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N is for PFtLFiF Introduction to Recursion new Allocating memory - PowerPoint PPT Presentation

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Compsci 201 Announcements Recursion, DNA-Link Preview Exam 1 Ask for Regrade in Gradescope by March 1 Regrades assignments if you pushed to github but did not resubmit in gradescope, fill out regrade form and we can look at your

  1. Compsci 201 Announcements Recursion, DNA-Link Preview • Exam 1 – Ask for Regrade in Gradescope by March 1 • Regrades assignments • if you pushed to github but did not resubmit in gradescope, fill out regrade form and we can look at your github if you have not modified it! • Assignment P3 last chance today on time • Assignment P4 out today with a Part1 and Part2 • Part 1 due March 5, Part 2 due March 19 Susan Rodger • APT 4 due Tuesday! • APT Quiz 1 – now on regular APT page February 28, 2020 • Not for credit, but finish if you didn’t 2/28/2020 Compsci 201, Spring 2020 1 2/28/2020 Compsci 201, Spring 2020 2 N is for … PFtLFiF • Introduction to Recursion • new • Allocating memory from the heap • Canonical problem-solving/programming tool • Useful for lists, trees, and when structure is self- referential (algorithmic too, not today) • null • Value when nothing has been allocated • Review linked lists in context of P4: DNA-link • You can work with a partner from your Discussion section • Choose next week, run code, finish after break 2/28/2020 Compsci 201, Spring 2020 3 2/28/2020 Compsci 201, Spring 2020 4

  2. Modify and Return linked list What does pass-by-value mean? • If we pass a pointer to first node and .. • Want to "remove first" • Java passes parameters by value • We must return a pointer to modified list • Pass a copy of the variable • void change(ListNode first) • A copy of list1 is passed • Call change(list) • first = first.next • list not changed after call first 2/28/2020 Compsci 201, Spring 2020 5 2/28/2020 Compsci 201, Spring 2020 7 Idiom: pass-and-return Invariants • Class level: true before each method executes • Change the list passed in, return the list. • Established at construction • Assign in the call, e.g. x = changeUp(x) • Re-established by each method Thing xx = new Thing(); • Loop level: true before each loop guard evaluation change(xx); • Established before first iteration of loop // can xx be different after call? • Re-established after each loop iteration // can write xx.mutate() // cannot assign to xx in change • Reason formally and informally about code xx = changeUp(xx); 2/28/2020 Compsci 201, Spring 2020 8 2/28/2020 Compsci 201, Spring 2020 10

  3. WOTO Google (DYM): Recursion http://bit.ly/201spring20-0226-2 • What is the Internet? • A network of networks …. • What is PageRank? • What’s a good website link? public int calc(int n){ return n*calc(n-1); } 2/28/2020 Compsci 201, Spring 2020 11 2/28/2020 Compsci 201, Spring 2020 12 Google recursion Self Reference and Recursion Did you mean …? • Those software engineers … • Does a Node reference itself? • Did you mean invented by Noam Shazeer, Duke • No, there’s a .next field, but … 1998: Math and Compsci • Does a recursive method call itself? • No, calls clones of itself • Careful, could make “infinite” number of calls … • What’s in a folder? • Files and other folders. Is that self-referential? 2/28/2020 Compsci 201, Spring 2020 13 2/28/2020 Compsci 201, Spring 2020 14

  4. Noam Shazeer, Duke 2008 When to use recursion • https://www.newyorker.com/magazine/2018/12/10/the-friendship-that-made-google-huge • The structure of the problem lends itself … • Compsci 201 alum, passionate about problem- • Folders/Directories contain … solving • Nodes in a linked list contain … • The algorithmic structure lends itself … • Sorting algorithms as we’ll see … • Factorial? Just say no … 2/28/2020 Compsci 201, Spring 2020 15 2/28/2020 Compsci 201, Spring 2020 16 Size of a linked list Vocabulary • All recursive code has a base case • You've seen a loop to do this • A simple case where no recursion necessary • Goal: try to understand why this is correct • Example in linked list? null, no recursion • We'll use example from arithmetic too • sometimes one node case too • Vocabulary with both structure and algorithm • Base case always identified with an if statement. 2/28/2020 Compsci 201, Spring 2020 17 2/28/2020 Compsci 201, Spring 2020 18

