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 transcript:

Thinking Recursively xkcd #878

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

Fibonacci Sequence Famous recursively defined sequence

Naïve Implementation Direct code translation

Fibonacci Multiple recursive calls = combinatorial explosion:

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

Reduced Load Parameters store old work…

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

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

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?

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

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?

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?

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

Number Of Digits Code: – Assumes number >= 0

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

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

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

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?

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?

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

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

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"

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

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

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

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

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

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? …

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