answer:def enhanced_split(path: str) -> list: Splits the given path into directory part and file name part. Args: path (str): The file path or URL to split. Returns: list: A list containing the directory part and the file name part. if not path: return ["", ""] # Normalize the path by replacing backslashes with forward slashes normalized_path = path.replace('', '/') # Find the last slash last_slash_index = normalized_path.rfind('/') # Extract directory and filename if last_slash_index == -1: # No slashes found; the whole path is the filename directory = "" filename = path else: directory = path[:last_slash_index] filename = path[last_slash_index + 1:] return [directory, filename]

answer:class Monomial: def __init__(self, exponents, coefficient): self.exponents = exponents # dictionary representing variables and their exponents (e.g., {1: 2} for x1^2) self.coefficient = coefficient # coefficient of the monomial def __pow__(self, power): if power < 0: raise ValueError("Negative powers are not supported for monomials.") if power == 0: return Monomial({}, 1) # Any monomial to the power of 0 is 1 new_exponents = {var: exp * power for var, exp in self.exponents.items()} new_coefficient = self.coefficient ** power return Monomial(new_exponents, new_coefficient) def __repr__(self): return f'Monomial({self.exponents}, {self.coefficient})' class Polynomial: def __init__(self, monomials): self.monomials = monomials # list of Monomial instances def simplify(self): simplified_terms = {} for monomial in self.monomials: exp_tuple = tuple(sorted(monomial.exponents.items())) if exp_tuple in simplified_terms: simplified_terms[exp_tuple].coefficient += monomial.coefficient else: simplified_terms[exp_tuple] = Monomial(dict(monomial.exponents), monomial.coefficient) # Remove monomials with a coefficient of zero self.monomials = [monomial for monomial in simplified_terms.values() if monomial.coefficient != 0] return self def __repr__(self): return f'Polynomial({self.monomials})'

answer:from collections import deque def find_all_shortest_paths(graph: dict, start: str, end: str) -> list: Finds all unique shortest paths between start and end nodes in an undirected graph. Args: graph (dict): A dictionary representing the adjacency list of the graph. start (str): The starting node. end (str): The ending node. Returns: list: A list of lists, each containing a unique shortest path from start to end. Example: graph = { 'A': ['B', 'C'], 'B': ['A', 'D', 'E'], 'C': ['A', 'F', 'G'], 'D': ['B'], 'E': ['B', 'H'], 'F': ['C'], 'G': ['C'], 'H': ['E'] } find_all_shortest_paths(graph, 'A', 'H') should return [['A', 'B', 'E', 'H']] def bfs_paths(graph, start, end): queue = deque([(start, [start])]) visited = {start: 0} # Node to distance mapping shortest_paths = [] shortest_length = float('inf') while queue: node, path = queue.popleft() if len(path) > shortest_length: continue for neighbor in graph.get(node, []): if neighbor not in path: new_path = path + [neighbor] if neighbor == end: if len(new_path) < shortest_length: shortest_paths = [new_path] shortest_length = len(new_path) elif len(new_path) == shortest_length: shortest_paths.append(new_path) elif len(new_path) <= shortest_length: queue.append((neighbor, new_path)) return shortest_paths return bfs_paths(graph, start, end)

answer:from typing import List def josephus_sequence(n: int, k: int) -> List[int]: Generates and returns the sequence of eliminated soldiers in the Josephus problem. :param n: Number of soldiers :param k: Every k-th soldier will be eliminated :return: List of soldiers in the order they are eliminated soldiers = list(range(1, n + 1)) elimination_sequence = [] index = 0 while soldiers: index = (index + k - 1) % len(soldiers) elimination_sequence.append(soldiers.pop(index)) return elimination_sequence