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question:# Coding Assessment Question Scenario Imagine you are working on a robot automation system. One of the tasks involves guiding the robot through a path, represented as a grid of cells. Each cell in the grid has a specific energy cost associated with moving through it. The robot starts at the top-left cell and needs to reach the bottom-right cell. The robot can only move either down or right at any point in time. Your job is to determine the minimum energy cost required for the robot to reach the bottom-right cell from the top-left cell. Task Write a function `min_energy_cost` that computes the minimum energy cost for the robot to travel from the top-left cell to the bottom-right cell in a given grid. Requirements 1. If the grid is empty, raise a `ValueError` with the message "Grid is empty". 2. If any cell in the grid has an energy cost less than 0, raise a `ValueError` with the message "Energy cost cannot be negative". Function Signature ```python def min_energy_cost(grid: List[List[int]]) -> int: pass ``` Inputs - `grid` (List[List[int]]): A 2D list where each element is a non-negative integer representing the energy cost of that cell. Output - (int): The minimum energy cost to travel from the top-left cell to the bottom-right cell. Constraints - The grid will have at least 1 row and 1 column. - Each cell in the grid will contain a non-negative integer. Example ```python >>> min_energy_cost([[1, 3, 1], [1, 5, 1], [4, 2, 1]]) 7 >>> min_energy_cost([[1, 2, 3], [4, 5, 6]]) 12 >>> min_energy_cost([]) Traceback (most recent call last): ... ValueError: Grid is empty >>> min_energy_cost([[1, -1, 3], [4, 5, 6]]) Traceback (most recent call last): ... ValueError: Energy cost cannot be negative ``` Implement this function ensuring it handles all edge cases and constraints as specified.

answer:from typing import List def min_energy_cost(grid: List[List[int]]) -> int: if not grid or not grid[0]: raise ValueError("Grid is empty") rows, cols = len(grid), len(grid[0]) for row in grid: if any(cell < 0 for cell in row): raise ValueError("Energy cost cannot be negative") # Create a DP table to store the minimum energy cost at each cell dp = [[0] * cols for _ in range(rows)] dp[0][0] = grid[0][0] # Initialize the first row for j in range(1, cols): dp[0][j] = dp[0][j - 1] + grid[0][j] # Initialize the first column for i in range(1, rows): dp[i][0] = dp[i - 1][0] + grid[i][0] # Fill in the rest of the dp table for i in range(1, rows): for j in range(1, cols): dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j] return dp[rows - 1][cols - 1]

question:# Minimal Roman Numeral Conversion **Context**: Roman numerals are a numeric system used in ancient Rome. The basic symbols are: - `I` (1) - `V` (5) - `X` (10) - `L` (50) - `C` (100) - `D` (500) - `M` (1000) When smaller symbols appear before larger ones, they are subtracted (e.g., `IV` for 4, `IX` for 9). When they appear after, they're added (e.g., `VI` for 6, `XIII` for 13). **Prompt**: Create a function to convert a given integer into its smallest possible Roman numeral equivalent. Focus on understanding Roman numeral rules and how to structure the conversion algorithm efficiently. **Function Signature**: ```python def int_to_roman(num: int) -> str: Converts an integer to its Roman numeral representation. :param num: The integer to convert (1 ≤ num ≤ 3999) :return: A string representing the Roman numeral form of the given integer ``` # Requirements: 1. **Input**: A single integer `num` in the range from 1 to 3999 inclusive. 2. **Output**: A string that represents the Roman numeral of `num`. 3. Use dictionaries or lists to map integer values to their Roman numeral counterparts for efficient conversion. 4. Ensure correct handling of subtractive combinations in the numeral system (e.g., `IV`, `IX`, `XL`, etc.). # Examples: ```python >>> int_to_roman(1994) 'MCMXCIV' >>> int_to_roman(58) 'LVIII' >>> int_to_roman(9) 'IX' >>> int_to_roman(14) 'XIV' ``` # Constraints: 1. Your code should use a dictionary or list to store Roman numeral mappings. 2. Implement the logic in a clear, readable, and well-structured manner. 3. The function must follow best practices for efficiency considering the constraints.

answer:def int_to_roman(num: int) -> str: Converts an integer to its Roman numeral representation. :param num: The integer to convert (1 ≤ num ≤ 3999) :return: A string representing the Roman numeral form of the given integer value_map = [ (1000, 'M'), (900, 'CM'), (500, 'D'), (400, 'CD'), (100, 'C'), (90, 'XC'), (50, 'L'), (40, 'XL'), (10, 'X'), (9, 'IX'), (5, 'V'), (4, 'IV'), (1, 'I') ] roman_numeral = '' for value, symbol in value_map: while num >= value: roman_numeral += symbol num -= value return roman_numeral

