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Compsci 201 V is for Algorithmic Paradigms Huffman Compression Virtual Memory Part 1 of 4 When 4Gb becomes the cloud Virtual Reality IRL isn't cutting it? Susan Rodger April 15, 2020 4/15/2020 Compsci 201, Spring 2020 1

  1. Compsci 201 V is for … Algorithmic Paradigms Huffman Compression • Virtual Memory Part 1 of 4 • When 4Gb becomes the cloud • Virtual Reality • IRL isn't cutting it? Susan Rodger April 15, 2020 4/15/2020 Compsci 201, Spring 2020 1 4/15/2020 Compsci 201, Spring 2020 2 P7 Assignment – Create Announcements Optional – Extra Credit • APT-7 due Thursday, April 16 • APT-8 due Tuesday, April 21 • Make something creative about CompSci 201 • Assignment P6 Huffman due April 22 • Earn 2 points to your highest exam score. • All late work turned in by April 22 (APTs and Asgns) • What you create • Except Huffman grace through April 23 • Video (to share) • Exam 2 last chance to take through Friday 4/17 • Advertisement for CompSci 201 • Final Exam will be on April 30 – any time on this day • Story/Song about CompSci 201 • Green Dance • APT Quiz 2 is April 12-18 – Your own work! • Comic/Poem (to share) • Or Just give us feedback (not to share) • Assignment P7 Optional out – Extra Credit! 4/15/2020 Compsci 201, Spring 2020 3 4/15/2020 Compsci 201, Spring 2020 4

  2. Plan for the Day Sample Create 5 From CompSci 101 • Algorithm Paradigms via APTs • Backtracking Algorithms • Greedy Algorithms • Next week: more algorithmic paradigms • Huffman Compression • Quintessential 201 (and greedy) assignment? • Greedy, trees, arrays, recursion, priority queues, reading files, writing files, bits, bytes, oh my! 4/15/2020 Compsci 201, Spring 2020 9 4/15/2020 Compsci 201, Spring 2020 10 Backtracking Summary GridGame Backtracking Redux • Enumerate all possible moves/choices • Helper method: do and undo • Nqueen? Each column and each row in column • Blob-fill? Each neighbor: fill, and unfill • GridGame: try a move, follow it, undo/repeat • State/Board often two-dimensional array/grid ".X.X" ".X.X" ".X.X" • Not efficient, but thorough: try it all " X .X." " X .X." "..X." ".X.." ".X. X " ".X.." "...." "...." "...." 4/15/2020 Compsci 201, Spring 2020 11 4/15/2020 Compsci 201, Spring 2020 12

  3. Collaborative APT Solving BackTrackRat • http://www.cs.duke.edu/csed/newapt/ratroute.html • http://www.cs.duke.edu/csed/newapt/ratroute.html • How many paths to reach cheese? 3 below • Take a step toward the cheese, try every step … • E,E,S,S,S,S • If that works? Add +1 to total • S,S,S,S,E,E • If that doesn't work? back-track • S,S,E,E,S,S: always closer, never further to goal • Create Grid • Remember cheese goal E – moves east • Take steps and count S – moves south 4/15/2020 Compsci 201, Spring 2020 14 4/15/2020 Compsci 201, Spring 2020 18 Backtracking APTs Rat/Transform input to grid • Often use grid[][] to store state/moves ["X..X.X.", "XX.C.X.", ".......", • In Java this is actually an array of arrays "..X.X..", ".......", "R.XX..." ] • int[][] a = new int[4][4 ] for example • Input: String[], transform to char[][] • [0][0] is upper left, 0 th row/column • What is a[0]? What is a[0][0]? X..X.X. XX.C.X. ....... • Often move must be explicitly undone • Start at rat and ... ..X.X.. • Sometimes just try everything • Try each step closer to cheese ....... R.XX... 4/15/2020 Compsci 201, Spring 2020 19 4/15/2020 Compsci 201, Spring 2020 20

  4. Transform, Initialize, Solve Base cases for cheese-finding • State and • Off the grid? No paths to cheese behavior: • On an 'X'? No paths to cheese local or • On the cheese? One path to cheese instance variables • Scope? • Rectangle? • loop bounds 4/15/2020 Compsci 201, Spring 2020 21 4/15/2020 Compsci 201, Spring 2020 23 Try every possible step that … WOTO • Closer to the cheese only, see line 50 http://bit.ly/201spring20-0415-1 • What do we return? Recursive help 4/15/2020 Compsci 201, Spring 2020 24 4/15/2020 Compsci 201, Spring 2020 26

