sivaramaiah
 dsjava2 02/26/2020 4:50am (UTC)  The Fibonacci sequence (denoted by f0, f1, f2 …) is as follows: Fibonacci sequence 2 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … That is, f0 = 0 and f1 = 1 and each succeeding term is the sum of the two preceding terms. For example, the next two terms of the sequence are 34 + 55 = 89 and 55 + 89 = 144 Many algorithms have both iterative and recursive formulations. Typically, recursion is more elegant and requires fewer variables to make the same calculations. Recursion takes care of its book-keeping by stacking arguments and variables for each method call. This stacking of arguments, while invisible to the user, is still costly in time and space. Fibonacci sequence is recursively defined by f0 = 0, f1 = 1, fi+1 = fi + fi-1 for i = 1, 2 … Fibonacci class is implemented in Program 2, with iterative and recursive methods, and tested by main() driver. Program 2: Fibonacci sequence ------------------------------------------------------------- import java.io.*; class Fibonacci {   public int fibonacciSeq(int n) // Iterative method { int term1 = 0, term2 = 1, nextTerm = 0; if( n == 0 || n == 1) return n; int count = 2; while( count <= n ) { nextTerm = term1 + term2; term1 = term2; term2 = nextTerm; count++; } return nextTerm; } public int recFibonacciSeq(int n) // Recursive method { if( n == 0 || n == 1) return n; else return( recFibonacciSeq(n-1) + recFibonacciSeq(n-2) ); } } /////////////////// FibonacciDemo.java //////////////////////// class FibonacciDemo { public static void main(String[] args) throws IOException { Fibonacci fib = new Fibonacci(); BufferedReader kb = new BufferedReader(new InputStreamReader(System.in)); // nth value in the Fibonacci sequence System.out.print("Enter n: "); int n = Integer.parseInt(kb.readLine()); System.out.println("Iterative method: Fibonacci number " + n + " is " + fib.fibonacciSeq(n) ); System.out.println("Recursive method: Fibonacci number " + n + " is " + fib.recFibonacciSeq(n) ); } ----------------------------------------------------------- Output of this program is: Enter n: 12 Iterative method: Fibonacci number 12 is 144 Recursive method:  MCA PROJECT DETAILS ------------------------------------- Jntu all Lab manuals ------------------------------------- Jntu Syllabus Books ------------------------------------- Paper presentations ------------------------------------- Seminars ------------------------------------- Campus Papers ------------------------------------- Competetive Exams GATE ------------------------------------- GRE ------------------------------------- TOEFL ------------------------------------- IELTS ------------------------------------- CAT ------------------------------------- GMAT ------------------------------------- Templates ------------------------------------- Students Resume Preparation tips ------------------------------------- Job zone(Interview questions) ------------------------------------- Google Adsence html code ------------------------------------- Web sites --------x--------------x-----------
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