Problem Statement

Print Fibonacci Series Using Memoization and Recursion.

Given a positive integer n, print the Fibonacci series up to the nth term using memoization and recursion.

Examples:

Solution:

The Fibonacci series can be calculated using memoization and recursion. The key idea is to store the previously calculated Fibonacci numbers in a memoization table to avoid redundant calculations. We define a recursive function fibonacci that takes an input n and returns the Fibonacci number at position n.

The base case occurs when n is 0 or 1, in which case we return n as the Fibonacci number. For any other value of n, we check if the Fibonacci number at position n is already calculated and stored in the memoization table. If it is, we directly return the value. Otherwise, we recursively calculate the Fibonacci number by summing the previous two Fibonacci numbers (calculated recursively) and store it in the memoization table for future use.

The overall algorithm follows these steps:

1. Initialize a memoization table to store the Fibonacci numbers.

2. Implement the recursive function fibonacci that takes n

   as input.

   • Check if n is 0 or 1. If so, return n.
   • Check if the Fibonacci number at position n is already present in the memoization table. If so, return the value.
   • Otherwise, calculate the Fibonacci number by recursively calling the fibonacci function for n-1 and n-2, summing the results, and store it in the memoization table.

3. In the main function, take input n from the user.

4. Call the fibonacci function with n as input and print the Fibonacci series up to the nth term.