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Recursion: How It Works 7 January 2019 OSU CSE 1 Question - PowerPoint PPT Presentation

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Recursion: How It Works 7 January 2019 OSU CSE 1 Question Considered Before How should you think about recursion so you can use it to develop elegant recursive methods to solve certain problems? Answer : Pretend there is a FreeLunch

  1. Recursion: How It Works 7 January 2019 OSU CSE 1

  2. Question Considered Before • How should you think about recursion so you can use it to develop elegant recursive methods to solve certain problems? • Answer : Pretend there is a FreeLunch class with a method that has the same contract as the code you’re trying to write (but it works only for smaller problems) 7 January 2019 OSU CSE 2

  3. Question Considered Before • Why do those recursive methods work? • Answer : Following the “confidence- building” approach, you can argue as follows: – Does it work on all “smallest” cases? 7 January 2019 OSU CSE 3

  4. Question Considered Before • Why do those recursive methods work? • Answer : Following the “confidence- building” approach, you can argue as follows: – Does it work on all “smallest” cases? ✓ – Does it work on all “next smallest” cases? 7 January 2019 OSU CSE 4

  5. Question Considered Before • Why do those recursive methods work? • Answer : Following the “confidence- building” approach, you can argue as follows: – Does it work on all “smallest” cases? ✓ – Does it work on all “next smallest” cases? ✓ – Does it work on all “next smallest” cases? 7 January 2019 OSU CSE 5

  6. Question Considered Before • Why do those recursive methods work? • Answer : Following the “confidence- building” approach, you can argue as follows: – Does it work on all “smallest” cases? ✓ – Does it work on all “next smallest” cases? ✓ – Does it work on all “next smallest” cases? ✓ – ... (Formally, proof by mathematical induction) 7 January 2019 OSU CSE 6

  7. Question Considered Now • How do those recursive methods work? – As promised, we have come back to this, but we continue to advise... – If you insist on thinking about recursion this way (rather than simply sating your curiosity about how it works), you may never be fully capable of developing elegant recursive solutions to problems! 7 January 2019 OSU CSE 7

  8. Example private static String reversedString(String s) { if (s.length() == 0) { return s; } else { String sub = s.substring(1); String rSub = reversedString(sub); return rSub + s.charAt(0); } } 7 January 2019 OSU CSE 8

  9. Trace reversedString("OSU") s = "OSU" if (s.length() == 0) { ... } else { s = "OSU" String sub = s.substring(1); s = "OSU" sub = "SU" String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 9

  10. Trace reversedString("OSU") s = "OSU" if (s.length() == 0) { ... } else { s = "OSU" String sub = s.substring(1); s = "OSU" sub = "SU" String rSub = reversedString(sub); Question: This is a recursive call, so how does it work? return rSub + s.charAt(0); 7 January 2019 OSU CSE 10

  11. Trace reversedString("OSU") s = "OSU" if (s.length() == 0) { ... } else { s = "OSU" String sub = s.substring(1); s = "OSU" sub = "SU" String rSub = reversedString(sub); Answer: Exactly like this one, and every other call! return rSub + s.charAt(0); 7 January 2019 OSU CSE 11

  12. How Every Call Works • First, the tracing table for the code making the call is suspended and that tracing table is pushed onto the runtime stack – The runtime stack, often called simply “ the stack”, is effectively just a stack of tracing tables (think Stack<TracingTable> ), each partially filled in with the results of the code in that tracing table as executed so far 7 January 2019 OSU CSE 12

  13. How Every Call Works • A new tracing table is created, containing the code for the method body being called • The argument values are copied from the suspended tracing table into the formal parameters to start the new tracing table • Execution in the new tracing table continues until it calls a method... 7 January 2019 OSU CSE 13

  14. The currently executing Trace reversedString("OSU") tracing table gets to here ... s = "OSU" if (s.length() == 0) { ... } else { String sub = s.substring(1); String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 14

  15. ... and the (top of the) stack Trace reversedString("OSU") of suspended tables is here. s = "OSU" if (s.length() == 0) { ... } else { String sub = s.substring(1); String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 15

  16. This call suspends the Trace reversedString("OSU") current tracing table ... s = "OSU" if (s.length() == 0) { ... } else { String sub = s.substring(1); String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 16

  17. ... the suspended tracing Trace reversedString("OSU") table is pushed ... 7 January 2019 OSU CSE 17

  18. ... and the tracing table for Trace reversedString("OSU") length begins. this = "OSU" /* * Body for length method * from class String; we * do not have this, so how * do we know what it does? * We look at its contract! * When it finishes, we know * it has not changed this * (it could not even if it * wanted to), and it returns * the length of this . */ this = "OSU" length = 3 7 January 2019 OSU CSE 18

  19. How Every Return Works • When the currently executing tracing table reaches a return statement, or for a void method falls off the end of the body, the results of the call are reflected in the tracing table on the top of the stack • That tracing table is popped off the stack and it becomes the currently executing tracing table, resuming execution from the point where it was suspended 7 January 2019 OSU CSE 19

  20. Trace reversedString("OSU") When this call returns ... this = "OSU" /* * Body for length method * from class String; we * do not have this, so how * do we know what it does? * We look at its contract! * When it finishes executing * it has not changed this * (it could not even if it * wanted to), and it returns * the length of this */ this = "OSU" length = 3 7 January 2019 OSU CSE 20

  21. ... its results are reflected in Trace reversedString("OSU") the calling table ... 7 January 2019 OSU CSE 21

  22. ... and that table is popped Trace reversedString("OSU") to resume execution. s = "OSU" if (s.length() == 0) { ... } else { String sub = s.substring(1); String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 22

  23. Execution continues to the Trace reversedString("OSU") next call ... s = "OSU" if (s.length() == 0) { ... } else { s = "OSU" String sub = s.substring(1); String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 23

  24. ... and when that call returns, Trace reversedString("OSU") to the next call ... s = "OSU" if (s.length() == 0) { ... } else { s = "OSU" String sub = s.substring(1); s = "OSU" sub = "SU" String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 24

  25. ... which is a recursive call! Trace reversedString("OSU") But it is nothing special. s = "OSU" if (s.length() == 0) { ... } else { s = "OSU" String sub = s.substring(1); s = "OSU" sub = "SU" String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 25

  26. The current tracing table is Trace reversedString("OSU") suspended and pushed ... 7 January 2019 OSU CSE 26

  27. ... and a new table for the Trace reversedString("OSU") body of the called method ... s = "SU" if (s.length() == 0) { ... } else { String sub = s.substring(1); String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 27

  28. ... begins with its own Trace reversedString("OSU") variables and values. s = "SU" if (s.length() == 0) { ... } else { String sub = s.substring(1); String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 28

  29. Soon, this tracing table Trace reversedString("OSU") reaches a recursive call! s = "SU" if (s.length() == 0) { ... } else { s = "SU" String sub = s.substring(1); s = "SU" sub = "U" String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 29

  30. The current tracing table is Trace reversedString("OSU") suspended and pushed ... 7 January 2019 OSU CSE 30

  31. ... and a new table for the Trace reversedString("OSU") body of the called method ... s = "U" if (s.length() == 0) { ... } else { String sub = s.substring(1); String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 31

  32. ... begins with its own Trace reversedString("OSU") variables and values. s = "U" if (s.length() == 0) { ... } else { String sub = s.substring(1); String rSub = reversedString(sub); return rSub + s.charAt(0); 7 January 2019 OSU CSE 32

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