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Exploring Recursion Concepts: CSCI 240 Review

Dive into recursion concepts, practical examples, and recursive problem-solving strategies by reviewing CSCI 240 materials from IUPUI. Learn through examples like factorial, GCD, and directory search.

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Exploring Recursion Concepts: CSCI 240 Review

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  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@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! = 1n! = n* (n-1)!where n is not negative. Base Case Recursive Case

  5. Implementation int factorial(int N) { if (N == 0) return 1; return N*factorial(N-1); } Base Case Recursive Case Sedgewick Program 5.1

  6. Factorial Sample Execution iFactorial(4): 4*iFactorial(3) iFactorial(3): 3*iFactorial(2) iFactorial(2): 2*iFactorial(1) iFactorial(1): 1*iFactorial(0) iFactorial(0): 1 iFactorial(4): 4*6 = 24 iFactorial(3): 3*2 = 6 iFactorial(2): 2*1 = 2 iFactorial(1): 1*1 = 1 iFactorial(0): 1 Dive Phase Surface 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(3*N+1); } What’s 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: Euclid’s 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->next); } void traverse(link h, void (*visit)(link)) { if (h == NULL) return; (*visit)(h); traverse(h->next, 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->next, 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->item, v)) { link t = x->next; free(x); return t; } x->next = delete(x->next, v); return x; } Sedgewick Program 5.5

  12. Building Bridges: Looping • Recursion and looping follow similar thought processes. • A loop’s termination condition serves the same role as a recursive base case. • A loop’s control variable serves the same role as a general case. sum = 0; i = 1; while (i <= 10) { sum += i; i++; } int iFactorial(int n) { if (n == 0) // base case { return 1; } else // n > 0, recursive case { return n*iFactorial(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(@"C:\","*.tmp")); Console.WriteLine( "Press enter to continue"); Console.ReadLine(); } } } This implementation is in C#.

  15. Implementation of Directory Search (cont) // <returns> Number of files found that match the pattern</returns> 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(asDirectory)) { liFileCounter += iDirectorySearch(lsSubdirectory, ssSearchPattern); } return liFileCounter; } Base Case Recursive Case

  16. Acknowledgements • Robert Sedgewick. Algorithms in C.

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