NCS 301 DATA STRUCTURE USING C

Transcription

1 NCS 301 DATA STRUCTURE USING C Unit-1 Part-2 Recursion Hammad Mashkoor Lari Assistant Professor Allenhouse Institute of Technology Introduction Recursion is defined as defining anything in terms of itself. Recursion is used to solve problems involving iterations in reverse order. Why Recursion NOT Loop? 1. Loop--Its okay with single or set of statements to carry out certain task 2. Recursion alternative to iteration in making a function execute repeatedly. Re=back + currere=to run to happen again Subject Notes by Hammad Lari 1

2 Basic Example Recursion is when a method call itself. Example of Factorial function: N!=1.2.3.(n-1).n Definition C method for factorial Int factorial(int n) If(n==0) Else Return 1; f n = Return n* factorial(n-1); 1 if n = 0 n f n 1 else Basic Requirements for Recursion For implementing and designing good recursive program we must make certain assumptions: 1. Base case:-terminating condition for problem 2. If Condition:-recursive algorithm 3. Every time a new recursive call is made a new memory space is allocated to each auto variable used by recursive routine. 4. Each time recursive call is there the duplicate values of local variables of a recursive call are pushed onto the stack within its respective call and all these values are available to respective functions. Call when it is popped from the stack. 5. Recursive case: Else part of recursive definition calls the function recursively. Example:- Int factorial(int n) If(n==0) Else return 1; //base case Return n *factorial(n-1); //recursive case Subject Notes by Hammad Lari 2

3 Types of Recursion Whether a function calls itself from within itself Recursion Whether two functions call one another mutually Int abc() abc(); Direct Recursion may be further categorized as: Linear recursion Binary Recursion Multiple Recursion Indirect Int abc() xyz(); Int xyz() abc(); Linear Recursion Linear recursion begins by testing a set of base cases there should be at least one. Every possible chain of recursive calls must eventually reach a base case and the handling of each base case should not use recursion. Example:- Algorithm LinearSum(A,n): Input: an array integer array A and integer n=1,such that A has at least n elements. Output: the sum of first n integers in A If n=1 then Else Return a[0] Return Linear Sum(A,n-1)+A[n-1] Subject Notes by Hammad Lari 3

4 Recursion trace Return 14+A[4]=14+6=20 LinearSum(A,5) Return 9+A[3]=9+5=14 LinearSum(A,4) LinearSum(A,3) LinearSum(A,2) LinearSum(A,1) Return 5+A[2]=5+4=9 Return 3+A[1]=3+2=5 Return A[0]=3 Binary Recursion Binary Recursion occurs whenever there are two recursive calls for each non base case. Example:- Algorithm BinarySum(A,i,n) Input: An array A and integers i and n Output: The sum of integers in A starting at index I if n=1 then else return A[i] return BinarySum[A,I,n/2]+BinarySum[A,i+n/2,n/2] Subject Notes by Hammad Lari 4

5 Recursion trace 0,8 0,4 4,4 0,2 2,2 4,2 6,2 0,1 1,1 2,1 3,1 4,1 5,1 6,1 7,1 Multiple Recursion In multiple recursion we make not just one or two but many recursive calls. One example is Summation puzzles. Example:-.pot + pan=bib.dog + cat=pig.boy + girl=baby Subject Notes by Hammad Lari 5

6 Storage Classes Features auto static external register Storage Stack of memory PMA or memory PMA or memory CPU registers Default value Garbage value Zero Zero Garbage value Scope Life Local to Till control remains in Local to Persists between different function calls global Till Program execution Local to Till the control remains within the Practice Questions for C programming Attempt all programs in C using Recursion Technique 1. Write a program to calculate factorial of a number N.(number being entered by user) 2. Write a program to print Fibonacci series up to N.(number being entered by user) 3. Write a program to print reverse of an integer number N. (number being entered by user) 4. Write a program to check if entered number N is a prime or not. Subject Notes by Hammad Lari 6

7 Class Website Subject Notes by Hammad Lari 7