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Thinking Recursively xkcd #878. Recursion Recursive call is divider – Instructions before happen as stack is built – Instructions after happen as stack.

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Presentation on theme: "Thinking Recursively xkcd #878. Recursion Recursive call is divider – Instructions before happen as stack is built – Instructions after happen as stack."— Presentation transcript:

1 Thinking Recursively xkcd #878

2 Recursion Recursive call is divider – Instructions before happen as stack is built – Instructions after happen as stack torn down

3 Fibonacci Sequence Famous recursively defined sequence

4 Naïve Implementation Direct code translation

5 Fibonacci Multiple recursive calls = combinatorial explosion:

6 Better Fibonacci Redefined Fibonacci function: – Parameters keep track of previous values – Call must include first two terms:

7 Reduced Load Parameters store old work…

8 Recursive Helpers This is ugly: Can make it a recursive helper: Call from main:

9 Moral Parameters are your main tool – Use them to "store" information – Use them to change where work happens

10 Recursive Design Recursive function design – What is base case? – What is one step? – What parameters do I need? Do I want/need extra ones to simplify problem?

11 Number of Digits How many digits does an integer have? – What is base case? – What is one step? – What parameters do I need?

12 Number of Digits How many digits does integer have? – What is base case? Anything < 10 is 1 digit – What is one step? – What parameters do I need?

13 Number of Digits How many digits does integer have? – What is base case? Anything < 10 is 1 digit – What is one step? Digits(n) = 1 + Digits(n/10) – What parameters do I need?

14 Number of Digits How many digits does integer have? – What is base case? Anything < 10 is 1 digit – What is one step? Digits(n) = 1 + Digits(n/10) – What parameters do I need? n

15 Number Of Digits Code: – Assumes number >= 0

16 Recursion With Array Want to total an array using recursion: – What is base case? Size 0 will equal 0 – What is one step? Total(size n) = nth element + Total(size n-1) – What parameters do I need? Array, size

17 Recursion With Array Want to total an array using recursion: Work backwards through array, pretending it gets smaller

18 Palindrome Is a string a Palindrome? (e.g. "radar") – What is base case? – What is one step? – What parameters do I need?

19 Palindrome Is a string a Palindrome? (e.g. "radar") – What is base case? 0 or 1 letters is a palindrome : "d" If first letter != last, is NOT a palindrome : "ben" – What is one step? – What parameters do I need?

20 Palindrome Is a string a Palindrome? (e.g. "radar") – What is base case? 0 or 1 letters is a palindrome : "d" If first letter != last, is NOT a palindrome : "ben" – What is one step? "madamImadam" Test all but first and last – What parameters do I need?

21 Palindrome Is a string a Palindrome? (e.g. "radar") – What is base case? 0 or 1 letters is a palindrome : "d" If first letter != last, is NOT a palindrome : "ben" – What is one step? "madamImadam" Test all but first and last – What parameters do I need? Current string

22 Palindrome Is a string a Palindrome? (e.g. "radar")

23 Palindrome Is a string a Palindrome? (e.g. "radar") – What is base case? 0 or 1 letters is a palindrome : "d" If first letter != last, is NOT a palindrome : "ben" – What is one step? Test all but first and last – What parameters do I need? Current string Do I want/need extra ones to simplify problem? Indexes to point to "start" and "end"

24 Palindrome Extra parameters avoid making new strings: Use as helper function:

25 Binary Search – Pick middle of remaining search space – Too high? Eliminate middle and above – Too low? Eliminate middle and below

26 Binary Search Binary search – What is base case? – What is one step? – What parameters do I need?

27 Binary Search Binary search – What is base case? – What is one step? – What parameters do I need? List, value looking for, lowest possible location, highest possible location

28 Binary Search Binary search – What is base case? If lowest possible location > highest possible location, it can't be there – What is one step? – What parameters do I need? List, value looking for, lowest possible location, highest possible location

29 Binary Search Binary search – What is base case? If lowest possible location > highest possible location, it can't be there – What is one step? Find middle If key == middle, return middle location If key < middle, highest is now middle -1 If key > middle, lowest is now middle + 1 – What parameters do I need? …

30 Binary Search Binary search – recursive helper Non-recursive starter:

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