# Python Program to Print nth Fibonacci Number using Dynamic Programming with Bottom-Up Approach

This is a Python program to print nth Fibonacci number using dynamic programming with bottom-up approach.

Problem Description

Fibonacci numbers are defined by the sequence f(0) = 0, f(1) = 1 and f(n) = f(n – 1) + f(n – 2) for n >= 2. The program prompts the user to enter n and it prints the nth Fibonacci number.

Problem Solution

1. The function fibonacci is defined.
2. fibonacci takes a number n and returns the nth Fibonacci number.
3. It creates a list r where r[n] will contain the nth Fibonacci number.
4. r[0] and r[1] are first initialized to 0 and 1 respectively.
5. The function then fills r by using the formula r[i] = r[i – 1] + r[i – 2].
6. The nth Fibonacci number is then returned.

Program/Source Code

Here is the source code of a Python program to print the nth Fibonacci number using dynamic programming with bottom-up approach. The program output is shown below.

```def fibonacci(n):
"""Return the nth Fibonacci number."""
if n == 0:
return 0

# r[i] will contain the ith Fibonacci number
r = [-1]*(n + 1)
r[0] = 0
r[1] = 1

for i in range(2, n + 1):
r[i] = r[i - 1] + r[i - 2]

return r[n]

n = int(input('Enter n: '))

ans = fibonacci(n)
print('The nth Fibonacci number:', ans)```
Program Explanation

1. The user is prompted to enter n.
2. fibonacci is called to compute the nth Fibonacci number.
3. The result is then displayed.

Runtime Test Cases
```Case 1:
Enter n: 7
The nth Fibonacci number: 13

Case 2:
Enter n: 1
The nth Fibonacci number: 1

Case 3:
Enter n: 3
The nth Fibonacci number: 2```

Sanfoundry Global Education & Learning Series – Python Programs.

To practice all Python programs, here is complete set of 150+ Python Problems and Solutions.

Note: Join free Sanfoundry classes at Telegram or Youtube

If you find any mistake above, kindly email to [email protected]