question:# Coding Assessment Question Scenario: You're working on a data analysis project where you need to summarize time series data efficiently. Given a list of timestamps, you need to implement a function to count the number of occurrences of each unique timestamp, while maintaining the original order of their first appearance in the list. Problem Statement: Implement a Python function `count_timestamps(timestamps: List[str]) -> List[Tuple[str, int]]` that receives a list of timestamps in string format and returns a list of tuples. Each tuple should contain a timestamp and its count, preserving the order of first occurrence. Requirements: 1. The function should handle both empty and non-empty lists. 2. Non-list inputs should raise a `TypeError`. 3. Each timestamp in the input list is a string representing a valid date-time format. 4. The result should preserve the order of first appearances of timestamps. 5. Optimize for efficient counting and order preservation. Input: - A list of strings `timestamps`, where each string is a timestamp in any valid date-time format. Output: - A list of tuples: Each tuple contains a string (timestamp) and an integer (count of occurrences). Constraints: - You may assume that input list size is up to (10^5). - The solution should efficiently handle counting and ordering simultaneously with a complexity not exceeding (O(n log n)). Function Signature: ```python from typing import List, Tuple def count_timestamps(timestamps: List[str]) -> List[Tuple[str, int]]: ``` Example Cases: ```python assert count_timestamps([]) == [] assert count_timestamps(["2023-01-01T00:00:00", "2023-01-01T00:00:00", "2023-01-02T00:00:00"]) == [("2023-01-01T00:00:00", 2), ("2023-01-02T00:00:00", 1)] assert count_timestamps(["2023-01-01T00:00:00", "2023-01-02T00:00:00", "2023-01-01T00:00:00"]) == [("2023-01-01T00:00:00", 2), ("2023-01-02T00:00:00", 1)] assert count_timestamps(["2023-01-01T00:00:00"]) == [("2023-01-01T00:00:00", 1)] assert count_timestamps(["2023-01-01T00:00:00", "2023-01-02T00:00:00", "2023-01-03T00:00:00"]) == [("2023-01-01T00:00:00", 1), ("2023-01-02T00:00:00", 1), ("2023-01-03T00:00:00", 1)] assert count_timestamps(["2023-01-01T00:00:00", "2023-01-02T00:00:00", "2023-01-01T00:00:00", "2023-01-01T00:00:00"]) == [("2023-01-01T00:00:00", 3), ("2023-01-02T00:00:00", 1)] ``` Additional Information: - Make sure to use efficient data structures for counting and order preservation. - Consider edge cases such as single element lists and repeated timestamps as part of your implementation. Implement the `count_timestamps` function as per the outlined requirements.

question:# Coding Challenge: Enhance Binary Search Tree with Additional Functionalities Context You have a robust implementation of a Binary Search Tree (BST), which supports the basic operations such as insertion, deletion, and search efficiently. However, there are some additional operations that can extend the versatility and usability of your BST. Task Extend the `BinarySearchTree` class by implementing two additional functions: 1. **Find K-th Smallest Element**: This operation finds and returns the k-th smallest element in the BST. 2. **Count Nodes in Range**: This operation counts and returns the number of nodes that fall within a specified range [low, high]. Specifications **Operation 1: Find K-th Smallest Element** - **Function Signature**: `def find_kth_smallest(self, k):` - **Input**: `k` - The position of the smallest element to find. - **Output**: The k-th smallest element in the BST. **Constraints**: - `k` is a positive integer such that `1 <= k <= n`, where `n` is the number of nodes in the tree. **Operation 2: Count Nodes in Range** - **Function Signature**: `def count_nodes_in_range(self, low, high):` - **Input**: `low` - The lower bound of the range, `high` - The upper bound of the range. - **Output**: The count of nodes whose values fall within the range [low, high]. Additional Requirements - Ensure that standard BST properties are maintained. - Optimize for both time and space complexity. # Example Usage ```python # Initialize a binary search tree bst = BinarySearchTree() # Insert elements bst.insert(10) bst.insert(5) bst.insert(20) bst.insert(3) bst.insert(7) bst.insert(15) bst.insert(25) # Find the 3rd smallest element print(bst.find_kth_smallest(3)) # Should print 7 # Count nodes in the range [7, 20] print(bst.count_nodes_in_range(7, 20)) # Should print 4 ``` # Constraints - Do not use any additional data structures beyond what is required for the operations. - Handle edge cases such as k being out of range or empty tree scenarios gracefully. - Performance expectations are O(h) for the basic operations, where h is the height of the tree, and O(n) for any traversal-based solutions, where n is the number of nodes in the tree. **Note**: You may modify the `Node` and `BinarySearchTree` classes as necessary to implement these functionalities. **Class Definitions** (hypothetical structure for clarity): ```python class Node: def __init__(self, key): self.left = None self.right = None self.val = key class BinarySearchTree: def __init__(self): self.root = None def insert(self, key): # Your implementation here def delete(self, key): # Your implementation here def search(self, key): # Your implementation here def find_kth_smallest(self, k): # Your implementation here def count_nodes_in_range(self, low, high): # Your implementation here ``` **Hint**: For the `find_kth_smallest` function, consider using an in-order traversal to exploit the BST's inherent ordering of nodes.

