Calculate fibonacci program

If the original recursion tree were to be implemented then this would have been the tree but now for n times the recursion function is called Original tree for recursion. Optimized tree for recursion for code above fib 5 fib 4 fib 3 fib 2 fib 1 Extra Space: O n if we consider the function call stack size, otherwise O 1. Method 2 Use Dynamic Programming We can avoid the repeated work done in method 1 by storing the Fibonacci numbers calculated so far.

The formula can be derived from above matrix equation. Array MAX ]; f. Method 7 Another approach Using formula : In this method we directly implement the formula for nth term in the fibonacci series. Round Math. Skip to content. Change Language. Related Articles. Table of Contents. Improve Article. Save Article. Like Article. Function for nth Fibonacci number. This code is contributed by Tdra. Write Fib n ;. GFG g;. Fibonacci Series using Dynamic Programming.

Python Pillow. Python Turtle. Verbal Ability. Interview Questions. Company Questions. Artificial Intelligence. Cloud Computing. Data Science. Angular 7. Machine Learning. Data Structures. Operating System. Computer Network. We will declare a function fibonacci which will calculate the Fibonacci number at position n.

If n equals 0 or 1, it returns n. The above diagram shows a function call for calculating the fourth Fibonacci number. On taking a closer look at the diagram you will notice that we are making repeated calls for the same values.

Calls for the same values are highlighted in the same color in the diagram. We can avoid these repeated calls and improve the time complexity of our code.

In the recursive programs for Fibonacci numbers discussed above, we were making repetitive calls to function for the same value, increasing the time complexity of our code. But we can improve this, if we can store values for these calls, we can reduce the complexity of the program to a huge extent.

We will make the recursive call, but this time we will be storing the value for each recursive call in an array, thus making sure that we are doing the whole recursive calculation for a value only once.

Time Complexity: O n as we make calls for value from 1 to n only once. Space complexity: O n as we use an array to store values of recursive calls. The basic idea is, to sum up, the previous two numbers to get the following term and keep on repeating this process until we get the nth term.

We will make an array to store values of elements and use a loop to sum previous elements to get the Fibonacci element. We can optimize the space used in the above program as we only need the nth element from the array. We can keep track of the last two elements and keep on updating them as we progress. Below is the implementation for the space-optimized approach. The most crucial part of implementing this approach is matrix multiplication. We will be multiplying the 2X2 matrix.

A 2X2 matrix is multiplied in the following manner. Suppose we have the following two matrices, and after multiplying these two, we have to put the result in another matrix c.