Symbol(clack:cancel)

solutions/0000_0029/0025.Fibonacci/euler_25.py

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+"""
+The Fibonacci sequence is defined by the recurrence relation:
+F_n = F_{n-1} + F_{n-2}, where F_1 = 1 and F_2 = 1.
+
+Hence the first 12 terms will be: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
+The 12th term, F_12, is the first term to contain three digits.
+
+What is the index of the first term in the Fibonacci sequence to contain 1000-digits?
+"""
+
+import math
+import time
+
+
+def timer(func):
+    def wrapper(*args, **kwargs):
+        start_time = time.time()
+        result = func(*args, **kwargs)
+        end_time = time.time()
+        during = end_time - start_time
+        if during > 1:
+            print(f"function {func.__name__} taken: {during:.6f} seconds")
+        elif during > 0.001:
+            print(f"function {func.__name__} taken: {during * 1000:.3f} milliseconds")
+        else:
+            print(
+                f"function {func.__name__} taken: {during * 1000000:.3f} microseconds"
+            )
+        return result
+
+    return wrapper
+
+
+def big_sum(a: str, b: str) -> str:
+    length = max(len(a), len(b))
+    carry = 0
+    result = []
+    for i in range(length):
+        digit_a = int(a[-i - 1]) if i < len(a) else 0
+        digit_b = int(b[-i - 1]) if i < len(b) else 0
+        sum_digit = digit_a + digit_b + carry
+        result.append(str(sum_digit % 10))
+        carry = sum_digit // 10
+    if carry:
+        result.append(str(carry))
+    return "".join(result[::-1])
+
+
+def find_fibonacci_index(digits: int) -> int:
+    a, b = "1", "1"
+    index = 1
+    while len(a) < digits:
+        a, b = b, big_sum(a, b)
+        index += 1
+    return index
+
+
+@timer
+def main_in_bigint():
+    print(find_fibonacci_index(1000))
+
+
+def binet(n: int) -> int:
+    index = math.ceil(
+        (math.log10(math.sqrt(5)) + (n - 1)) / math.log10(0.5 * (1 + math.sqrt(5)))
+    )
+    return index
+
+
+@timer
+def main_use_binet():
+    print(f"{binet(1000)}")
+
+
+if __name__ == "__main__":
+    main_in_bigint()
+    main_use_binet()

solutions/0000_0029/0025.Fibonacci/readme.md

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+# binet's formula
+
+[Binet's Formula](https://mathworld.wolfram.com/BinetsFormula.html)
+
+这个真的是厉害的方法。