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Introduction to Recursion

Lecture 6. Introduction to Recursion. Please fasten your seat belts. LB. Whatintheheckisrecursion?. LB. Solving a problem in terms of itself. wget Given a URL Read in the file Save it to disk Scan through file Find any JPG or GIF references then save them

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Introduction to Recursion

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  1. Lecture 6 Introduction to Recursion Please fasten your seat belts.

  2. LB Whatintheheckisrecursion?

  3. LB Solving a problem in terms of itself. • wget • Given a URL • Read in the file • Save it to disk • Scan through file • Find any JPG or GIF references then save them • Find any HTML references then call wget

  4. LB Solving a problem in terms of itself • ShowMe • Given the name of a directory • Read the directory • Process each entry • If an entry is a file then • Print it on the screen • Else // It’s a directory!!! • ShowMe(the Entry)

  5. LB Solving a problem in terms of itself n! Is it: n * (n-1) * (n-2) * ... 3 * 2 * 1 Or n * (n - 1)!

  6. LB Solving a problem in terms of itself 7! Is it: 7 * 6 * 5 * 4 * 3 * 2 * 1 Or 7 * 6!

  7. Recursion Defined A procedure or function which calls itself. • Powerful mechanism for repetition. • Makes algorithms more compact and simple. • Module calls a “clone” of itself. • Very useful, especially for dynamic data types.

  8. Three Characteristics of Recursion • Calls itself recursively • Has some terminating condition • Moves “closer” to the terminating condition. Know this!!!

  9. Two Flavors of Recursion if (terminating condition) then do final actions else move one step closer to terminating condition call “clone” of module endif - or - if (NOT (terminating condition)) then move one step closer to terminating condition call “clone” of module endif

  10. Everyday Example with Final Actions procedure Pay_The_Bills() if (No_More_Bills_To_Pay) then Mail_The_Bills else Grab a bill Determine payment Write a check Place check in envelope Place stamp on envelope Pay_The_Bills() endif endprocedure //Pay_The_Bills

  11. Everyday Example with No Final Actions procedure Wash_The_Dishes() if (More_Dirty_Dishes) then Grab a dirty dish Wash it Put it in drainer Wash_The_Dishes() endif endprocedure //Wash_The_Dishes

  12. LB Canonical Example function fact returnsa Num(N iot in Num) // Don’t forget comments!!! if(N = 0) then fact returns 1 else fact returns N * fact(N - 1) endif endfunction // fact

  13. A Recursive Procedure Problem: Count from N to 10. procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen Call the procedure CountToTen (7)

  14. Tracing The Recursion To keep track of recursive execution, do what a computer does: maintain information on an activation stack. Each stack frame contains: • Module identifier and variables • Any unfinished business ModuleID: Data values Unfinished business

  15. procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=7

  16. 7 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=7

  17. 7 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=7

  18. 7 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=8 CountToTen: count=7

  19. 7 8 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=8 CountToTen: count=7

  20. 7 8 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=8 CountToTen: count=7

  21. 7 8 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  22. 7 8 9 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  23. 7 8 9 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  24. 7 8 9 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=10 CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  25. 7 8 9 10 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=10 CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  26. 7 8 9 10 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=10 CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  27. 7 8 9 10 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=11 CountToTen: count=10 CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  28. 7 8 9 10 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=10 CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  29. 7 8 9 10 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  30. 7 8 9 10 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=8 CountToTen: count=7

  31. 7 8 9 10 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=7

  32. 7 8 9 10 Return to the algorithm.

  33. Reversing the Work and Recursion Problem: Count from 10 to N. procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen Now the work will happen as the frames pop off the stack!

  34. procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen CountToTen: count=7

  35. procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen CountToTen: count=7

  36. procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=8 CountToTen: count=7

  37. procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=8 CountToTen: count=7

  38. procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  39. procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  40. procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=10 CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  41. procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=10 CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  42. procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=11 CountToTen: count=10 CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  43. 10 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=10 CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  44. 10 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=10 CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  45. 10 9 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  46. 10 9 procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=9 CountToTen: count=8 CountToTen: count=7

  47. 10 9 8 procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=8 CountToTen: count=7

  48. 10 9 8 procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen procedure CountToTen (count iot in Num) if (count <= 10) then print (count) // work CountToTen (count + 1) // recurse endif endprocedure //CountToTen CountToTen: count=8 CountToTen: count=7

  49. 10 9 8 7 procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen CountToTen: count=7

  50. 10 9 8 7 procedure CountToTen (count iot in Num) if (count <= 10) then CountToTen (count + 1) // recurse print (count) // work endif endprocedure //CountToTen CountToTen: count=7

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