  5. Compsci 201 Lynn Conway Algorithmic Paradigms Huffman Compression See Wikipedia and http://lynnconway.com • Joined Xerox Parc in 1973 Part 2 of 4 • Revolutionized VLSI design • with Carver Mead • NAE '89, IEEE Pioneer '09 • Dynamic scheduling early '60s IBM • Transgender, fired in '68 We’ve come so far, so fast, that ever so many others could begin shedding old habits too. After all, freedom isn’t just an external concept, framed by our laws. It’s a gift of the Susan Rodger spirit that we must give ourselves, in this case by going towards brighter shades of ‘out’. Bottom line: If you want to change the future, start living as if you’re already there. April 15, 2020 https://www.huffingtonpost.com/lynn-conway/the-many-shades-of-out_b_3591764.html Compsci 201, Fall 2018, 11/16/2018 27 4/15/2020 Compsci 201, Spring 2020 28 DFS+BFS+Thinking Greedy Algorithm: Huff Prelude Greedy Algorithms • Optimization: Best choice, maximal or minimal • In change making with US coins: minimize # coins • Make a choice that looks good locally • Choose highest denomination. Repeat • But local best leads to global optimum • Works with infinite number of each coin • In later courses: prove greedy is optimal • Example with $0.32 and no nickels? • Shortest path algorithm: choose "closest" point, • Canonical example? Change with minimal # coins move there: overall best. Careful on "closest" • Change for $0.63, change for $0.32 • Huffman Compression: optimal per-character • What if we're out of nickels, change for $0.32? • Can't compress better one-char-at-a-time 4/15/2020 Compsci 201, Spring 2020 29 4/15/2020 Compsci 201, Spring 2020 30

  6. Greedy APTs Olympic Candles APT • https://www2.cs.duke.edu/csed/newapt/olympic.html • Given (different) heights of N-candles • How is Olympic Candles greedy? • Day one: light one, Day two: light two, … • What candle should be lit on first night? Why? • When lit? Burns one inch of height • How many days until candles out? • https://www2.cs.duke.edu/csed/newapt/voterigging.html • [2,2,2] --- 3 nights • How is VoteRigging greedy? • [ 1 ,2,2], [ 0 , 1 ,2], XXX, not greedy doesn’t work • From whom should a vote be taken? Why? • [ 1 ,2,2], [1, 1 , 1 ], [ 0,0,0 ] • [5,2,2,1] --- 3 nights • [ 4 ,2,2,1], [ 3 , 1 ,2,1], [ 2 , 0,1 ,1] 4/15/2020 Compsci 201, Spring 2020 31 4/15/2020 Compsci 201, Spring 2020 32 Greedy Olympic Solution Candle Pseudo-code • On night N, which candles chosen to burn? • Can we sort in reversed order? • The tallest N candles, decrement each, repeat • Comparator.reverseOrder()? no! • N = 1,2,3,… until you don't have enough • How to determine tallest N candles? • What's complexity here? • Worst-case? Re-sort each time, repeat N times • Final result? O(N 2 log N), why? 4/15/2020 Compsci 201, Spring 2020 33 4/15/2020 Compsci 201, Spring 2020 34

  7. Algorithmic Processes that Scale Huffman is a greedy algorithm http://bit.ly/201spring19-april12-huff • What is the 'A' in APT? • Typically efficiency is NOT an issue here? • What about in a tech/job interview? • Consider Olympic candles, what candles burn? • Have to burn N 2 candles in worst-case • Find "best" better than log(n) per candle? no • What does efficiency mean for algorithms? • Is O(N 2 ) ok for sorting? https://www.youtube.com/watch?v=aV8Wey9Ixj0 4/15/2020 Compsci 201, Spring 2020 35 4/15/2020 Compsci 201, Spring 2020 36 Compsci 201 Overview of Huffman Algorithmic Paradigms Lossy v Lossless Compressoin Huffman Compression • RAW format compared to JPEG format Part 3 of 4 • Tradeoffs – another example of "it depends" • Why do you ZIP files/folders? • Upload to Dropbox/Box/Google Drive • What are advantages of MP3 Susan Rodger • You were 0-3 years old April 15, 2020 4/15/2020 Compsci 201, Spring 2020 37 4/15/2020 Compsci 201, Spring 2020 38

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