### 如何使用 Python 合并两个有序数组 #### 方法概述 合并两个已排序的数组可以通过多种方式进行处理。一种简单的方法是先将第二个数组追加到第一个数组后面，再整体排序；然而这种做法效率较低，时间复杂度为 \(O((m+n)\log(m+n))\)[^4]。更优的方式是从后向前依次比较两数组中的最大值，并将其放置在最终结果的位置上，这样可以达到线性时间复杂度 \(O(m + n)\)，同时保持空间复杂度为 \(O(1)\)[^3]。 #### 实现细节 下面展示了一种高效的实现方式，该方法通过双指针技术从两端向中间扫描两个输入数组： ```python def merge_two_sorted_arrays(nums1, m, nums2, n): """ Merges two sorted arrays into one. Args: nums1 (List[int]): The first array with enough space to hold all elements from both arrays. m (int): Number of initialized elements in the first array. nums2 (List[int]): The second array that needs to be merged. n (int): Number of elements in the second array. Returns: None: Modifies `nums1` in place. """ p1 = m - 1 # Pointer for end of actual data in nums1 p2 = n - 1 # Pointer for last element in nums2 write_index = m + n - 1 # Position where next largest value should go while p1 >= 0 and p2 >= 0: # Continue until we exhaust either list if nums1[p1] > nums2[p2]: nums1[write_index] = nums1[p1] p1 -= 1 else: nums1[write_index] = nums2[p2] p2 -= 1 write_index -= 1 # If there are still items remaining in nums2 but none left in nums1, # copy them over directly since they must already be smaller than everything currently placed. while p2 >= 0: nums1[write_index] = nums2[p2] p2 -= 1 write_index -= 1 ``` 这段代码定义了一个名为 `merge_two_sorted_arrays` 的函数，它接受四个参数：分别是主数组及其有效长度、辅助数组以及其大小。注意这里假定 `nums1` 已经预留出了足够的空白位置用于容纳来自 `nums2` 的全部成分[^3]。 --- #### 测试例子 为了验证上述逻辑是否正确无误，我们可以准备几组测试用例来进行检验: ```python if __name__ == "__main__": test_cases = [ { "input": ([1, 2, 3, 0, 0, 0], 3, [2, 5, 6], 3), "output": [1, 2, 2, 3, 5, 6], }, { "input": ([1], 1, [], 0), "output": [1], }, { "input": ([0], 0, [1], 1), "output": [1], } ] all_passed = True for idx, case in enumerate(test_cases): nums1, m, nums2, n = case["input"] expected_output = case["output"] merge_two_sorted_arrays(nums1, m, nums2, n) if nums1 != expected_output: print(f"Test Case #{idx+1}: Failed") print(f"\tInput: {case['input']}") print(f"\tExpected Output: {expected_output}, But Got: {nums1}") all_passed = False if all_passed: print("All Test Cases Passed!") ``` 运行以上脚本将会逐一校验每一条规则下的预期成果与实际产出之间的一致性情况。 ---