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Recursion: Thinking About It 7 January 2019 OSU CSE 1 Recursion - PowerPoint PPT Presentation

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Recursion: Thinking About It 7 January 2019 OSU CSE 1 Recursion A remarkably important concept and programming technique in computer science is recursion A recursive method is simply one that calls itself There are two quite

  1. Recursion: Thinking About It 7 January 2019 OSU CSE 1

  2. Recursion • A remarkably important concept and programming technique in computer science is recursion – A recursive method is simply one that calls itself • There are two quite different views of recursion! – We ask for your patience as we introduce them one at a time... 7 January 2019 OSU CSE 2

  3. Question Considered Now • How should you think about recursion so you can use it to develop elegant recursive methods to solve certain problems? 7 January 2019 OSU CSE 3

  4. Question Considered Next • Why do those recursive methods work? 7 January 2019 OSU CSE 4

  5. Question Considered Only Later • How do those recursive methods work? – Don’t worry; we will come back to this – If you start by insisting on knowing the answer to this question, you may never be fully capable of developing elegant recursive solutions to problems! 7 January 2019 OSU CSE 5

  6. Suppose... • You need to reverse a String • Contract specification looks like this: /** * Reverses a String. * ... * @ensures * reversedString = rev (s) */ private static String reversedString(String s) {...} 7 January 2019 OSU CSE 6

  7. Suppose... Try to implement it • You need to reverse a String (i.e., write the method • Contract specification looks like this: body). /** * Reverses a String. * ... * @ensures * reversedString = rev (s) */ private static String reversedString(String s) {...} 7 January 2019 OSU CSE 7

  8. One Possible Solution private static String reversedString(String s) { String rs = ""; for ( int i = 0; i < s.length(); i++) { rs = s.charAt(i) + rs; } return rs; } 7 January 2019 OSU CSE 8

  9. Trace It s = "abc" rs = "" for ( int i = 0; i < s.length(); i++) { rs = s.charAt(i) + rs; } 7 January 2019 OSU CSE 9

  10. Trace It: Iteration 1 s = "abc" rs = "" for ( int i = 0; i < s.length(); i++) { s = "abc" rs = "" i = 0 rs = s.charAt(i) + rs; } 7 January 2019 OSU CSE 10

  11. Trace It: Iteration 1 s = "abc" rs = "" for ( int i = 0; i < s.length(); i++) { s = "abc" rs = "" i = 0 rs = s.charAt(i) + rs; s = "abc" rs = "a" i = 0 } 7 January 2019 OSU CSE 11

  12. Trace It: Iteration 2 s = "abc" rs = "" for ( int i = 0; i < s.length(); i++) { s = "abc" rs = "a" i = 1 rs = s.charAt(i) + rs; s = "abc" rs = "a" i = 0 } 7 January 2019 OSU CSE 12

  13. Trace It: Iteration 2 s = "abc" rs = "" for ( int i = 0; i < s.length(); i++) { s = "abc" rs = "a" i = 1 rs = s.charAt(i) + rs; s = "abc" rs = "ba" i = 1 } 7 January 2019 OSU CSE 13

  14. Trace It: Iteration 3 s = "abc" rs = "" for ( int i = 0; i < s.length(); i++) { s = "abc" rs = "ba" i = 2 rs = s.charAt(i) + rs; s = "abc" rs = "ba" i = 1 } 7 January 2019 OSU CSE 14

  15. Trace It: Iteration 3 s = "abc" rs = "" for ( int i = 0; i < s.length(); i++) { s = "abc" rs = "ba" i = 2 rs = s.charAt(i) + rs; s = "abc" rs = "cba" i = 2 } 7 January 2019 OSU CSE 15

  16. Trace It: Ready to Return s = "abc" rs = "" for ( int i = 0; i < s.length(); i++) { s = "abc" rs = "ba" i = 2 rs = s.charAt(i) + rs; s = "abc" rs = "cba" i = 2 } s = "abc" rs = "cba" 7 January 2019 OSU CSE 16

  17. Oh, Did I Mention... • There is already a static method in the class FreeLunch , with exactly the same contract: /** * Reverses a String. * ... * @ensures * reversedString = rev (s) */ private static String reversedString(String s) {...} 7 January 2019 OSU CSE 17

  18. A Free Lunch Sounds Good! • The slightly nasty thing about the FreeLunch class is that its methods will not directly solve your problem: you have to make your problem “smaller” first • This reversedString code will not work: private static String reversedString(String s) { return FreeLunch.reversedString(s); } 7 January 2019 OSU CSE 18

