Symbol(clack:cancel)

solutions/0000_0029/0024.Permutations/euler_24.py

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+"""
+A permutation is an ordered arrangement of objects.
+For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4.
+If all of the permutations are listed numerically or alphabetically, we call it lexicographic order.
+The lexicographic permutations of 0, 1 and 2 are:
+012   021   102   120   201   210
+
+What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
+"""
+
+import time
+from itertools import permutations
+
+
+def timer(func):
+    def wrapper(*args, **kwargs):
+        start_time = time.time()
+        result = func(*args, **kwargs)
+        end_time = time.time()
+        print(f"Execution time: {end_time - start_time:.6f} seconds")
+        return result
+
+    return wrapper
+
+
+def ordered_permutations(n: int) -> list[int]:
+    digits = list(range(10))
+    all_permutations = permutations(digits)
+    for _ in range(n - 1):
+        next(all_permutations)
+    return next(all_permutations)
+
+
+@timer
+def main_iter():
+    n = 1000000
+    result = ordered_permutations(n)
+    print(f"used iter: {''.join(map(str, result))}")
+
+
+def get_permutation(seq, k):
+    """
+    返回序列 seq 的第 k 个字典序排列 (1-based)
+
+    参数:
+        seq: 可迭代对象（列表、元组、字符串等），元素需有序
+        k: 第 k 个排列（从1开始计数）
+
+    返回:
+        与输入类型相同的排列结果
+    """
+    n = len(seq)
+
+    # 预计算阶乘
+    factorial = [1]
+    for i in range(1, n):
+        factorial.append(factorial[-1] * i)
+
+    # 将输入转为列表（复制一份避免修改原序列）
+    elements = list(seq)
+    k -= 1  # 转为0-based索引
+
+    # 构建结果
+    result = []
+    for i in range(n, 0, -1):
+        index = k // factorial[i - 1]  # 当前位选择的元素索引
+        result.append(elements.pop(index))
+        k %= factorial[i - 1]  # 更新剩余位
+
+    # 根据输入类型返回相应格式
+    if isinstance(seq, str):
+        return "".join(result)
+    return result
+
+
+@timer
+def main_math():
+    n = 1000000
+    result = get_permutation("0123456789", n)
+    print(f"used math: {result}")
+
+
+if __name__ == "__main__":
+    main_iter()
+    main_math()