The variable first stores 0 and the variable second stores 1 initially as these are the first 2 terms of the Fibonacci series. So, we have already printed them as shown below.Īs shown above, we have three variables. Now, we know that the first 2 terms of the Fibonacci series are 0 and 1. So, even if we have just stored the last 2 terms, we can calculate the next term. This is because the Nth term depends upon only the last 2 terms. However, we don’t need t store all the terms. If you notice, in the previous method, we stored all the terms of the Fibonacci series and then printed the entire series in one go. The idea for optimization is pretty simple. Python Program to Print the Fibonacci seriesĪgain, the same relation between the terms of the Fibonacci series will be used to solve the problem. However, we can optimize the space complexity of this algorithm. So, can we improve this algorithm in terms of time or space? Well, it seems difficult to optimize the algorithm in terms of time because we have to traverse N terms to get the Nth Fibonacci term. Space Complexity (Auxiliary Space): Since we used the dp array to store the terms of the Fibonacci series, we can say that the auxiliary space or extra space used is O(N). This is because we traverse till we find the Nth term. Time Complexity: The time complexity of this algorithm is O(N) where N is the number of terms of the Fibonacci series that we have to print. Fibonacci Series Program in Python using Dynamic Programming Now that we know the complete procedure, let us write the code for the same. For printing the Fibonacci Series to N terms, we simply iterate over this list and print all the elements. So, we have all the N terms of the Fibonacci series stored in the list. This is shown below.įinally, we have the list dp as shown below. Now, at last, we will calculate Fib5 = Fib4 + Fib3 = 3 + 2 = 5. Next, we calculate Fib4 = Fib3 + Fib2 = 2 + 1 = 3. Let us now calculate Fib3 = Fib2 + Fib1 = 1 + 1 = 2. So, we will iterate till we are able to fill the list with N Fibonacci terms. In Python, we can use negative indexing to get the last 2 values of the list as shown below. Now, to calculate the second term, we will take out the last 2 values from the list and add them. So, we have the 0th and 1st terms already in the list. Also, the terms of the Fibonacci series start from 0. These are the first 2 terms of the Fibonacci series. So, we can use this relation to print the Fibonacci series. the Nth term is the sum of (N-1)th and (N-2)th terms. So, we have understood the relation between the Fibonacci terms i.e. Python Program to Print the Fibonacci series We have to print the Fibonacci Series till Nth term. This integer will denote the number of terms in the Fibonacci series. How to Print Fibonacci Series in Python till N Terms So, now that we know the concept of the Fibonacci series, let us understand the how to print the Fibonacci series in Python till N terms. So, in general, we can say that the following relation holds for all the Fibonacci terms after 1st term: This behavior continues throughout as shown below. Now, the rest all the terms are the sum of the previous 2 terms. So, we say that the 0th Fibonacci term is F0 = 0 and the 1st Fibonacci term is F1 = 1. The index of the first term is 0 and the index of the second term is 1. The first two terms of the series are fixed. The Fibonacci Series is a special series in mathematics. So, let’s start first by understanding the meaning of the Fibonacci series. We will discuss the meaning of the Fibonacci series, the Fibonacci Series program in python using iteration, and the Fibonacci series in Python using recursion. In this article, we will discuss the Fibonacci series in Python.
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