Compsci 201 201 Recursio sion, D DNA-Lin ink P Previe iew Susan Rodger February 28, 2020 2/28/2020 Compsci 201, Spring 2020 1
Announcements • Exa Exam 1 1 – Ask f for R Reg egrade in in Gradesco cope by by March 1 1 • Regrades a assig ignm nment ents • 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! • Assig ignm nment nt P P3 las ast c chanc ance t e today o on time • Assig ignm nment nt P P4 out to today wit ith a h a Par art1 and and P Par art2 • Part 1 due March 5, Part 2 due March 19 • APT T 4 4 due T ue Tue uesday! • APT APT Quiz iz 1 – now on on regular ular APT APT pag age • Not for credit, but finish if you didn’t 2/28/2020 Compsci 201, Spring 2020 2
N is for … • new • Allocating memory from the heap • null • Value when nothing has been allocated 2/28/2020 Compsci 201, Spring 2020 3
PFtLFiF • Introduct uctio ion t n to Recur cursio ion • Canonical problem-solving/programming tool • Useful for lists, trees, and when structure is self- referential (algorithmic too, not today) • Review link linked lis lists in in cont ntext o of P4: D 4: DNA-link ink • 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 4
Modify and Return linked list • If we e pass a a poin inter t to fir irst no node and and .. .. • Want to "remove first" • We must return a pointer to modified list • void change(ListNode first) • Call change(list) • first = first.next • list not changed after call first 2/28/2020 Compsci 201, Spring 2020 5
What does pass-by-value mean? • Java p passes es p param ameter ers b by va value ue • Pass a copy of the variable • A copy of list1 is passed 2/28/2020 Compsci 201, Spring 2020 7
Idiom: pass-and-return • Cha hange t the lis he list p passed in, in, r return t the he lis list. • Assign in the call, e.g. x = changeUp(x) Thing xx = new Thing(); change(xx); // can xx be different after call? // can write xx.mutate() // cannot assign to xx in change xx = changeUp(xx); 2/28/2020 Compsci 201, Spring 2020 8
Invariants • Class l level el: t : true ue b bef efore e e each m ch met etho hod e execut ecutes • Established at construction • Re-established by each method • Loop level el: t true b ue bef efore e e each l ch loop guar ard e eval alua uatio ion • Established before first iteration of loop • Re-established after each loop iteration • Rea eason f formally and and inf informally ab about ut co code 2/28/2020 Compsci 201, Spring 2020 10
WOTO http:// //bi bit.ly/2 /201spr pring20-02 0226 26-2 2/28/2020 Compsci 201, Spring 2020 11
Google (DYM): Recursion • What i is the e Inter erne net? • A network of networks …. • What i is PageR eRank nk? • What’s a good website link? public int calc(int n){ return n*calc(n-1); } 2/28/2020 Compsci 201, Spring 2020 12
Self Reference and Recursion • Does a a Node r ref eferenc nce i e itself lf? • No, there’s a .next field, but … • Does a a recur cursiv ive m metho hod c call i l itself elf? • No, calls clones of itself • Careful, could make “infinite” number of calls … • Wha hat’s in in a a fold lder? • Files and other folders. Is that self-referential? 2/28/2020 Compsci 201, Spring 2020 13
Google recursion Did you mean …? • Tho Those s software eng engin ineers … • Did you mean invented by Noam Shazeer, Duke 1998: Math and Compsci 2/28/2020 Compsci 201, Spring 2020 14
Noam Shazeer, Duke 2008 https://www.newyorker er.com/magaz azin ine/ e/20 2018/ 18/12/ 12/10/ 10/the-frien endship ip-that-ma made-goog oogle-hug uge • • Compsc sci 201 a alu lum, p pas assio iona nate a about ut p problem lem- solving ing 2/28/2020 Compsci 201, Spring 2020 15
When to use recursion • The The structure o of the p he problem lend lends it itself lf … • Folders/Directories contain … • Nodes in a linked list contain … • The alg The algorithmic structure lend lends it itself … … • Sorting algorithms as we’ll see … • Factorial? Just say no … 2/28/2020 Compsci 201, Spring 2020 16
Size of a linked list • You' u've s see een a a lo loop t to do this his • Goal al: t try t to und understand why hy thi his is is correct • We'll u ll use e example le from a arit ithm hmetic t ic too • Vocabula ulary w with b h both struc uctur ure a e and a algorit ithm hm 2/28/2020 Compsci 201, Spring 2020 17
