Recursion

1. Recursion

2. Recursion • The process of solving a problem by reducing it to smaller versions of itself • Example: Factorial

3. Recursive algorithm • An algorithm is called recursive if it solves a problem by reducing the problem to smaller versions of itself • A recursive algorithm can be implemented using a recursive function

4. Recursive function • A function that calls itself • What is the danger? • we need to avoid infinite recursion • A recursive function must have • recursive call(s) to the function with a smaller instance of the problem • one or more base cases to stop recursion

5. Finding a recursive solution • A recursive solution to a problem must be written carefully • The idea is for each successive recursive call to take us one step closer to the base case (a situation in which the problem can easily be solved)

6. General format formany recursive functions if (some easily-solved condition) // base case solution statement(s); else // general case recursive function call(s);

7. Example • Write a recursive function Fact() to find the factorial of n. • What should Fact(4) return? • What can be a good base case that represents an easily-solved situation? • What can be a good general case that takes us closer to the base case?

8. Example int Fact (int n) { if (n == 1) // base case return 1; else // general case return n * Fact(n-1); } // this is an example of tail recursion

9. Example – Trace of calls Returns 4 * Fact(3) = 4 * 6 = 24 Call 1: Fact(4) n = 4 Returns 3 * Fact(2) = 3 * 2 = 6 Call 2: Fact(3) n = 3 Returns 2 * Fact(1) = 2 * 1 = 2 Call 3: Fact(2) n = 2 n = 1 Returns 1 Call 4: Fact(1) n = 1

10. Assignment • Write a recursive function Power() to calculate xn, where n is a non-negative integer. • Extend the Power() function so that it works for any integer n.

11. Empty base case • Recursive functions can have empty base cases • What action should take place? • What should be the return type? • Write a recursive function that will display all integers from n down to 1.

12. Iteration or Recursion? • Key factors • nature of the problem • efficiency • Every recursive call has its own set of parameters and local variables • time and space overhead associated with executing a recursive function • Certain problems are inherently recursive and a recursive solution is the most natural one

13. Command Line Arguments

14. Command Line Arguments • Arguments can be passed to any program being executed from a command-line based OS like DOS or UNIX • UNIX Example: cp fileA fileB • cp is the name of the program (command) to be executed • fileA and fileB are command-line arguments • In C/C++, the program can be written to accept command-line-arguments

15. C/C++ syntax • The following syntax is used in the main() function to capture command-line arguments int main(int argc, char *argv[]) • In this case, the operating system passes in two parameters to the function • argc is an integer specifying the number of command-line arguments • argv is an array of pointers where each pointer points to one of the command-line arguments stored as a C-type string

16. C++ syntax (Cont ..) • In some systems (like UNIX), argv[0] points to a string that is the entire path to the program (executable) including its name • In other systems, argv[0] points to garbage • You can use any argv[i] like a C-type string • In C++, if the program is not written to accept command-line arguments, it is not necessary to specify the parameters in the argument list of the function signature

17. Example #include <iostream> #include <string> using namespace std; void main(int argc, char *argv[]) { string fname, lname; fname = argv[1]; lname = argv[2]; cout << argc << " " << argv[1] << " " << argv[2] << endl; } g++ -o comlinarg comlinarg.cpp ./comlinarg John Malkovich 3 John Malkovich