question:# Problem Statement You need to create a class named `MaxHeap` that implements a max heap data structure. A max heap is a binary tree where each parent node's value is greater than or equal to the values of its children, and the highest value node is at the root. The class should include methods for insertion, deletion (of the maximum element), heapifying, and viewing the maximum element. This problem will help you practice manipulating heap data structures. Implement the following methods in the `MaxHeap` class: 1. Adding an element. 2. Removing the maximum element. 3. Viewing the maximum element. 4. Heapifying an array. 5. Extracting max element. # Function Specifications 1. **Add Function** ```python def add(self, value: int) -> None: ``` - **Input**: An integer value to be added to the heap. - **Output**: None. The value is added to the heap while maintaining the max heap property. - **Constraints**: The heap can have duplicates. 2. **Remove Max Function** ```python def remove_max(self) -> int: ``` - **Input**: None. - **Output**: An integer value which is the max value in the heap. This value is removed from the heap. - **Constraints**: Raises IndexError if the heap is empty. 3. **Get Max Function** ```python def get_max(self) -> int: ``` - **Input**: None. - **Output**: The max value in the heap without removing it. - **Constraints**: Raises IndexError if the heap is empty. 4. **Heapify Function** ```python def heapify(self, arr: List[int]) -> None: ``` - **Input**: A list of integers. - **Output**: None. The list is reorganized into the max heap order. - **Constraints**: In-place transformation of the input list. 5. **Extract Max Function** ```python def extract_max(self) -> int: ``` - **Input**: None. - **Output**: The max element from the heap. - **Constraints**: Raises IndexError if the heap is empty. # Examples ```python h = MaxHeap() h.add(5) h.add(10) h.add(3) assert h.get_max() == 10 h.add(15) assert h.get_max() == 15 assert h.remove_max() == 15 assert h.get_max() == 10 h.add(8) assert h.get_max() == 10 h.heapify([4, 10, 3, 5, 1]) assert h.get_max() == 10 assert h.extract_max() == 10 assert h.get_max() == 5 ```

question:# Binary Search Tree (BST) Iterator Objective: Your task is to create a `BSTIterator` class for an initially given binary search tree (BST). This iterator should provide an interface to iterate over the elements of the BST in ascending order. Requirements: 1. Implement the `BSTIterator` class with an initializer that accepts the root of a BST. 2. Include methods `has_next` and `next`: - `has_next()` returns `True` if there are still elements to be traversed and `False` otherwise. - `next()` returns the next smallest element in the BST. Class Definition: ```python class BSTIterator: def __init__(self, root: Optional[TreeNode]) -> None: self.stack = [] self._leftmost_inorder(root) def _leftmost_inorder(self, node: Optional[TreeNode]) -> None: while node: self.stack.append(node) node = node.left def has_next(self) -> bool: return len(self.stack) > 0 def next(self) -> int: if not self.has_next(): raise ValueError("No more elements in BST") topmost_node = self.stack.pop() if topmost_node.right: self._leftmost_inorder(topmost_node.right) return topmost_node.val ``` Testing: - Construct multiple BSTs and test the iterator: 1. Fully populated tree. 2. Empty tree. 3. Single-node tree. - Verify the output of `BSTIterator` matches in-order traversal of the BST. Example: ```python class TreeNode: def __init__(self, val=0, left=None, right=None): self.val = val self.left = left self.right = right root = TreeNode(7, TreeNode(3), TreeNode(15, TreeNode(9), TreeNode(20))) iterator = BSTIterator(root) print(iterator.next()) # 3 print(iterator.next()) # 7 print(iterator.has_next()) # True print(iterator.next()) # 9 print(iterator.has_next()) # True print(iterator.next()) # 15 print(iterator.has_next()) # True print(iterator.next()) # 20 print(iterator.has_next()) # False ``` **Output**: ```shell 3 7 True 9 True 15 True 20 False ``` Ensure to handle edge cases and that the iterator traverses the tree correctly in ascending order.