feat(0052): 添加欧拉52题“排列倍数”的最优算法实现

solutions/0052.PermutedMultiples/euler_52.py

@@ -0,0 +1,80 @@
+"""
+It can be seen that the number, 125874, and its double, 251748,
+contain exactly the same digits, but in a different order.
+
+Find the smallest positive integer, x, such that
+2x, 3x, 4x, 5x, and 6x contain the same digits.
+"""
+
+import time
+
+
+def timer(func):
+    def wrapper(*args, **kwargs):
+        start_time = time.time()
+        result = func(*args, **kwargs)
+        end_time = time.time()
+        elapsed_time = end_time - start_time
+        print(f"{func.__name__} time: {elapsed_time:.6f} seconds")
+        return result
+
+    return wrapper
+
+
+def has_same_digits(x, y):
+    return sorted(str(x)) == sorted(str(y))
+
+
+def signature(n):
+    count = [0] * 10
+    while n:
+        count[n % 10] += 1
+        n //= 10
+    return tuple(count)
+
+
+def find_smallest_permuted_multiple():
+    x = 1
+    while True:
+        if not x % 9 == 0:
+            x += 1
+            continue
+        for i in range(2, 7):
+            if not has_same_digits(x, x * i):
+                break
+        else:
+            return x
+        x += 1
+
+
+def better_permuted_multiple():
+    n = 1
+    while True:
+        start = 10 ** (n - 1)
+        # 核心约束：x * 6 必须仍是n位数
+        end = int(10**n / 6) + 1
+
+        # 步长为9：利用模9同余原理
+        for x in range((start + 8) // 9 * 9, end, 9):
+            sig = signature(x)
+            # 检查2x到6x是否共享相同签名
+            if all(signature(k * x) == sig for k in range(2, 7)):
+                return x
+        n += 1
+
+
+@timer
+def main():
+    result = find_smallest_permuted_multiple()
+    print(f"{result}")
+
+
+@timer
+def main_better():
+    result = better_permuted_multiple()
+    print(f"{result}")
+
+
+if __name__ == "__main__":
+    main()
+    main_better()