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The task is to reorder the sign list such that the signs are in the order required for the DLN program, which mandates that the zeroth crossin","res":"To solve this problem, we need to reorder the list of signs based on the specific ordering requirement of the DLN program. The key insight is understanding how the \"DLN order\" maps to the Gauss code.\n\n### 1. Understanding the Problem\n\n*   **Gauss Code**: A list of integers representing a link diagram. Each crossing appears twice: once with a positive sign (when traversing the strand in a specific "},{"prompt":"You are tasked with preprocessing a large text dataset for a natural language processing project. Implement a function `clean_text(text)` that processes a given string `text` according to the following rules:\n\n1. Convert all characters to lowercase.\n2. Eliminate all special characters and punctuation, except for apostrophes (`'`) and hyphens (`-`).\n3. Remove all numeric characters.\n4. Collapse mul","res":"```python\nimport re\n\ndef clean_text(text):\n    \"\"\"\n    Preprocess a text string according to the following rules:\n    1. Convert all characters to lowercase.\n    2. Eliminate all special characters and punctuation, except for apostrophes (') and hyphens (-).\n    3. Remove all numeric characters.\n    4. Collapse multiple whitespace characters into a single space and trim leading and trailing spaces"},{"prompt":"You are given a 2D grid with dimensions `m x n`. Each cell in the grid is identified by its row and column indices. The cells are numbered vertically from top to bottom, starting from the leftmost column and moving to the right.\n\nDefine a function `coordsToNumV(row: int, col: int, dimensions: List[int]) -\u003e Optional[int]` that accepts the row and column indices of a cell and the dimensions of the g","res":"Let me carefully analyze the problem statement and the sample inputs/outputs to understand the numbering scheme.\n\n**Understanding the Grid:**\n- Grid is `m x n` where `dimensions = [m, n]`\n- `m` = number of rows, `n` = number of columns\n\n**Key observations from the description:**\n1. \"The top edge of the first cell in each column is numbered 1, 3, 5, ..., up to `2*m - 1`.\"\n2. \"The bottom edge of eac"},{"prompt":"You are tasked with implementing a `BankAccount` class that simulates basic banking operations. The class should support the following functionalities:\n\n- **Deposit**: Add a specified amount to the account balance. The deposit amount must be positive.\n- **Withdraw**: Subtract a specified amount from the account balance. The withdrawal amount must be positive and cannot exceed the current balance.\n","res":"```python\nclass BankAccount:\n    def __init__(self, initial_balance=0, interest_rate=0.0):\n        if initial_balance \u003c 0:\n            raise ValueError(\"Initial balance cannot be negative\")\n        self.balance = initial_balance\n        self.interest_rate = interest_rate\n\n    def deposit(self, amount):\n        if amount \u003c= 0:\n            raise ValueError(\"Deposit amount must be positive\")\n        "},{"prompt":"You are given a CSV file with a header row. Your task is to write a Python function that reads the file and returns the number of rows and columns. The function should print the number of rows and columns in the format \"Number of rows: X\" and \"Number of columns: Y\". Assume the CSV file is well-formed and the header row is present.\n\n**Sample Input:**\nA CSV file named `data.csv` with the following c","res":"```python\nimport csv\n\n\ndef count_csv_dimensions(filepath: str) -\u003e None:\n    \"\"\"\n    Read a CSV file and print the number of rows and columns.\n    \n    The number of rows excludes the header row.\n    The number of columns is determined from the header row.\n    \n    Args:\n        filepath: Path to the CSV file.\n    \"\"\"\n    with open(filepath, 'r', newline='') as f:\n        reader = csv.reader(f)\n   "},{"prompt":"You are tasked with implementing a `Book` class to manage books in a library system. The class should support the following functionalities:\n\n- **Initialization**: Create a book object with the following attributes:\n  - `title`: A string representing the title of the book.\n  - `author`: A string representing the author of the book.\n  - `publication_year`: An integer representing the year the book ","res":"```python\nclass Book:\n    def __init__(self, title: str, author: str, publication_year: int, isbn: str):\n        self.title = title\n        self.author = author\n        self.publication_year = publication_year\n        self.isbn = isbn\n\n    def display_info(self) -\u003e None:\n        print(f\"Title: {self.title}, Author: {self.author}, Year: {self.publication_year}, ISBN: {self.isbn}\")\n\n    def update_p"},{"prompt":"You are tasked with implementing a function to compute the check digit for a given string of digits using the Luhn algorithm. The Luhn algorithm is used to validate a variety of identification numbers, such as credit card numbers. Your function should adhere to the following steps:\n\n1. Starting from the rightmost digit, double every second digit. If doubling a digit results in a number greater tha","res":"```python\ndef calculate_luhn_check_digit(digits: str) -\u003e int:\n    \"\"\"\n    Calculate the Luhn check digit for a given string of digits.\n    \n    Steps:\n    1. Starting from the rightmost digit, double every second digit.\n       If doubling results in a number \u003e 9, subtract 9.\n    2. Sum all digits.\n    3. Check digit = smallest non-negative integer such that (sum + check_digit) % 10 == 0.\n    \n    "},{"prompt":"You are given a list of integers representing the ages of a group of people. Some ages are missing and denoted as `None`, and there may be negative numbers indicating erroneous data entries. Your task is to compute the median age, considering only valid ages (i.e., non-negative integers). If there are no valid ages, return `None`.\n\n**Input:**\n- A list of integers, where each integer can be a non-n","res":"```python\ndef compute_median_ages(ages):\n    \"\"\"\n    Compute the median age from a list of ages, considering only valid ages\n    (non-negative integers). Returns None if no valid ages exist.\n    \n    Args:\n        ages: A list containing integers, None values, or negative integers.\n        \n    Returns:\n        A float representing the median of valid ages, or None if no valid ages.\n    \"\"\"\n    # "},{"prompt":"You are given a list of integers representing the outcomes of multiple sets of five dice rolls. Each set of five dice rolls is a sequence of integers. Your task is to determine the score for each set based on the following rule: a \"large straight\" is defined as a sequence of five dice rolls where each die shows a number one greater than the previous die (e.g., 1, 2, 3, 4, 5 or 2, 3, 4, 5, 6). For ","res":"```python\ndef calculate_large_straight_score(dice_rolls: list) -\u003e list:\n    \"\"\"\n    Calculate the score for each set of five dice rolls based on large straight rule.\n    \n    A large straight is a sequence of five dice where each die shows a number one greater\n    than the previous die (e.g., 1,2,3,4,5 or 2,3,4,5,6).\n    \n    Args:\n        dice_rolls: A list of integers where the length is a multi"},{"prompt":"You are tasked with implementing a function `build_log_likelihood_functions` for a financial model `fm` with several parameters. Each parameter is stored in a dictionary `fm.p` where keys are parameter names and values are their current estimates. Your goal is to generate a list of log-likelihood functions, one for each parameter, using the `build_LL_function` method of the `fm` object. The `build","res":"```python\ndef build_log_likelihood_functions(pv, fm, of, df, cf):\n    \"\"\"\n    Build a list of log-likelihood functions, one for each parameter in fm.p.\n    \n    Parameters:\n    - pv: a list of parameter values in the same order as the keys in fm.p.\n    - fm: the financial model object.\n    - of: a dictionary containing observed frequencies for each parameter.\n    - df: a dictionary containing 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