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question:# Word Ladder Transformation Pathfinding Challenge You are given an initial word, a target word, and a list of intermediate words (word dictionary). Each transformation involves changing exactly one letter to form a new word that must exist in the word dictionary. Your task is to find the shortest possible sequence of transformations from the initial word to the target word. If no such transformation sequence exists, return an empty list. Word Ladder Overview: The Word Ladder problem can be solved efficiently using the Breadth-First Search (BFS) algorithm, which explores all possible single-letter transformations level by level. * **Time Complexity**: O(n * m^2) where `n` is the number of words in the dictionary and `m` is the length of the words. * **Space Complexity**: O(n) # Task: 1. Implement the `word_ladder_path` function that finds the shortest transformation path from a start word to an end word using the words provided in the dictionary. 2. Ensure that your implementation handles all edge cases appropriately. 3. The function should return a list of strings representing the transformation path from the start word to the end word. # Function Signature: ```python def word_ladder_path(begin_word: str, end_word: str, word_list: list) -> list: ``` # Input: * `begin_word` (String): The initial word from which the transformation begins. * `end_word` (String): The target word to which the transformation ends. * `word_list` (List[String]): A list of strings representing the word dictionary. # Output: * A list of strings representing the shortest transformation path from `begin_word` to `end_word`. If no transformation is possible, return an empty list. # Constraints: * All words in the input list, as well as `begin_word` and `end_word`, will have the same length `m` where 1 <= m <= 10. * The length of the word list will be between 1 and 5000. * All words consist of lowercase English letters. # Example: ```python >>> word_ladder_path("hit", "cog", ["hot","dot","dog","lot","log","cog"]) ["hit", "hot", "dot", "dog", "cog"] >>> word_ladder_path("hit", "cog", ["hot","dot","dog","lot","log"]) [] >>> word_ladder_path("a", "c", ["a","b","c"]) ["a", "c"] >>> word_ladder_path("abc", "xyz", ["abz", "axy", "ayz", "xyz"]) ["abc", "abz", "ayz", "xyz"] >>> word_ladder_path("same", "same", ["same"]) ["same"] ``` # Requirements: 1. Your solution should use BFS for efficiency and correctness. 2. Handle all edge cases properly, including when no transformation is possible.

answer:from collections import deque def word_ladder_path(begin_word: str, end_word: str, word_list: list) -> list: if end_word not in word_list: return [] word_list = set(word_list) queue = deque([[begin_word]]) visited = set([begin_word]) while queue: current_path = queue.popleft() current_word = current_path[-1] if current_word == end_word: return current_path for i in range(len(current_word)): for char in 'abcdefghijklmnopqrstuvwxyz': next_word = current_word[:i] + char + current_word[i+1:] if next_word in word_list and next_word not in visited: visited.add(next_word) new_path = list(current_path) new_path.append(next_word) queue.append(new_path) return []

question:# Binary Search Tree (BST) Unique Addition: Coding Challenge **Context**: In this task, you need to create a class for a Binary Search Tree (BST) that allows only unique values. Each value in the BST must be unique, meaning duplicates are not allowed. **Objective**: Write functions to insert a value into the BST, check if a value exists in the BST, and return an in-order traversal of the BST. **Class Specifications**: 1. **class Node** - Attributes: * `value`: The value of the node. * `left`: Reference to the left child node. * `right`: Reference to the right child node. 2. **class BST** - Methods: 1. **def __init__(self)** - Initializes an empty BST. 2. **def insert(self, value: int) -> bool** - Input: * `value`: The value to insert. - Output: * `True` if the value is successfully inserted. * `False` if the value already exists in the BST (no duplicates allowed). 3. **def exists(self, value: int) -> bool** - Input: * `value`: The value to check. - Output: * `True` if the value exists in the BST. * `False` if the value does not exist in the BST. 4. **def in_order(self) -> list** - Output: * A list of BST values resulting from an in-order traversal. **Example**: ```python # Create a new BST instance bst = BST() # Insert values into the BST bst.insert(50) # True bst.insert(30) # True bst.insert(70) # True bst.insert(20) # True bst.insert(40) # True bst.insert(60) # True bst.insert(60) # False (duplicate) bst.insert(10) # True # Check existence of values print(bst.exists(30)) # True print(bst.exists(100)) # False # Get in-order traversal print(bst.in_order()) # [10, 20, 30, 40, 50, 60, 70] ``` **Requirements**: - The BST should have the properties of a Binary Search Tree: * Left subtree of a node contains only nodes with values less than the node's value. * Right subtree of a node contains only nodes with values greater than the node's value. - No duplicate values are allowed, and the insert method should handle duplicate values appropriately. - Implement necessary checks and traversal to maintain the BST properties. This question tests understanding of BST properties, how to handle duplicates, and performing in-order traversal, similar to the Vigenère Cipher question's requirement for handling different character types and preserving their properties while implementing core functionalities.

