CSCI 240 Abstract Data Types

1
Department of Computer and Information
Science,School of Science, IUPUI
CSCI 240
Review of Recursion For those of you that have
slept since then
Dale Roberts, Lecturer IUPUI droberts_at_cs.iupui.edu
2
Why Recursion?

• If sequence, ifs, and loops are enough, why
  recursion?
• Subset of looping problems, where the problem
  breaks down into identical pieces
• We will use a series of problems with
  straightforward recursive solutions to motivate
  our discussion.
• Practical example? Directory Search!

3
Introduction to Recursion

• Problem based approach
• A simple example factorial
• Simple definition of recursion
• Bridges Parallels with looping
• See if you can do it GCD
• A realistic example Directory Search
• Conclusion

4
Simple Example Factorial

• An easy first example is to consider the problem
  of implementing a function that calculates a
  factorial.
• Recall from math that factorial is defined as
  0! 1 n! n (n-1)! where n is not
  negative.

Base Case
Recursive Case
5
Implementation

• int factorial(int N)
• if (N 0)
• return 1
• return Nfactorial(N-1)

Base Case
Recursive Case
Sedgewick Program 5.1
6
Factorial Sample Execution
iFactorial(4) 4iFactorial(3) iFactorial(3)
3iFactorial(2) iFactorial(2) 2iFactorial(1) iFa
ctorial(1) 1iFactorial(0) iFactorial(0) 1
iFactorial(4) 46 24 iFactorial(3) 32
6 iFactorial(2) 21 2 iFactorial(1) 11
1 iFactorial(0) 1
Surface Phase
Dive Phase
Maximum Depth 5
7
A simple definition of recursion

• Recursion simply means a function that calls
  itself.
• In order to keep the recursion from going on
  forever, you must make sure you hit a termination
  condition called the base case.
• The number of nested invocations is called the
  depth of recursion.
• Function may call itself directly or indirectly.
  (All of our examples are direct.)

8
Questionable Recursive Program

• int puzzle(int N)
• if (N 1)
• return 1
• if (N 2 0)
• return puzzle(N/2)
• else
• return puzzle(3N1)

Whats Makes this Program Questionable?
This recursive call is not smaller than the
original. Cannot prove it terminates. But it
does.
Sedgewick Program 5.2
9
Sample Recursive Program Euclids Greatest
Common Divisor

• int gcd(int m, int n)
• if (n 0)
• return m
• return gcd(n, m n)

Sedgewick Program 5.3
10
Sample Recursive Program Linked List

• int count(link x)
• if (x NULL)
• return 0
• return 1 count(x-gtnext)
• void traverse(link h, void (visit)(link))
• if (h NULL)
• return
• (visit)(h)
• traverse(h-gtnext, visit)

Sedgewick Program 5.5
11
Sample Recursive Program Linked List (cont)

• void traverseR(link h, void (visit)(link))
• if (h NULL) return
• traverseR(h-gtnext, visit)
• (visit)(h)
• link delete(link x, Item v)
• / Delete a nodes, and returns remainder of
  list /
• if (x NULL) return NULL
• if (eq(x-gtitem, v))
• link t x-gtnext free(x) return t
• x-gtnext delete(x-gtnext, v)
• return x

Sedgewick Program 5.5
12
Building Bridges Looping

• Recursion and looping follow similar thought
  processes.
• A loops termination condition serves the same
  role as a recursive base case.
• A loops control variable serves the same role as
  a general case.

sum 0 i 1 while (i lt 10) sum
i i
int iFactorial(int n) if (n 0) // base
case return 1 else // n
gt 0, recursive case return
niFactorial(n-1)
Termination Condition
Loop control and recursive case both move toward
termination condition
What happens if loop control and recursive case
does not move toward termination condition?
13
Realistic Example Directory Searching

• A more common example of recursion is searching
  through a hard disk directory structure.
• Analysis
• Directories are made up of files and
  subdirectories.
• Process the files within a directory, and then
  process each if its subdirectories recursively.
• Count the number of files that match the search
  pattern.
• What is the base case?
• What is the recursive case?
• What is the maximum depth of recursion?
• How many .tmp files do you think are on your C
  drive?

14
Implementation of Directory Search

• using System
• using System.IO
• namespace RecursiveDirectoryFileSearch
• class RecursiveDirectoryFileSearch
• static void main(string args)
• Console.WriteLine("Found 0
  occurrences.",
• iDirectorySearch(_at_"C\",".tmp"))
• Console.WriteLine(
• "Press enter to continue")
• Console.ReadLine()

This implementation is in C.
15
Implementation of Directory Search (cont)

• // ltreturnsgt Number of files found that
  match the patternlt/returnsgt
• internal static int iDirectorySearch(
• string asDirectory,
• string asSearchPattern)
• // Local variables
• int liFileCounter 0
• // Process each file
• foreach (string lsFileName in
• Directory.GetFiles(asDirectory,
  asSearchPattern))
• Console.WriteLine(lsFileName)
• liFileCounter
• // Process each subdirectory
• foreach (string lsSubdirectory in
• Directory.GetDirectories(asDirecto
  ry))

Base Case
Recursive Case
16
Acknowledgements

• Robert Sedgewick. Algorithms in C.