the great mathematician Leonardo Pizan, known under the pseudonym Fibonacci, left us the famous numerical sequence. Each of its elements, starting with the third, is the sum of the previous two.
rn the Fibonacci sequence is determined as follows:
& Phi; ₀ = 0
& Phi; ₁ = 1
& Phi; ₙ = & Phi; ₙ₋₁ + & PHI; ₙ₋₂ for n & gt; 1
the beginning of the sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
rnyou are given a natural number A. Your task & mdash; Determine whether this number is part of the Fibonacci sequence. If yes, then withdraw its serial number N (index), such that & Phi; n = A. If the number 1 occurs in the sequence, assume that its index is 1. If the number a is not the number of fibonacci, remove -1.
The one is introduced by the whole non -negative number a (0 & le; a & le; 10 & sup1; ⁸).
Bring one whole number: serial number N for which & Phi; n = A. If such a number does not exist, derive -1.
55
10
EN
RU
EN
RU
# Получаем на вход число A
a = int(input())
# Обрабатываем частный случай для 0
if a == 0:
print(0)
else:
# Инициализируем первые два члена последовательности и их индекс n.
# f0 соответствует φ(n-1), f1 соответствует φ(n)
f0, f1 = 0, 1
n = 1
# Используем цикл while для генерации чисел Фибоначчи,
# пока текущее число f1 меньше искомого числа a.
while f1 < a:
# Это "магия" Python для параллельного присваивания.
# Новое значение f0 становится старым f1,
# а новое f1 становится суммой старых f0 и f1.
# Это эквивалентно:
# temp = f1
# f1 = f0 + f1
# f0 = temp
f0, f1 = f1, f0 + f1
n += 1
# После выхода из цикла проверяем, почему он завершился.
# Если f1 равно a, значит, мы нашли число.
if f1 == a:
print(n)
# Если f1 стало больше a, значит, мы "проскочили" искомое число,
# и его нет в последовательности.
else:
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