✨ 新增欧拉第41、42题Python解法

solutions/0041.PandigitalPrime/euler_41.py

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+"""
+We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once.
+For example, 2143 is a 4-digit pandigital and is also prime.
+
+What is the largest n-digit pandigital prime that exists?
+"""
+
+import random
+import time
+from functools import lru_cache
+from itertools import permutations
+
+
+def timer(func):
+    def wrapper(*args, **kwargs):
+        start_time = time.perf_counter()
+        result = func(*args, **kwargs)
+        end_time = time.perf_counter()
+        print(f"Execution time: {end_time - start_time} seconds")
+        return result
+
+    return wrapper
+
+
+def miller_rabin_test(n: int, k: int = 10) -> bool:
+    if n < 2:
+        return False
+    if n == 2 or n == 3:
+        return True
+    if n % 2 == 0 or n % 3 == 0:
+        return False
+    r, s = 0, n - 1
+    while s % 2 == 0:
+        r += 1
+        s //= 2
+    for _ in range(k):
+        a = random.randrange(2, n - 1)
+        x = pow(a, s, n)
+        if x == 1 or x == n - 1:
+            continue
+        for _ in range(r - 1):
+            x = pow(x, 2, n)
+            if x == n - 1:
+                break
+        else:
+            return False
+    return True
+
+
+@lru_cache(maxsize=128)
+def is_even_or_five_ending(num: int) -> bool:
+    """快速检查是否为偶数或以5结尾"""
+    return num % 2 == 0 or num % 5 == 0
+
+
+@timer
+def main() -> None:
+    str_nums = "987654321"
+    stop = False
+    for i in range(9, 0, -1):
+        if sum(int(digit) for digit in str_nums[-i:]) % 3 == 0:
+            continue
+        for perm in permutations(str_nums[-i:], i):
+            num = int("".join(perm))
+            if is_even_or_five_ending(num):
+                continue
+            if miller_rabin_test(num):
+                print(num)
+                stop = True
+                break
+        if stop:
+            break
+
+
+if __name__ == "__main__":
+    main()