Python/project_euler/problem_25/sol1.py
Nelson Stoik 4d4ce400ec
Add typehints and default input for project_euler/problem_25 (#2901)
* add typehints and docstrings

* add typehint and default value

* add typehint and default value. Removed unused variable.

* do not modifiy the given solution

* add doctests

* update sol1 after running black

* add typehint, docstring, and doctest

* update sol2 after running black
2020-10-07 09:27:25 +05:30

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"""
The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn1 + Fn2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144
The 12th term, F12, is the first term to contain three digits.
What is the index of the first term in the Fibonacci sequence to contain 1000
digits?
"""
def fibonacci(n: int) -> int:
"""
Computes the Fibonacci number for input n by iterating through n numbers
and creating an array of ints using the Fibonacci formula.
Returns the nth element of the array.
>>> fibonacci(2)
1
>>> fibonacci(3)
2
>>> fibonacci(5)
5
>>> fibonacci(10)
55
>>> fibonacci(12)
144
"""
if n == 1 or type(n) is not int:
return 0
elif n == 2:
return 1
else:
sequence = [0, 1]
for i in range(2, n + 1):
sequence.append(sequence[i - 1] + sequence[i - 2])
return sequence[n]
def fibonacci_digits_index(n: int) -> int:
"""
Computes incrementing Fibonacci numbers starting from 3 until the length
of the resulting Fibonacci result is the input value n. Returns the term
of the Fibonacci sequence where this occurs.
>>> fibonacci_digits_index(1000)
4782
>>> fibonacci_digits_index(100)
476
>>> fibonacci_digits_index(50)
237
>>> fibonacci_digits_index(3)
12
"""
digits = 0
index = 2
while digits < n:
index += 1
digits = len(str(fibonacci(index)))
return index
def solution(n: int = 1000) -> int:
"""
Returns the index of the first term in the Fibonacci sequence to contain
n digits.
>>> solution(1000)
4782
>>> solution(100)
476
>>> solution(50)
237
>>> solution(3)
12
"""
return fibonacci_digits_index(n)
if __name__ == "__main__":
print(solution(int(str(input()).strip())))