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question:# Reverse a Linked List using Recursion In this exercise, you will implement the `reverse_linked_list` function, which uses recursion to reverse a singly linked list. The function takes as input the head node of a linked list and returns the new head of the list after reversing it. Function Signature ```python def reverse_linked_list(head: ListNode) -> ListNode: ``` Input: - `head`: The head node of a singly linked list. Output: - A `ListNode` representing the new head of the reversed linked list. Constraints: 1. The linked list can be empty (i.e., `head` can be `None`). 2. The function should handle lists with a single node correctly. 3. Ensure the recursion depth does not exceed the maximum recursion limit of the programming environment. # Example Usage: ```python class ListNode: def __init__(self, val=0, next=None): self.val = val self.next = next # Example 1: Reverse a list with multiple elements node1 = ListNode(1) node2 = ListNode(2) node3 = ListNode(3) node1.next = node2 node2.next = node3 new_head = reverse_linked_list(node1) # The new_head should represent the reversed list: 3 -> 2 -> 1 -> None # Example 2: Single element list single_node = ListNode(1) new_head_single = reverse_linked_list(single_node) # The new_head_single should be the same single_node, as the list is already reversed # Example 3: Empty list empty_list = None new_head_empty = reverse_linked_list(empty_list) # The new_head_empty should be None, as there's nothing to reverse ``` # Implementation Notes: Your function should recursively reverse the linked list by following these steps: - If the list is empty or contains only one node, return the head as is. - Otherwise, recursively reverse the rest of the list. - Then adjust the next pointers to complete the reversal. - Ensure clear and readable code with comments explaining the key steps. Here is the implementation outline to guide you: ```python class ListNode: def __init__(self, val=0, next=None): self.val = val self.next = next def reverse_linked_list(head: ListNode) -> ListNode: # Base case: If the list is empty or has reached the last node if head is None or head.next is None: return head # Recurse on the next node new_head = reverse_linked_list(head.next) # Adjust the pointers head.next.next = head head.next = None return new_head ```

answer:class ListNode: def __init__(self, val=0, next=None): self.val = val self.next = next def reverse_linked_list(head: ListNode) -> ListNode: Reverses a singly linked list using recursion. Args: head (ListNode): The head node of the linked list. Returns: ListNode: The new head of the reversed linked list. # Base case: If the list is empty or has reached the last node if head is None or head.next is None: return head # Recurse on the next node new_head = reverse_linked_list(head.next) # Adjust the pointers head.next.next = head head.next = None return new_head

question:# Question: Hexadecimal and String Conversion Functions You are tasked with implementing two functions for converting hexadecimal strings to their ASCII string representations and vice versa. Function 1: `hex_to_ascii(hex_string: str) -> str` Implement a function that takes a hexadecimal string and converts it to its ASCII string representation. **Inputs:** * `hex_string (str)`: A string representing a sequence of hexadecimal values, e.g., "48656c6c6f". **Outputs:** * `str`: The ASCII string representation of the hexadecimal input. **Constraints:** * The input string must be a valid hexadecimal string with an even number of characters. * Each pair of hexadecimal digits (one byte) must form a valid ASCII character. Input Examples: - `"48656c6c6f"` - `"576f726c64"` Output Examples: - `"Hello"` - `"World"` Function 2: `ascii_to_hex(ascii_string: str) -> str` Implement a function that takes an ASCII string and converts it to its hexadecimal string representation. **Inputs:** * `ascii_string (str)`: A string representing an ASCII text, e.g., "Hello". **Outputs:** * `str`: The hexadecimal string representation of the ASCII input. **Constraints:** * The input string must be a valid ASCII string. Input Examples: - `"Hello"` - `"World"` Output Examples: - `"48656c6c6f"` - `"576f726c64"` # Requirements 1. You must handle edge cases such as invalid hexadecimal formats or non-ASCII characters. 2. Efficiently convert between the two representations with minimal use of memory and time. 3. Implement proper error conditions where inputs do not meet expected formats or constraints. Examples Example 1: ```python >>> hex_to_ascii("48656c6c6f") 'Hello' >>> hex_to_ascii("576f726c64") 'World' ``` Example 2: ```python >>> ascii_to_hex('Hello') '48656c6c6f' >>> ascii_to_hex('World') '576f726c64' ``` Write the implementations for both functions ensuring they fulfill the requirements and handle all edge cases appropriately.

answer:def hex_to_ascii(hex_string: str) -> str: Converts a hexadecimal string to its ASCII string representation. if len(hex_string) % 2 != 0: raise ValueError("Hexadecimal string must have an even number of characters") try: ascii_string = bytes.fromhex(hex_string).decode('ascii') except ValueError: raise ValueError("Invalid hexadecimal string or non-ASCII characters encountered") return ascii_string def ascii_to_hex(ascii_string: str) -> str: Converts an ASCII string to its hexadecimal string representation. try: hex_string = ascii_string.encode('ascii').hex() except UnicodeEncodeError: raise ValueError("Non-ASCII characters found in input string") return hex_string

