBN 0-321-57351-X. AlgorithmsF O U R T H E D I T I O N 1st edition (1982) 2nd edition (1988) 3rd edition (1997) R O B E R T S E D G E W I C K K E V I N W A Y N E 4th edition (2011) 3rd book scanned
 by Google books Available in hardcover and Kindle. Amazon ($60/$35 to buy), Chegg ($25 to rent), ...・Online: Labyrinth Books (122 Nassau St).・Brick-and-mortar: reserve: Engineering library.・On 12