from abc import ABC, abstractmethod
from typing import Any, Dict, List

class BaseProblem(ABC):
    """
    Abstract base class for all algorithm problems.
    """

    @abstractmethod
    def generate_case(self, **kwargs) -> Dict[str, Any]:
        """
        Generate a random test case based on parameters.
        """
        pass

    @abstractmethod
    def solve(self, input_data: Any, algorithm: str) -> Any:
        """
        Solve the problem using the specified algorithm.
        """
        pass

    @abstractmethod
    def verify(self, input_data: Any, result: Any) -> bool:
        """
        Verify the correctness of the result (optional, or compare with standard answer).
        """
        pass