Print Fibonacci Series

Create a generator function ‘generatorFunction’, which takes the number of Fibonacci numbers to return (say this is ‘n’). In this function, create a variable ‘count’ initially assigned to one. Create two more variables, ‘a’ and ‘b’, each assigned to 0 and 1, respectively. Now, use a while loop on ‘count’ variable from ‘1’ to’ ‘n’. In each iteration, first, yield ‘a’ and then assign ‘b’ to ‘a’ and ‘a + b’ to ‘b’.

Now, create an empty list, iterate over the ‘generator’ object and insert the items in the list. And Finally, return the list.
 

The steps are as follows:-
 

// Generator function to generate Fibonacci numbers

function generatorFunction(int n):

1. Initialize a variable ‘count’, which is initially assigned to 1.
2. Initialize two more variables, ‘a’ and ‘b’, each assigned to 0 and 1, respectively.
3. While count <= n:
   • yield a.
   • Assign ‘b’ to ‘a’ and ‘a + b’ to ‘b’.
   • Increment count.

// Function to generate first n Fibonacci numbers

function generateFibonacciNumbers(int n):

1. Create an empty list, ‘listOfIntegers’, which stores the Fibonacci Numbers.
2. Iterate over each item produced by generatorFunction(n):
   • Insert the value in the list ‘listOfIntegers’.
3. Return ‘listOfIntegers’.

To calculate the nth Fibonacci number efficiently, we can use memoization. Memoization is a technique of storing previously computed values to avoid redundant calculations.

Algorithm:

Create a function fibMemoization(n, memo) that takes an integer n as input and a vector memo to store the computed Fibonacci values.

Inside the fibMemoization function:

Implement base cases:

• If n is 0, return 0, as the 0th Fibonacci number is 0.
• If n is 1, return 1, as the 1st Fibonacci number is 1.

If the Fibonacci value for n is already computed (stored in memo[n]), return it.

Otherwise, calculate the Fibonacci value for n using recursion:

• Calculate fibMemoization(n - 1, memo) to get the (n - 1)th Fibonacci number.
• Calculate fibMemoization(n - 2, memo) to get the (n - 2)th Fibonacci number.
• Add these two values to get the nth Fibonacci number and store it in memo[n].

Return the computed Fibonacci value for n.

Create a function getFibonacciNumber(n) that takes an integer n as input:

• Initialize a memoization table memo of size n + 1 with all values set to -1.
• Call the fibMemoization(n, memo) function to calculate the nth Fibonacci number using memoization.
• Return the computed nth Fibonacci number.