Dale Roberts 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

Dale Roberts Why Recursion? If if’s, loop’s, and sequence is 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!

Dale Roberts Introduction to Recursion Problem based approach A simple example: factorial Simple definition of recursion Bridges: Parallels with looping See if you can do it: GCF A realistic example: Directory Search Conclusion

Dale Roberts 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

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

Dale Roberts 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 Surface Phase Dive Phase Maximum Depth = 5

Dale Roberts A simple definition of recursion Recursion simply means a function that calls itself. The conditions that cause a function to call itself again are called the recursive case. 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.)

Dale Roberts Fundamental Rules of Recursion Obeys 1.) Base cases 2.) Making progress through recursion 3.) Design rule: assuming all recursive call work (details hidden) 4.) Compound interest rule: do not duplicate recursive calls Always specify the base case; otherwise, indefinite recursive will occur and cause “stack-overflow” error.

Dale Roberts Questionable Recursive Program int puzzle(int N) { if (N == 1) if (N == 1) return 1; return 1; if (N % 2 == 0) if (N % 2 == 0) return puzzle(N/2); return puzzle(N/2); else else return puzzle(3*N+1); 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

Dale Roberts Sample Recursive Program: Euclid’s Greatest Common Factor int gcf(int m, int n) { if (n == 0) if (n == 0) return m; return m; return gcf(n, m % n); return gcf(n, m % n);} Sedgewick Program 5.3

Dale Roberts Sample Recursive Program: Linked List int count(link x) { if (x == NULL) if (x == NULL) return 0; return 0; return 1 + count(x->next); return 1 + count(x->next);} void traverse(link h, void (*visit)(link)) { if (h == NULL) if (h == NULL) return; return; (*visit)(h); (*visit)(h); traverse(h->next, visit); traverse(h->next, visit);} Sedgewick Program 5.5

Dale Roberts Sample Recursive Program: Linked List (cont) void traverseR(link h, void (*visit)(link)) { if (h == NULL) return; if (h == NULL) return; traverseR(h->next, visit); traverseR(h->next, visit); (*visit)(h); (*visit)(h);} link delete(link x, Item v) { /* Deleted 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; } { link t = x->next; free(x); return t; } x->next = delete(x->next, v); return x; } Sedgewick Program 5.5

Dale Roberts Sample recursive programs (Tree Traversal) In-order: (LNR) void inorder(tree_pointer ptr) { if (ptr) if (ptr) { inorder(ptr->left_child); inorder(ptr->left_child); printf(“%d”, ptr->data); printf(“%d”, ptr->data); inorder(ptr->right_child); inorder(ptr->right_child); }} Pre-order: (NLR) void preorder(tree_pointer ptr) { if (ptr) if (ptr) { printf(“%d”, ptr->data); printf(“%d”, ptr->data); preorder(ptr->left_child); preorder(ptr->left_child); preorder(ptr->right_child); preorder(ptr->right_child); }} Post-order: (LRN) void postorder(tree_pointer ptr) { if (ptr) if (ptr) { postorder(ptr->left_child); postorder(ptr->left_child); postorder(ptr->right_child); postorder(ptr->right_child); printf(“%d”, ptr->data); printf(“%d”, ptr->data); }}

Dale Roberts 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?

Dale Roberts 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?

Dale Roberts Implementation of Directory Search using System; using System.IO; namespace RecursiveDirectoryFileSearch { class RecursiveDirectoryFileSearch { static void Main(string[] args) { Console.WriteLine("Found {0} occurrences.", Console.WriteLine( "Press enter to continue"); Console.ReadLine(); } This implementation is in C#.

Dale Roberts Implementation of Directory Search (cont) // Number of files found that match the pattern 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

Dale Roberts Acknowledgements Robert Sedgewick. Algorithms in C.