✨ 新增欧拉第34、35题解法及说明

solutions/0034/euler_34.py

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+"""
+145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
+
+Find the sum of all numbers which are equal to the sum of the factorial of their digits.
+
+Note: As 1!=1 and 2!=2 are not sums they are not included.
+"""
+
+import time
+from functools import lru_cache
+
+
+def timer(func):
+    def wrapper(*args, **kwargs):
+        start_time = time.time()
+        result = func(*args, **kwargs)
+        end_time = time.time()
+        print(f"{func.__name__} time: {end_time - start_time:.6f} seconds")
+        return result
+
+    return wrapper
+
+
+@lru_cache(maxsize=None)
+def factorial(n: int) -> int:
+    if n == 0:
+        return 1
+    elif n == 1:
+        return 1
+    elif n == 2:
+        return 2
+    elif n == 3:
+        return 6
+    elif n == 4:
+        return 24
+    elif n == 5:
+        return 120
+    elif n == 6:
+        return 720
+    elif n == 7:
+        return 5040
+    elif n == 8:
+        return 40320
+    elif n == 9:
+        return 362880
+    elif n == 10:
+        return 3628800
+    else:
+        return n * factorial(n - 1)
+
+
+def sum_digits(n: int) -> int:
+    tmp = str(n)
+    return sum(factorial(int(digit)) for digit in tmp)
+
+
+@timer
+def main() -> None:
+    res = list()
+    for i in range(12, 9999999):
+        if sum_digits(i) == i:
+            res.append(i)
+    print(sum(res))
+
+
+if __name__ == "__main__":
+    main()

solutions/0034/readme.md

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+参考 [Factorion](https://mathworld.wolfram.com/Factorion.html)
+
+---
+
+本来想的是，是否可以确定满足这个规则的数列上限。口算估计是999999，然后就是暴力计算了。
+看到结果，则比较让我惊讶，这样的数只有两个：145和40585。
+
+再加上看别人的思考，从我个人来说，可能不是所有问题都适合这个思路？