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question:# Context In a given text-based data pipeline, a common task is to ensure data consistency by checking if certain strings are valid palindromes. A palindrome is a sequence that reads the same backward as forward, ignoring spaces, punctuation, and case. Your task is to verify if a given string qualifies as a palindrome by implementing an algorithm to do so efficiently. # Task Write a function `validate_palindrome(s: str) -> bool` that verifies whether a given string `s` is a valid palindrome according to given rules. # Input - A string `s` (0 ≤ |s| ≤ 10^5), where |s| represents the length of the string. # Output - Return `True` if the string `s` is a palindrome, `False` otherwise. # Constraints - The function should handle all alphanumeric characters. - The function should be case-insensitive. - Non-alphanumeric characters should be ignored. # Requirements: - You should not use extra space proportional to the size of the input (consider in-place algorithms). # Example: ```python def validate_palindrome(s: str) -> bool: # Implement your function here # Example cases print(validate_palindrome("A man, a plan, a canal: Panama")) # True print(validate_palindrome("race a car")) # False print(validate_palindrome("")) # True print(validate_palindrome(" ")) # True print(validate_palindrome("0P")) # False ``` # Notes: - An empty string or string with only non-alphanumeric characters should return `True` as per the definition of a palindrome.

answer:def validate_palindrome(s: str) -> bool: This function checks if the given string is a valid palindrome ignoring cases, spaces, and non-alphanumeric characters. l, r = 0, len(s) - 1 while l < r: # Move l to the next alphanumeric character while l < r and not s[l].isalnum(): l += 1 # Move r to the previous alphanumeric character while l < r and not s[r].isalnum(): r -= 1 # Check if the characters are equal (case-insensitive) if s[l].lower() != s[r].lower(): return False l += 1 r -= 1 return True

question:You are tasked with creating a utility function that determines the number of digits in a given non-negative integer. Given how critical performance can be, your solution should ensure constant time complexity. **Function Signature** ```python def number_of_digits(n: int) -> int: ``` # Input * `n` - A non-negative integer (0 ≤ n ≤ 10^100) # Output * Return the number of digits in the integer n. # Constraints * You must ensure your function has a time complexity of O(1). * Handle edge cases where `n` is zero, and large numbers adequately. * Do not use standard library functions that automatically convert the number to string to count its length. # Example ```python assert number_of_digits(0) == 1 assert number_of_digits(5) == 1 assert number_of_digits(12345) == 5 ``` # Notes Your implementation should handle very large numbers efficiently using the constraints provided. Also ensure to properly manage any edge cases that could lead to errors or incorrect results.

answer:def number_of_digits(n: int) -> int: Returns the number of digits in the integer n. if n == 0: return 1 return len(str(n))

question:# RandomizedSet Implementation In this task, you'll implement a data structure named `RandomizedSet` that supports insertion, deletion, and random element retrieval operations in average O(1) time complexity. The structure ensures that each element has an equal probability of being selected when retrieving a random element. Requirements 1. **Function Signature** - `def __init__(self):` Initializes the data structure. - `def insert(self, val: int) -> None:` Inserts an item `val` to the set if it is not already present. - `def remove(self, val: int) -> None:` Removes an item `val` from the set if it is present. - `def random_element(self) -> int:` Returns a random element from the current set of elements. 2. **Examples** ```python randomized_set = RandomizedSet() randomized_set.insert(1) # Inserts 1 randomized_set.remove(2) # Does nothing since 2 is not present randomized_set.insert(2) # Inserts 2 print(randomized_set.random_element()) # Should return either 1 or 2 randomly with equal probability randomized_set.remove(1) # Removes 1 print(randomized_set.random_element()) # Should return 2, as 2 is the only element present ``` 3. **Constraints** - The elements to be inserted or removed will be integers within the range `-10^6` to `10^6`. - It is guaranteed that `random_element` will only be called when there is at least one element in the set. Implement the `RandomizedSet` class as described.

answer:import random class RandomizedSet: def __init__(self): Initialize your data structure here. self.dict = {} self.list = [] def insert(self, val: int) -> bool: Inserts a value to the set. Returns True if the set did not already contain the specified element. if val in self.dict: return False self.dict[val] = len(self.list) self.list.append(val) return True def remove(self, val: int) -> bool: Removes a value from the set. Returns True if the set contained the specified element. if val not in self.dict: return False # Move the last element to the place of the element to delete last_element = self.list[-1] idx = self.dict[val] self.list[idx] = last_element self.dict[last_element] = idx # Remove the last element self.list.pop() del self.dict[val] return True def random_element(self) -> int: Get a random element from the set. return random.choice(self.list)

question:Implement a Doubly Linked List with Specific Operations **Context**: You are required to design and implement a Doubly Linked List to support a small text editor's undo functionality. Your implementation needs to support the following operations efficiently: 1. Adding a character to the text. 2. Deleting the most recently added character. 3. Displaying the text. # Function Signature ```python class DoublyLinkedListNode: A node in a doubly linked list. def __init__(self, value): self.value = value self.next = None self.prev = None class DoublyLinkedList: def __init__(self): Initialize an empty doubly linked list. self.head = None self.tail = None def add_character(self, char: str) -> None: Add a character to the end of the text. Parameters: char (str): The character to be added. Returns: None pass def delete_character(self) -> bool: Delete the most recently added character from the text. Returns: bool: True if a character was successfully deleted, False if the text was already empty. pass def display_text(self) -> str: Display the current text. Returns: str: The current text as a single string. pass ``` # Input and Output Formats - **add_character(char: str)**: Takes a single character string as input and adds it to the end of the text. - **delete_character()**: Removes the most recently added character and returns `True`. If the text is empty, returns `False`. - **display_text()**: Returns the current state of the text as a single concatenated string. # Constraints - The function `add_character` will be called with exactly one character each time. # Example: ```python dll = DoublyLinkedList() dll.add_character('a') dll.add_character('b') dll.add_character('c') print(dll.display_text()) # Output: "abc" dll.delete_character() print(dll.display_text()) # Output: "ab" ``` # Performance Requirements - Efficient handling of add and delete operations, i.e., should operate in constant time: O(1).

answer:class DoublyLinkedListNode: A node in a doubly linked list. def __init__(self, value): self.value = value self.next = None self.prev = None class DoublyLinkedList: def __init__(self): Initialize an empty doubly linked list. self.head = None self.tail = None def add_character(self, char: str) -> None: Add a character to the end of the text. Parameters: char (str): The character to be added. Returns: None new_node = DoublyLinkedListNode(char) if self.tail is None: # Empty list self.head = new_node self.tail = new_node else: # Add to the end new_node.prev = self.tail self.tail.next = new_node self.tail = new_node def delete_character(self) -> bool: Delete the most recently added character from the text. Returns: bool: True if a character was successfully deleted, False if the text was already empty. if self.tail is None: return False if self.head == self.tail: # Only one element in the list self.head = None self.tail = None else: # Remove the last element self.tail = self.tail.prev self.tail.next = None return True def display_text(self) -> str: Display the current text. Returns: str: The current text as a single string. current = self.head result = [] while current is not None: result.append(current.value) current = current.next return "".join(result)