  19. Recognizing the Smaller Problem • A key to recursive thinking is the ability to recognize some smaller instance of the same problem “hiding inside” the problem you need to solve • Here, suppose we recognize the following property of string reversal: rev (<x> * a) = rev (a) * <x> 7 January 2019 OSU CSE 19

  20. The Smaller Problem • If we had some way to reverse a string of length 4, say, then we could reverse a string of length 5 by: – removing the character on the left end – reversing what’s left – adding the character that was removed onto the right end 7 January 2019 OSU CSE 20

  21. The Smaller Problem • If we had some way to reverse a string of This is a smaller instance of exactly the same problem as we need to solve. length 4, say, then we could reverse a string of length 5 by: – removing the character on the left end – reversing what’s left – adding the character that was removed onto the right end 7 January 2019 OSU CSE 21

  22. Time for Our Free Lunch • We can use the FreeLunch class now: private static String reversedString(String s) { String sub = s.substring(1); String revSub = FreeLunch.reversedString(sub); String result = revSub + s.charAt(0); return result; } 7 January 2019 OSU CSE 22

  23. Trace It s = "abc" String sub = s.substring(1); s = "abc" sub = "bc" String revSub = FreeLunch.reversedString(sub); s = "abc" sub = "bc" revSub = "cb" String result = revSub + s.charAt(0); s = "abc" sub = "bc" revSub = "cb" result = "cba" 7 January 2019 OSU CSE 23

  24. Trace It How do you trace over this call? By s = "abc" looking at the contract, as usual! String sub = s.substring(1); s = "abc" sub = "bc" String revSub = FreeLunch.reversedString(sub); s = "abc" sub = "bc" revSub = "cb" String result = revSub + s.charAt(0); s = "abc" sub = "bc" revSub = "cb" result = "cba" 7 January 2019 OSU CSE 24

  25. Almost Done With Lunch • Is this code correct? private static String reversedString(String s) { String sub = s.substring(1); String revSub = FreeLunch.reversedString(sub); String result = revSub + s.charAt(0); return result; } 7 January 2019 OSU CSE 25

  26. Almost Done With Lunch • Is this code correct? private static String reversedString(String s) { String sub = s.substring(1); String revSub = FreeLunch.reversedString(sub); String result = revSub + s.charAt(0); return result; This call has a precondition: s must not be } the empty string (which can be gleaned from the String API with a careful reading). 7 January 2019 OSU CSE 26

  27. Almost Done With Lunch • Is this code correct? This call has a precondition: s must not be the empty string (which can be gleaned from private static String reversedString(String s) { the String API with a careful reading). String sub = s.substring(1); String revSub = FreeLunch.reversedString(sub); String result = revSub + s.charAt(0); return result; } 7 January 2019 OSU CSE 27

  28. Accounting for Empty s private static String reversedString(String s) { if (s.length() == 0) { return s; } else { String sub = s.substring(1); String revSub = FreeLunch.reversedString(sub); String result = revSub + s.charAt(0); return result; } } 7 January 2019 OSU CSE 28

  29. Accounting for Empty s private static String reversedString(String s) { if (s.length() == 0) { return s; } else { String sub = s.substring(1); String revSub = This test could also be done as: FreeLunch.reversedString(sub); s.equals("") String result = revSub + s.charAt(0); but not as: return result; s == "" } } 7 January 2019 OSU CSE 29

  30. Accounting for Empty s private static String reversedString(String s) { if (s.length() == 0) { return s; } else { String sub = s.substring(1); String revSub = FreeLunch.reversedString(sub); Returning an empty string could String result = revSub + s.charAt(0); also be written as: return result; return ""; } } 7 January 2019 OSU CSE 30

  31. Oh, Did I Mention... • Sorry, there is no FreeLunch ! 7 January 2019 OSU CSE 31

  32. There Is No FreeLunch ?!? private static String reversedString(String s) { if (s.length() == 0) { return s; } else { String sub = s.substring(1); String revSub = FreeLunch.reversedString(sub); String result = revSub + s.charAt(0); return result; } } 7 January 2019 OSU CSE 32

  33. There Is No FreeLunch ?!? private static String reversedString(String s) { if (s.length() == 0) { return s; } else { String sub = s.substring(1); String revSub = reversedString(sub); String result = revSub + s.charAt(0); return result; } } 7 January 2019 OSU CSE 33

  34. We Don’t Need a FreeLunch We just wrote the code for reversedString , private static String reversedString(String s) { so we can call our own version rather than the if (s.length() == 0) { one from FreeLunch . return s; } else { String sub = s.substring(1); String revSub = reversedString(sub); String result = revSub + s.charAt(0); return result; } } 7 January 2019 OSU CSE 34

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