  5. RecDemo.java Understanding Recursion • Visualize: RecDemo.java • The base case anchors the recursion https://coursework.cs.duke.edu/201spring20/classcode/blob/master/src/RecDemo.java • There's no loop! Why? • Sequence of recursive calls • Stacked up until base returns • The recursive call "decreases" • Must get toward base case 2/28/2020 Compsci 201, Spring 2020 19 2/28/2020 Compsci 201, Spring 2020 20 RecDemo.java – rest of it About to count # nodes in list • Call create(4) finished, call count(list) • What does list point to ? list.next ? 2/28/2020 Compsci 201, Spring 2020 21 2/28/2020 Compsci 201, Spring 2020 22

  6. First recursive call made Second recursive call made • E Each method on the stack/pile of methods has its • Three calls of count made: where is active call? own local state: what does list reference? • Parameter list points at 1, what happens? • Node 3 in doit/first call, node 2 in recursive call 2/28/2020 Compsci 201, Spring 2020 23 2/28/2020 Compsci 201, Spring 2020 24 What do we see? Last call: base case reached • Each method invocation • The active call has list == null has its own state: • Base case reached! Return 0 parameter, local • Where is this value returned? variables, line number • To the call: the stack frame "above" • Addition happens back up call-chain • Goal: trust recursion • Trust is hard • Debugging on trust? Not so easy 2/28/2020 Compsci 201, Spring 2020 25 2/28/2020 Compsci 201, Spring 2020 26

  7. How did recursion work? How do you calculate N! • Structure of a linked list is essential • Multiply 1 x 2 x 3 x … x N • For a non-null list, # nodes is: count me, and recursively count the rest, add together public int fact(int n){ int prod = 1; for(int k=2; k <= n; k++){ • Recursion in general: process one case, one prod *= k; number, one node. Make a recursive call, use } result. return prod; • Code must use return value of recursive call } • For lists? Deal with one node only in code 2/28/2020 Compsci 201, Spring 2020 27 2/28/2020 Compsci 201, Spring 2020 28 Don ’ t do this! Recursive Terminology n=4 • Recursive methods must have a base case • int x = fact(4); public int fact(int n){ t n){ i if (n == 1) return 1; • Simple to do, don’t need “help” return n*fact(n-1); r • return 4*fact(3) } } • Recursive calls make progress toward base case • The call of fact(3) calls a “clone” or “copy” • Some measure gets smaller, toward base case • Doesn’t call “itself”, is re-entrant code • What’s n! public int fact(int n){ • It’s n * (n-1)! if (n == 1) return 1; • What’s the base case? 1! Is 1 (or 0! Is 1) return n*fact(n-1); } 2/28/2020 Compsci 201, Spring 2020 29 2/28/2020 Compsci 201, Spring 2020 30

  8. Don ’ t do this 2 Don ’ t do this 3 n=4 n=4 • int x = fact(4); public int fact(int n){ t n){ • int x = fact(4); public int fact(int n){ t n){ if (n == 1) return 1; i if (n == 1) return 1; • return 4*fact(3) return n*fact(n-1); r • return 4*fact(3) return n*fact(n-1); } } } } n=3 n=3 • return 3 * fact(2) public int fact(int n){ nt n){ public int fact(int n){ nt n){ if (n == 1) return 1; if (n == 1) return 1; return n*fact(n-1); return n*fact(n-1); } } } n=2 public int fact(int n){ if (n == 1) return 1; public int fact(int n){ nt n){ if (n == 1) return 1; return n*fact(n-1); return n*fact(n-1); } } 2/28/2020 Compsci 201, Spring 2020 31 2/28/2020 Compsci 201, Spring 2020 32 Don ’ t do this 3 Base Case Reached n=4 n=4 • int x = fact(4); public int fact(int n){ t n){ • return 2*fact(1) public int fact(int n){ t n){ if (n == 1) return 1; if (n == 1) return 1; return n*fact(n-1); return n*fact(n-1); • return 4*fact(3) • Evaluates to 2*1 } } } } • Return to call of fact(1) n=3 n=3 • return 3 * fact(2) public int fact(int n){ nt n){ public int fact(int n){ nt n){ i if (n == 1) return 1; if (n == 1) return 1; i n=1 r return n*fact(n-1); return n*fact(n-1); r } } } } • When n is 2 …? public int fact(int n){ nt n){ if (n == 1) return 1; n=2 n=2 • return 2 * fact(1) return n*fact(n-1); } public int fact(int n){ nt n){ public int fact(int n){ nt n){ if (n == 1) return 1; if (n == 1) return 1; return n*fact(n-1); return n*fact(n-1); } } } } 2/28/2020 Compsci 201, Spring 2020 33 2/28/2020 Compsci 201, Spring 2020 34

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