answer:class Node: def __init__(self, value): self.value = value self.left = None self.right = None class BST: def __init__(self): self.root = None def insert(self, value: int) -> bool: if self.root is None: self.root = Node(value) return True else: return self._insert_recursive(self.root, value) def _insert_recursive(self, current_node, value) -> bool: if value == current_node.value: return False # duplicate value elif value < current_node.value: if current_node.left is None: current_node.left = Node(value) return True else: return self._insert_recursive(current_node.left, value) else: # value > current_node.value if current_node.right is None: current_node.right = Node(value) return True else: return self._insert_recursive(current_node.right, value) def exists(self, value: int) -> bool: return self._exists_recursive(self.root, value) def _exists_recursive(self, current_node, value) -> bool: if current_node is None: return False if value == current_node.value: return True elif value < current_node.value: return self._exists_recursive(current_node.left, value) else: # value > current_node.value return self._exists_recursive(current_node.right, value) def in_order(self) -> list: result = [] self._in_order_recursive(self.root, result) return result def _in_order_recursive(self, current_node, result): if current_node is not None: self._in_order_recursive(current_node.left, result) result.append(current_node.value) self._in_order_recursive(current_node.right, result)

question:# Coding Question: Binary Search Tree Operations for an Inventory Management System Background: A warehouse inventory management system uses a binary search tree (BST) to keep track of items based on their unique identification numbers. This system must efficiently support operations such as adding new items, removing items, finding items, and listing all items in order. Task: Implement the following operations in your BST class: 1. **Insert Item**: Add a new item with a given identification number. 2. **Remove Item**: Remove an item with a specific identification number. 3. **Find Item**: Check if an item with a given identification number exists. 4. **Inorder Traversal**: List all items in ascending order of their identification numbers. Your BST class must have the following methods implementing the required operations: ```python class TreeNode: def __init__(self, key: int): Initialize a tree node with the given key. :param key: Integer identification number of the item. self.key = key self.left = None self.right = None class BinarySearchTree: def __init__(self): Initialize an empty binary search tree. self.root = None def insert(self, key: int) -> None: Insert an item with the given identification number into the BST. :param key: Integer identification number of the item. pass def remove(self, key: int) -> None: Remove an item with the specified identification number from the BST. :param key: Integer identification number of the item to be removed. pass def find(self, key: int) -> bool: Check if an item with the given identification number exists in the BST. :param key: Integer identification number of the item. :return: True if the item exists, False otherwise. pass def inorder_traversal(self) -> list[int]: Return a list of all item identification numbers in ascending order. :return: List of integer identification numbers in ascending order. pass ``` Input/Output Format: * `insert(key: int)` - Adds a new item with the specific identification number. * `remove(key: int)` - Removes the item with the specified identification number. * `find(key: int)` - Returns True if the item exists, False otherwise. * `inorder_traversal()` - Returns a sorted list of all item identification numbers. Constraints: * All identification numbers are unique integers. * The number of items will not exceed 10^6. Example Usage: ```python # Example initialization and operations bst = BinarySearchTree() bst.insert(50) bst.insert(30) bst.insert(70) bst.insert(20) bst.insert(40) bst.insert(60) bst.insert(80) print(bst.find(60)) # Output: True print(bst.find(25)) # Output: False bst.remove(20) inorder_list = bst.inorder_traversal() print(inorder_list) # Output: [30, 40, 50, 60, 70, 80] bst.remove(30) inorder_list = bst.inorder_traversal() print(inorder_list) # Output: [40, 50, 60, 70, 80] ``` Ensure that your implementation efficiently handles the operations and maintains the BST property through all manipulations.