Vocabulary • All ll rec ecursive c code e ha has a a base case • A simple case where no recursion necessary • Example in linked list? null, no recursion • sometimes one node case too • Base c case alw always id iden entif ified w wit ith h an an if if statement. 2/28/2020 Compsci 201, Spring 2020 18
Understanding Recursion • Visua uali lize: : RecDe Demo mo.java • The base case anchors the recursion https://c ://coursework.cs.d .duke.e .edu/201 /201spring20/c 0/classcode/b /blob/m /master/s /src/R /RecDe Demo.j .java • Ther There's no no lo loop! W Why hy? • Sequence of recursive calls • Stacked up until base returns • The r The rec ecursive c call all "d "decreases" • Must get toward bas ase c e cas ase 2/28/2020 Compsci 201, Spring 2020 19
RecDemo.java 2/28/2020 Compsci 201, Spring 2020 20
RecDemo.java – rest of it 2/28/2020 Compsci 201, Spring 2020 21
About to count # nodes in list • Call ll create(4) finis ished hed, c , call ll count(list) • What does list point to ? list.next ? 2/28/2020 Compsci 201, Spring 2020 22
First recursive call made • Each h metho hod o on the s e stack ck/pile o ile of met etho hods h has as its own local s al state: w : what at d does l list r refer erence ence? • Node 3 in doit/first call, node 2 in recursive call 2/28/2020 Compsci 201, Spring 2020 23
Second recursive call made • Three ee c calls lls o of count nt m made: w : where i e is act ctiv ive c e call? ll? • Parameter list points at 1, what happens? 2/28/2020 Compsci 201, Spring 2020 24
What do we see? • Each m h metho hod invocatio ion n has i its ts o own sta tate: param ameter, l local al varia iable les, l , line n number er • Goal: t : trus ust r recur ursio ion • Trust is hard • Debugging on trust? Not so easy 2/28/2020 Compsci 201, Spring 2020 25
Last call: base case reached • The ac The active c cal all l ha has lis list = == null null • Base case reached! Return 0 • Where i e is t this v value ue r ret etur urned ned? • To the call: the stack frame "above" • Addit ition hap happens b bac ack up up call all-cha hain in 2/28/2020 Compsci 201, Spring 2020 26
How did recursion work? • Structure o of a a link linked lis list is is es essential • For a non-null list, # nodes is: count me, and recursively count the rest, add together • Rec ecursion in in gene eneral: p process o one c ne case, o one ne number, o , one n node. M Make a a recur ursiv ive c call ll, u use e result ult. • 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
How do you calculate N! • Mul ultip iply 1 x 1 x 2 x 2 x 3 x 3 x … x N x N public int fact(int n){ int prod = 1; for(int k=2; k <= n; k++){ prod *= k; } return prod; } 2/28/2020 Compsci 201, Spring 2020 28
Recursive Terminology • Recursi sive m meth thods m s must h st have a a bas ase c e cas ase • Simple to do, don’t need “help” • Recur cursiv ive c calls ls m make p progress t towar ard bas ase c e case • Some measure gets smaller, toward base case • Wha hat’s n! n! • It’s n * (n-1)! • What’s the base case? 1! Is 1 (or 0! Is 1) 2/28/2020 Compsci 201, Spring 2020 29
Don ’ t do this! n=4 • int int x = f = fact(4 (4); ); public int fact(int n){ if (n == 1) return 1; return n*fact(n-1); • return 4*fact(3) } • The c The cal all o of fac act(3) c cal alls a a “clo lone” o or “copy” • Doesn’t call “itself”, is re re-ent entrant ant c code public int fact(int n){ if (n == 1) return 1; return n*fact(n-1); } 2/28/2020 Compsci 201, Spring 2020 30
Don ’ t do this 2 n=4 • int int x = f = fact(4 (4); ); public int fact(int n){ if (n == 1) return 1; return n*fact(n-1); • return 4*fact(3) } n=3 public int fact(int n){ if (n == 1) return 1; return n*fact(n-1); } public int fact(int n){ if (n == 1) return 1; return n*fact(n-1); } 2/28/2020 Compsci 201, Spring 2020 31
Don ’ t do this 3 n=4 • int int x = f = fact(4 (4); ); public int fact(int n){ if (n == 1) return 1; return n*fact(n-1); • return 4*fact(3) } n=3 • retur urn n 3 * * f fact ct(2) 2) public int fact(int n){ if (n == 1) return 1; return n*fact(n-1); } n=2 public int fact(int n){ if (n == 1) return 1; return n*fact(n-1); } 2/28/2020 Compsci 201, Spring 2020 32
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