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question:You are given a list of integers `nums` sorted in non-decreasing order and an integer `target`. Your task is to find the starting and ending position of the target value in the array. If the target is not found in the array, return `[-1, -1]`. Implement the function `searchRange(nums, target)` that finds the range in which `target` appears. The function should follow these specifications: * The function should return a list of two integers indicating the start and end positions of the target in the array. * If the target is not present, the function should return `[-1, -1]`. * The function must have a logarithmic time complexity, ensuring efficiency even for large datasets. Example: ```python assert searchRange([5,7,7,8,8,10], 8) == [3,4] assert searchRange([5,7,7,8,8,10], 6) == [-1,-1] assert searchRange([], 0) == [-1,-1] ```

answer:def searchRange(nums, target): Returns the starting and ending positions of the target in the array. If the target is not found, return [-1, -1]. def find_left_index(nums, target): left, right = 0, len(nums) - 1 while left <= right: mid = (left + right) // 2 if nums[mid] < target: left = mid + 1 else: right = mid - 1 return left def find_right_index(nums, target): left, right = 0, len(nums) - 1 while left <= right: mid = (left + right) // 2 if nums[mid] <= target: left = mid + 1 else: right = mid - 1 return right left_index = find_left_index(nums, target) right_index = find_right_index(nums, target) # Check if target is not inside the array. if left_index <= right_index and left_index < len(nums) and nums[left_index] == target: return [left_index, right_index] else: return [-1, -1]

question:You are given an integer array `nums` of unique elements. Consider a new array `sorted_nums` which is the result of sorting `nums` in ascending order. Write an algorithm to determine the length of the smallest subsequence in `nums` that can be removed to make the remaining elements in the same order as `sorted_nums`. If no removal is needed, return `0`. Example: ``` Input: nums = [4, 2, 3, 1] Output: 2 Explanation: Removing the subsequence [4, 1] will result in [2, 3] which is sorted in ascending order. ```

answer:def length_of_smallest_subsequence_to_remove(nums): Returns the length of the smallest subsequence in nums that can be removed to make the remaining elements sorted in ascending order. def find_lis_length(nums): # Helper function to find the length of the Longest Increasing Subsequence (LIS) from bisect import bisect_left lis = [] for num in nums: pos = bisect_left(lis, num) if pos == len(lis): lis.append(num) else: lis[pos] = num return len(lis) length_of_lis = find_lis_length(nums) return len(nums) - length_of_lis

question:Given the root of a binary search tree (BST) and a value `val`, insert `val` into the BST such that the properties of the binary search tree are maintained. Return the root of the BST after the insertion. It is guaranteed that there are no duplicate values in the BST.

answer:class TreeNode: def __init__(self, val=0, left=None, right=None): self.val = val self.left = left self.right = right def insert_into_bst(root, val): Inserts a value into the BST and returns the root of the BST. :param root: TreeNode, the root of the BST. :param val: int, the value to be inserted. :return: TreeNode, the root of the BST after insertion. if root is None: return TreeNode(val) if val < root.val: root.left = insert_into_bst(root.left, val) else: root.right = insert_into_bst(root.right, val) return root

question:You have an array of integers `arr` where each element appears exactly twice, except for one element that appears exactly once. Implement a function that takes `arr` as input and returns the element that appears only once. Your solution should have a linear runtime complexity and use only constant extra space. Return the unique element in the array.

answer:def find_single_element(arr): Returns the element that appears only once in the array where every other element appears twice. Parameters: arr (list of int): The input array of integers. Returns: int: The unique element that appears only once. unique_element = 0 for num in arr: unique_element ^= num return unique_element