If the components being searched have non-uniform access memory storage (i. e., the time needed to access a storage location vary depending on the location accessed), the Fibonacci search may have the advantage over binary search in slightly reduce the average time needed to access a storage location. On average, this leads to about 4 % more comparisons to be executed, but it has the advantage that one only needs addition and subtraction to calculate the index of the accessed array components, while classical binary search needs bit-shift, division or multiplication, operations that were less common at the time Fibonacci search was first published.

If the item is less than entry Fk−1, discard the components from positions Fk−1 + 1 to n.(throughout the algorithm, p and q will be consecutive Fibonacci numbers)

```
"""
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:
print("Please specify a value")
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:
print("\nInvalid input, please try again.")
except NameError:
print("\n********* Invalid input, good bye!! ************\n")
import doctest
doctest.testmod()
```