question:# **Array Rotation and Sum Calculation** Given an array of integers, you are required to perform the following operations: 1. Rotate the array to the right by `k` places. 2. Calculate the sum of the elements of the rotated array. Implement a function `rotate_and_sum(arr: List[int], k: int) -> Tuple[List[int], int]` that performs these operations. **Task** 1. Rotate the array `arr` to the right by `k` places. 2. Calculate the sum of the elements of the rotated array. 3. Return a tuple containing the rotated array and the sum. **Function Signature** ```python from typing import List, Tuple def rotate_and_sum(arr: List[int], k: int) -> Tuple[List[int], int]: pass ``` Input - `arr`: A list of integers (1 <= len(arr) <= 10^5). - `k`: An integer representing the number of positions to rotate the array (0 <= k <= 10^5). Output - A tuple containing the rotated array and the sum of its elements. Constraints - The elements of the array are integers within the range [-10^5, 10^5]. Examples ```python >>> rotate_and_sum([1, 2, 3, 4, 5], 2) ([4, 5, 1, 2, 3], 15) >>> rotate_and_sum([0, -1, -2, -3], 1) ([-3, 0, -1, -2], -6) >>> rotate_and_sum([10, 20, 30], 3) ([10, 20, 30], 60) ``` **Note** - Ensure the rotation logic handles cases where `k` is larger than the length of the array efficiently. - Focus on both optimizing the rotation step and the summation for large input sizes. - Edge cases such as an array with a single element or an empty array should be considered.

answer:from typing import List, Tuple def rotate_and_sum(arr: List[int], k: int) -> Tuple[List[int], int]: if not arr: # Handling empty array edge case return arr, 0 n = len(arr) k = k % n # To handle cases where k is larger than n rotated_array = arr[-k:] + arr[:-k] array_sum = sum(rotated_array) return rotated_array, array_sum

question:# Scenario You are a software engineer responsible for creating an API for a new e-commerce platform. This API needs an efficient system to handle the inventory of products using various operations. To ensure the system's quality, the operations will be tested extensively. # Task Implement the following inventory operations as specified: 1. `add_product(inventory, product_name, quantity)`: Adds a specified quantity of a product to the inventory. 2. `remove_product(inventory, product_name, quantity)`: Removes a specified quantity of a product from the inventory. 3. `get_product_quantity(inventory, product_name)`: Returns the current quantity of a specified product in the inventory. 4. `list_inventory(inventory)`: Returns a list of products and their quantities sorted alphabetically by product name. # Specifications - **Input**: - `add_product`, `remove_product`: A dictionary `inventory` where keys are product names and values are quantities, a string `product_name`, and an integer `quantity`. - `get_product_quantity`: A dictionary `inventory` and a string `product_name`. - `list_inventory`: A dictionary `inventory`. - **Output**: - The modified `inventory` dictionary for `add_product` and `remove_product`. - The quantity of the specified product for `get_product_quantity`. - A list of tuples `(product_name, quantity)` sorted alphabetically for `list_inventory`. # Example Implementations ```python def add_product(inventory, product_name, quantity): # Implement logic for adding product to inventory pass def remove_product(inventory, product_name, quantity): # Implement logic for removing product from inventory pass def get_product_quantity(inventory, product_name): # Implement logic for getting product quantity pass def list_inventory(inventory): # Implement logic for listing inventory pass ``` # Constraints - You should handle invalid input cases gracefully by raising appropriate exceptions, such as `ValueError` for invalid quantity (e.g., below 0) or if the `product_name` does not exist in the inventory when removing or retrieving quantities. - Ensure that your solutions are efficient and follow best practices. - Quantities for products should be non-negative integers. # Performance Requirements - The time complexity should be kept as low as practical within the constraints of typical use cases. - Your code will be tested for efficiency and should handle reasonably large inventories (e.g., 10,000 products) within acceptable time limits.

answer:def add_product(inventory, product_name, quantity): Adds a specified quantity of a product to the inventory. Parameters: inventory (dict): The inventory dictionary. product_name (str): The name of the product to add. quantity (int): The quantity to add. Returns: dict: The updated inventory dictionary. if quantity < 0: raise ValueError("Quantity cannot be negative.") if product_name in inventory: inventory[product_name] += quantity else: inventory[product_name] = quantity return inventory def remove_product(inventory, product_name, quantity): Removes a specified quantity of a product from the inventory. Parameters: inventory (dict): The inventory dictionary. product_name (str): The name of the product to remove. quantity (int): The quantity to remove. Returns: dict: The updated inventory dictionary. if quantity < 0: raise ValueError("Quantity cannot be negative.") if product_name not in inventory: raise ValueError("Product does not exist in inventory.") if inventory[product_name] < quantity: raise ValueError("Not enough quantity in inventory to remove.") inventory[product_name] -= quantity if inventory[product_name] == 0: del inventory[product_name] return inventory def get_product_quantity(inventory, product_name): Returns the current quantity of a specified product in the inventory. Parameters: inventory (dict): The inventory dictionary. product_name (str): The name of the product to get the quantity of. Returns: int: The quantity of the product. if product_name not in inventory: raise ValueError("Product does not exist in inventory.") return inventory[product_name] def list_inventory(inventory): Returns a list of products and their quantities sorted alphabetically by product name. Parameters: inventory (dict): The inventory dictionary. Returns: list: A list of tuples (product_name, quantity) sorted alphabetically. return sorted(inventory.items())