Introduction to Recursion. Recursion Defined A procedure or function which calls itself. Powerful mechanism for repetition. Makes algorithms more compact.

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Presentation transcript:

Introduction to Recursion

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.

Three Characteristics of Recursion Calls itself recursively Has some terminating condition Moves “closer” to the terminating condition.

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Return to the algorithm.

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!

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

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

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

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

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

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

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

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

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

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

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

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

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

Return to the algorithm.

Palindrome: Problem A palindrome is a string that reads the same backward or forward e.g. R A C E C A R How do you check to see if a string is a palindrome –What is our sub-problem? –What is the base case? –What is the recursive case?

Palindrome public static bool IsPalindrome(string s, int left, int right) { if (left >= right) //terminating case 1 return true; else if (s[left] != s[right]) //terminating case 2 return false; else //recursion return IsPalindrome(s, left + 1, right -1); }