question:# Problem Statement Create a class `MatrixUtils` that provides various utilities for matrix operations. The methods should be designed to handle square matrices of integers efficiently, considering all edge cases and constraints. # Method Specifications: 1. **transpose(matrix: list) -> list**: - Calculates and returns the transpose of a given square matrix. - **Input**: A list of lists representing a square matrix of integers. - **Output**: A list of lists representing the transpose of the input matrix. - **Constraints**: Raise a ValueError if the input is not a square matrix. 2. **is_symmetric(matrix: list) -> bool**: - Checks whether a given square matrix is symmetric. - **Input**: A list of lists representing a square matrix of integers. - **Output**: A boolean value, `True` if the matrix is symmetric, otherwise `False`. - **Constraints**: Raise a ValueError if the input is not a square matrix. 3. **matrix_multiplication(matrix1: list, matrix2: list) -> list**: - Multiplies two given square matrices and returns the resultant matrix. - **Input**: Two lists of lists representing square matrices of integers. - **Output**: A list of lists representing the product of the two input matrices. - **Constraints**: Raise a ValueError if the input matrices are not of the same dimensions or not square matrices. 4. **determinant(matrix: list) -> int**: - Computes and returns the determinant of a given square matrix. - **Input**: A list of lists representing a square matrix of integers. - **Output**: An integer representing the determinant of the input matrix. - **Constraints**: Raise a ValueError if the input is not a square matrix. # Implementation Details - Ensure the methods can handle edge cases and constraints efficiently. - All methods should handle worst-case scenarios within reasonable time limits. - You may use any internal helper functions if necessary, but they should be encapsulated within the class. - Proper error handling for edge cases and invalid inputs should be implemented. Here is an initial structure of the class for reference: ```python class MatrixUtils: def transpose(self, matrix: list) -> list: # Your code here pass def is_symmetric(self, matrix: list) -> bool: # Your code here pass def matrix_multiplication(self, matrix1: list, matrix2: list) -> list: # Your code here pass def determinant(self, matrix: list) -> int: # Your code here pass ``` **Note** - Ensure to adhere to the method signatures. - Standard Python libraries can be used for auxiliary computations. - Raise a `ValueError` for invalid inputs according to the constraints mentioned for each method. # Example Usage ```python mu = MatrixUtils() matrix1 = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ] matrix2 = [ [9, 8, 7], [6, 5, 4], [3, 2, 1] ] print(mu.transpose(matrix1)) # Output: [ # [1, 4, 7], # [2, 5, 8], # [3, 6, 9] # ] print(mu.is_symmetric(matrix1)) # Output: False print(mu.matrix_multiplication(matrix1, matrix2)) # Output: [ # [30, 24, 18], # [84, 69, 54], # [138, 114, 90] # ] print(mu.determinant(matrix1)) # Output: 0 ```

answer:class MatrixUtils: def transpose(self, matrix: list) -> list: if not all(len(row) == len(matrix) for row in matrix): raise ValueError("Input is not a square matrix.") return [list(row) for row in zip(*matrix)] def is_symmetric(self, matrix: list) -> bool: if not all(len(row) == len(matrix) for row in matrix): raise ValueError("Input is not a square matrix.") for i in range(len(matrix)): for j in range(len(matrix)): if matrix[i][j] != matrix[j][i]: return False return True def matrix_multiplication(self, matrix1: list, matrix2: list) -> list: if not (all(len(row) == len(matrix1) for row in matrix1) and all(len(row) == len(matrix2) for row in matrix2) and len(matrix1) == len(matrix2)): raise ValueError("Input matrices are not of the same dimensions or not square matrices.") size = len(matrix1) result = [[0] * size for _ in range(size)] for i in range(size): for j in range(size): for k in range(size): result[i][j] += matrix1[i][k] * matrix2[k][j] return result def determinant(self, matrix: list) -> int: if not all(len(row) == len(matrix) for row in matrix): raise ValueError("Input is not a square matrix.") size = len(matrix) if size == 1: return matrix[0][0] if size == 2: return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0] det = 0 for c in range(size): submatrix = [row[:c] + row[c+1:] for row in matrix[1:]] det += ((-1) ** c) * matrix[0][c] * self.determinant(submatrix) return det

question:# Problem Statement: You are given a matrix of integers where each row is sorted in ascending order from left to right, and each column is sorted in ascending order from top to bottom. Your task is to implement a function that returns an element's position (row, column) in the matrix if it exists, otherwise returns (-1, -1). # Function Signature: ```python def search_matrix(matrix: list[list[int]], target: int) -> tuple[int, int]: ``` # Input: * `matrix`: A list of lists of integers (0 ≤ len(matrix) ≤ 300, 0 ≤ len(matrix[0]) ≤ 300, -10^9 ≤ matrix[i][j] ≤ 10^9) * `target`: An integer, the number to search for in the matrix. # Output: * A tuple `(row, column)` representing the position of the target number in the matrix, or `(-1, -1)` if the target is not found. # Constraints: * The function should be efficient with an upper bound time complexity of O(M + N) where `M` is the number of rows and `N` is the number of columns. * Each element in the matrix provides information relevant to sorting, and the function should take advantage of this layout to optimize the search. * You can use helper functions and additional data structures if needed. # Examples: ```python assert search_matrix([[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]], 5) == (1, 1) assert search_matrix([[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]], 20) == (-1, -1) assert search_matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]], 9) == (2, 2) assert search_matrix([[1]], 1) == (0, 0) assert search_matrix([[]], 1) == (-1, -1) ``` # Scenario: Imagine you are a botanist who maintains a large spreadsheet of plant growth data, organized such that each row represents a day and each column a different plant species. You want to determine where a certain growth milestone (target) first appears in this matrix. Your function will assist in efficiently locating this milestone or confirming its absence.

answer:def search_matrix(matrix: list[list[int]], target: int) -> tuple[int, int]: Returns the position (row, column) of target in the matrix if it exists, otherwise returns (-1, -1). The matrix is sorted in ascending order both row-wise and column-wise. if not matrix or not matrix[0]: return (-1, -1) rows = len(matrix) cols = len(matrix[0]) row = 0 col = cols - 1 while row < rows and col >= 0: if matrix[row][col] == target: return (row, col) elif matrix[row][col] > target: col -= 1 else: row += 1 return (-1, -1)