Recursion
Download as PPTX, PDF4 likes8,271 views
This document discusses recursion in programming. It defines recursion as a procedure that calls itself, with different parameters each time. It explains the key components of a recursive method including base cases and recursive calls. It provides examples of different types of recursion like single/multiple and direct/indirect recursion. Examples of recursively defined sequences and functions like factorials and Fibonacci series are given. Contact details are provided at the end.
Recursion
- 2. Disclaimer: This presentation is prepared by trainees of baabtra as a part of mentoring program. This is not official document of baabtra –Mentoring Partner Baabtra-Mentoring Partner is the mentoring division of baabte System Technologies Pvt . Ltd
- 3. Recursion Subhin P.V 111subru@gmail.com www.facebook.com/subhinv elayudhan twitter.com/111subru in.linkedin.com/in/Subhin P V 8129076036
- 4. WHAT IS RECURSION • In simple language Recursion is the repeated occurrence of a particular event • In programming Recursion is the repeated occurrence of a procedure as a result of the procedure calling itself. • Recursive procedure is the name given to the procedures calling themselves. • The parameters passed each time into the function must be different.
- 5. Content of a Recursive Method • Base case(s). – Values of the input variables for which we perform no recursive calls are called base cases (there should be at least one base case). – Every possible chain of recursive calls must eventually reach a base case. • Recursive calls. – Calls to the current method. – Each recursive call should be defined so that it makes progress towards a base case.
- 6. Types of Recursion • Single and Multiple Recursion – Recursion that only contains a single self- reference is known as single recursion. Eg: Factorial function – Recursion that contains multiple self-references is known as multiple recursion. Eg: Fibonacci function
- 7. Types of Recursion • Direct And Indirect Recursion – IF a Function F calls itself. (i.e) F calls F. Then this recursion is Direct Recursion. static int Direct (int n) { if (n<=0) return 0; else return n + Direct (n-1); }
- 8. Types of Recursion • Indirect Recursion – IF a Function F calls G. and Function G calls F. Then this recursion is Indirect Recursion. static int InDirect (int n) { if (n<=0) return 0; else return n + Buddy (n-1); } int Buddy (int n) { return InDirect (n); }
- 9. Recursively Defined Sequences •Example: •The sequence {an} of powers of 2 is given non recursively by an = 2n for n = 0, 1, 2, … . •The same sequence can also be defined Recursively: a0 = 1 an+1 = 2an for n = 0, 1, 2, …
- 10. RECURSIVELY DEFINED FUNCTIONS • Here is the non-recursive definition of the factorial function: – n! = 1· 2· 3· ··· · (n-1)· n • Here is the recursive definition of a factorial: (here f(n) = n!) • The Java code for the Factorial function: // recursive procedure for computing factorial public static int Factorial(int n) { if (n == 0) return 1; // base case else return n * Factorial(n- 1); // recursive case } elsenfn n nf )1( 0if1 )(
- 11. RECURSIVE ALGORITHMS • Example: Recursive Fibonacci Algorithm procedure fib(n: nonnegative integer) if n = 0 then fib(0) := 0 else if n = 1 then fib(1) := 1 else fib(n) := fib(n – 1) + fib(n – 2)
- 12. RECURSIVE ALGORITHMS(contd..) Recursive Fibonacci Evaluation:
- 14. If this presentation helped you, please visit our page facebook.com/baabtra and like it. Thanks in advance. www.baabtra.com | www.massbaab.com |www.baabte.com
- 15. Contact Us