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question:def maximalRectangle(matrix): Find the largest rectangle containing only 1s in a grid. :param matrix: List of list of integers representing the grid :return: Integer representing the area of the largest rectangle containing only 1s >>> maximalRectangle([[1, 0, 1, 0, 0], [1, 0, 1, 1, 1], [1, 1, 1, 1, 1], [1, 0, 0, 1, 0]]) 6 >>> maximalRectangle([[0, 1], [1, 1]]) 2 >>> maximalRectangle([[0, 0], [0, 0]]) 0 >>> maximalRectangle([[1, 1, 1, 0], [1, 1, 1, 1]]) 6 >>> maximalRectangle([[1]]) 1 >>> maximalRectangle([[0]]) 0

answer:def maximalRectangle(matrix): Find the largest rectangle containing only 1s in a grid. :param matrix: List of list of integers representing the grid :return: Integer representing the area of the largest rectangle containing only 1s if not matrix: return 0 # Preparation step: getting the dimensions of the matrix nrows = len(matrix) ncols = len(matrix[0]) # Initialize heights array to keep track of heights of '1's heights = [0] * ncols max_area = 0 for row in matrix: for col in range(ncols): if row[col] == 0: heights[col] = 0 else: heights[col] += 1 max_area = max(max_area, max_histogram_area(heights)) return max_area def max_histogram_area(heights): Finds the maximum rectangular area under given histogram heights. :param heights: List of integers representing the histogram heights :return: Integer representing the maximum rectangular area stack = [] max_area = 0 index = 0 while index < len(heights): if not stack or heights[index] >= heights[stack[-1]]: stack.append(index) index += 1 else: top_of_stack = stack.pop() area = (heights[top_of_stack] * ((index - stack[-1] - 1) if stack else index)) max_area = max(max_area, area) while stack: top_of_stack = stack.pop() area = (heights[top_of_stack] * ((index - stack[-1] - 1) if stack else index)) max_area = max(max_area, area) return max_area

question:class MovieRental: def __init__(self): Initialize the rental system. def addMovie(self, userId, movieId): Add a movie to the user's cart. :param userId: the ID of the user :param movieId: the ID of the movie def rentMovies(self, userId): Rent all the movies currently in the user's cart. :param userId: the ID of the user def getRentalHistory(self, userId): Retrieve the list of movies rented by the user in the past. :param userId: the ID of the user :return: a list of movie IDs from solution import MovieRental def test_add_movie(): rental = MovieRental() rental.addMovie(1, 101) assert rental.carts == {1: [101]} rental.addMovie(1, 102) assert rental.carts == {1: [101, 102]} def test_rent_movies(): rental = MovieRental() rental.addMovie(1, 101) rental.addMovie(1, 102) rental.rentMovies(1) assert rental.carts == {1: []} assert rental.history == {1: [101, 102]} def test_get_rental_history(): rental = MovieRental() rental.addMovie(1, 101) rental.addMovie(1, 102) rental.rentMovies(1) assert rental.getRentalHistory(1) == [101, 102] rental.addMovie(1, 103) assert rental.getRentalHistory(1) == [101, 102] rental.rentMovies(1) assert rental.getRentalHistory(1) == [101, 102, 103] def test_empty_cart(): rental = MovieRental() rental.rentMovies(1) # Renting without adding any movie assert rental.carts == {} def test_no_rental_history(): rental = MovieRental() assert rental.getRentalHistory(1) == []

answer:class MovieRental: def __init__(self): self.carts = {} self.history = {} def addMovie(self, userId, movieId): if userId not in self.carts: self.carts[userId] = [] self.carts[userId].append(movieId) def rentMovies(self, userId): if userId in self.carts and self.carts[userId]: if userId not in self.history: self.history[userId] = [] self.history[userId].extend(self.carts[userId]) self.carts[userId] = [] def getRentalHistory(self, userId): return self.history.get(userId, [])

question:def xor_cipher(string, keys): Encodes and decodes a string using XOR with the given keys in a round-robin fashion. Args: string: The string to be encoded/decoded. keys: The list of keys (integers) to use for XOR operation. Returns: The encoded/decoded string. ... def main(encoding_string, keys): Encodes and decodes the given string using the Xor Cipher with the specified keys. Args: encoding_string: The string to be encoded/decoded. keys: The list of keys (integers) to use for XOR operation. Returns: A tuple (encoded_string, decoded_string), where encoded_string is the result of encoding the original string and decoded_string is the result of decoding the encoded string. ... # Example usage if __name__ == "__main__": n = 3 keys = [4, 5, 6] encoding_string = "hello" encoded_string, decoded_string = main(encoding_string, keys) print(f"Encoded String: {encoded_string}") print(f"Decoded String: {decoded_string}")

answer:def xor_cipher(string, keys): Encodes and decodes a string using XOR with the given keys in a round-robin fashion. Args: string: The string to be encoded/decoded. keys: The list of keys (integers) to use for XOR operation. Returns: The encoded/decoded string. result = [] key_length = len(keys) for i, char in enumerate(string): xor_value = ord(char) ^ keys[i % key_length] result.append(chr(xor_value)) return ''.join(result) def main(encoding_string, keys): # Encoding the string encoded_string = xor_cipher(encoding_string, keys) # Decoding the string (decoding is the same as encoding with XOR) decoded_string = xor_cipher(encoded_string, keys) return encoded_string, decoded_string # Example usage if __name__ == "__main__": n = 3 keys = [4, 5, 6] encoding_string = "hello" encoded_string, decoded_string = main(encoding_string, keys) print(f"Encoded String: {encoded_string}") print(f"Decoded String: {decoded_string}")

question:def smallestNumberAfterDeletingOneDigit(S: str) -> str: Finds the smallest number that can be obtained by deleting exactly one digit from the given string S. :param S: A string consisting of digits 0-9 :return: The smallest number as a string after deleting one digit >>> smallestNumberAfterDeletingOneDigit("132") == "12" >>> smallestNumberAfterDeletingOneDigit("1001") == "001" # Returns '1' after leading zeros handling >>> smallestNumberAfterDeletingOneDigit("10") == "0" >>> smallestNumberAfterDeletingOneDigit("1234") == "123" >>> smallestNumberAfterDeletingOneDigit("22222") == "2222" >>> smallestNumberAfterDeletingOneDigit("10987654321") == "0987654321" >>> smallestNumberAfterDeletingOneDigit("9876543210") == "876543210" >>> smallestNumberAfterDeletingOneDigit("300") == "00" # Which is effectively '0' after removing leading zeros >>> smallestNumberAfterDeletingOneDigit("110") == "10" >>> smallestNumberAfterDeletingOneDigit("210") == "10"

answer:def smallestNumberAfterDeletingOneDigit(S): Finds the smallest number that can be obtained by deleting exactly one digit from the given string S. :param S: A string consisting of digits 0-9 :return: The smallest number as a string after deleting one digit smallest_number = S[:-1] # Initialize with removing the last digit for i in range(len(S)): candidate = S[:i] + S[i+1:] if candidate < smallest_number: smallest_number = candidate return smallest_number

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