"""
This is a pure Python implementation of Dynamic Programming solution to the fibonacci
sequence problem.
"""

class Fibonacci:
def __init__(self, N=None):
self.fib_array = []
if N:
N = int(N)
self.fib_array.append(0)
self.fib_array.append(1)
for i in range(2, N + 1):
self.fib_array.append(self.fib_array[i - 1] + self.fib_array[i - 2])
elif N == 0:
self.fib_array.append(0)
print(self.fib_array)

def get(self, sequence_no=None):
"""
>>> Fibonacci(5).get(3)
[0, 1, 1, 2, 3, 5]
[0, 1, 1, 2]
>>> Fibonacci(5).get(6)
[0, 1, 1, 2, 3, 5]
Out of bound.
>>> Fibonacci(5).get(-1)
[0, 1, 1, 2, 3, 5]
[]
"""
if sequence_no is not None:
if sequence_no < len(self.fib_array):
return print(self.fib_array[: sequence_no + 1])
else:
print("Out of bound.")
else:

if __name__ == "__main__":
print("\n********* Fibonacci Series Using Dynamic Programming ************\n")
print("\n Enter the upper limit for the fibonacci sequence: ", end="")
try:
N = int(input().strip())
fib = Fibonacci(N)
print(
"\n********* Enter different values to get the corresponding fibonacci "
"sequence, enter any negative number to exit. ************\n"
)
while True:
try:
i = int(input("Enter value: ").strip())
if i < 0:
print("\n********* Good Bye!! ************\n")
break
fib.get(i)
except NameError:
except NameError:
print("\n********* Invalid input, good bye!! ************\n")

import doctest

doctest.testmod()


#### Fibonacci Numbers

In mathematics, the Fibonacci numbers commonly denoted F(n), form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. The Sequence looks like this:

[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...]

## Applications

Finding N-th member of this sequence would be useful in many Applications:

• Recently Fibonacci sequence and the golden ratio are of great interest to researchers in many fields of

science including high energy physics, quantum mechanics, Cryptography and Coding.

## Steps

1. Prepare Base Matrice
2. Calculate the power of this Matrice
3. Take Corresponding value from Matrix

## Example

Find 8-th member of Fibonacci

### Step 0

| F(n+1)  F(n)  |
| F(n)    F(n-1)|


### Step 1

Calculate matrix^1
| 1 1 |
| 1 0 |


### Step 2

Calculate matrix^2
| 2 1 |
| 1 1 |


### Step 3

Calculate matrix^4
| 5 3 |
| 3 2 |


### Step 4

Calculate matrix^8
| 34 21 |
| 21 13 |


F(8)=21

## Others  