answer:class TreeNode: def __init__(self, key: int): self.key = key self.left = None self.right = None class BinarySearchTree: def __init__(self): self.root = None def insert(self, key: int) -> None: if self.root is None: self.root = TreeNode(key) else: self._insert(self.root, key) def _insert(self, node: TreeNode, key: int) -> None: if key < node.key: if node.left is None: node.left = TreeNode(key) else: self._insert(node.left, key) else: if node.right is None: node.right = TreeNode(key) else: self._insert(node.right, key) def remove(self, key: int) -> None: self.root = self._remove(self.root, key) def _remove(self, node: TreeNode, key: int) -> TreeNode: if node is None: return None if key < node.key: node.left = self._remove(node.left, key) elif key > node.key: node.right = self._remove(node.right, key) else: if node.left is None: return node.right elif node.right is None: return node.left min_larger_node = self._get_min(node.right) node.key = min_larger_node.key node.right = self._remove(node.right, min_larger_node.key) return node def _get_min(self, node: TreeNode) -> TreeNode: current = node while current.left is not None: current = current.left return current def find(self, key: int) -> bool: return self._find(self.root, key) def _find(self, node: TreeNode, key: int) -> bool: if node is None: return False if key == node.key: return True elif key < node.key: return self._find(node.left, key) else: return self._find(node.right, key) def inorder_traversal(self) -> list[int]: result = [] self._inorder_traversal(self.root, result) return result def _inorder_traversal(self, node: TreeNode, result: list[int]) -> None: if node: self._inorder_traversal(node.left, result) result.append(node.key) self._inorder_traversal(node.right, result)

question:# Question Context A software engineer is working on a simulation involving people moving around a grid. They need a function to calculate the Manhattan distance (also known as "taxicab" distance) between two points on a grid. You are tasked with creating this utility function. Task Write a function `manhattan_distance` that computes the Manhattan distance between two points on a grid. Function Signature ```python def manhattan_distance(point1: tuple, point2: tuple) -> int: ``` Input * `point1` (tuple): The coordinates of the first point in the form `(x1, y1)` where `x1` and `y1` are integers. * `point2` (tuple): The coordinates of the second point in the form `(x2, y2)` where `x2` and `y2` are integers. Output * (int): The Manhattan distance between the two points. Example ```python >>> manhattan_distance((1, 2), (4, 6)) 7 >>> manhattan_distance((0, 0), (3, 4)) 7 >>> manhattan_distance((-1, -1), (2, 3)) 7 ``` Constraints * Both points are described by tuples containing two integers. * Each coordinate `x` and `y` in the points can be any integer, positive or negative. Edge Cases * When both points are the same, the Manhattan distance should be 0. * When the points are aligned either vertically or horizontally, the distance should be the absolute difference in their respective coordinates.

answer:def manhattan_distance(point1: tuple, point2: tuple) -> int: Computes the Manhattan distance between two points on a grid. Parameters: point1 (tuple): The coordinates of the first point in the form (x1, y1) point2 (tuple): The coordinates of the second point in the form (x2, y2) Returns: int: The Manhattan distance between the two points. x1, y1 = point1 x2, y2 = point2 return abs(x1 - x2) + abs(y1 - y2)