1 / 12

Recursion

Recursion. CS-240/CS341. What is recursion?. a function calls itself direct recursion a function calls its invoker indirect recursion. f1. f. f2. Outline of a Recursive Function. function header { if (answer is known) return the answer else

lysandra-dodson
Download Presentation

Recursion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Recursion CS-240/CS341

  2. What is recursion? • a function calls itself • direct recursion • a function calls its invoker • indirect recursion f1 f f2

  3. Outline of a Recursive Function function header { if (answer is known) return the answer else recursive call to solve a "smaller" problem } base case recursive case

  4. Factorial (n) = n * Factorial (n-1) (for n > 0) Factorial (0) = 1 long factorial (int n) { if (n == 0) return 1; else return n * factorial (n-1); } base case Factorial (n) - recursive

  5. How Recursion Works • a recursive function call is like any other function call • each function call has its own activation record (space for storing parameters and local variables) • created when the function is called • destroyed when the function returns to its caller • activation records are stacked up as recursive calls are made • when the base case is reached the recursion “unwinds”

  6. 24 4 6 3 2 2 1 1 1 0 Recursive Call Tree RecFact (4) long factorial (int n) { if (n == 0) return 1; else return n * factorial (n-1); } What happens with factorial (-2)?

  7. long factorial (int n) { long fact =1; for (int i = n; i > 0; i--) fact = fact * i; return fact; } Factorial (n) - iterative Factorial (n) = n * (n-1) * (n-2) * ... * 1 for n > 0 Factorial (0) = 1

  8. Euclid'sAlgorithm • Finds the greatest common divisor of two nonnegative integers that are not both 0 • Recursive definition of gcd algorithm • gcd (a, b) = a (if b is 0) • gcd (a, b) = gcd (b, a % b) (if b != 0) • Write a recursive gcd function • prototype? • implementation?

  9. 6 54, 30 30, 24 24, 6 6, 0 6 6 6 Tracing gcd (54, 30) int gcd (int a, int b) { if (b == 0) return a; else return gcd (b, a % b); }

  10. int gcd (int a, int b) { int temp; while (b != 0) { temp = b; b = a % b; a = temp; } return a; } Iterative gcd?

  11. int fib (int n) { if (n <= 1) return n; else return fib (n – 1) + fib (n – 2); } fib (0) = 0 fib (1) = 1 fib (n) = fib (n – 1) + fib (n – 2) (for n >= 2) Another recursive definition Fibonacci numbers are the sequence of integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ….

  12. 5 5 4 3 2 1 0 1 1 1 0 3 2 1 0 2 2 3 2 1 1 1 1 1 1 0 1 0 1 0 Tracing fib(5)

More Related