reasoning-gym/reasoning_gym/games/countdown.py

from dataclasses import dataclass
from random import Random
from typing import Any, Optional

import sympy
from sympy import Symbol, symbols
from sympy.parsing.sympy_parser import parse_expr

from ..factory import ProceduralDataset, register_dataset

QUESTION_FORMAT_TEMPLATE = """{question}
Final answer format instructions:
1. Provide your solution as a arithmetic expression (no '=' sign).
2. Do not include the target number in the expression.
3. Use '*' for multiplication.
4. Use '/' for division.
5. Do not include any other text or formatting.
"""


@dataclass
class CountdownConfig:
    """Configuration for Countdown Number Game task generation"""

    min_numbers: int = 4  # Minimum numbers to provide
    max_numbers: int = 6  # Maximum numbers to provide
    min_value: int = 1  # Minimum value for source numbers
    max_value: int = 100  # Maximum value for source numbers
    min_target: int = 100  # Minimum target value
    max_target: int = 999  # Maximum target value
    operators: tuple = ("+", "-", "*", "/")  # Allowed operators
    shuffle: bool = True  # Whether to shuffle the order of source numbers
    seed: Optional[int] = None
    size: int = 500

    def validate(self) -> None:
        """Validate configuration parameters"""
        assert self.min_numbers > 1, "min_numbers must be greater than 1"
        assert self.max_numbers >= self.min_numbers, "max_numbers must be >= min_numbers"
        assert self.min_value > 0, "min_value must be positive"
        assert self.max_value >= self.min_value, "max_value must be >= min_value"
        assert self.min_target > 0, "min_target must be positive"
        assert self.max_target >= self.min_target, "max_target must be >= min_target"
        assert len(self.operators) > 0, "must specify at least one operator"
        assert all(op in ("+", "-", "*", "/") for op in self.operators), "invalid operator specified"


class CountdownDataset(ProceduralDataset):
    """Generates Countdown Number Game tasks"""

    def __init__(self, config: CountdownConfig):
        self._prompt_templates = [
            "Using the numbers {numbers}, create an expression that equals {target}.\nYou can only use each number once.",
            "Find a way to make {target} using some or all of these numbers: {numbers}.\nEach number can only be used once.",
            "Calculate {target} using the numbers {numbers}.\nEach number may be used at most once.",
        ]
        super().__init__(config=config, seed=config.seed, size=config.size)

    def __getitem__(self, idx: int) -> dict:
        """Generate a single Countdown Game task

        Returns:
            dict with keys:
                - question: str, the task description with numbers and target
                - answer: str, one possible solution expression
                - metadata: dict with generation parameters
        """
        rng = Random(self.seed + idx)

        # Generate a valid expression and its result
        expression, numbers, target = self._generate_expression(rng)

        # Optionally randomize the order of numbers
        if self.config.shuffle:
            rng.shuffle(numbers)

        numbers_str = ", ".join(map(str, numbers))

        question = rng.choice(self._prompt_templates)
        question = question.format(numbers=numbers_str, target=target)

        return {
            "question": QUESTION_FORMAT_TEMPLATE.format(question=question),
            "answer": expression,
            "metadata": {
                "numbers": numbers,
                "target": target,
                "expression": expression,
            },
        }

    def _generate_candidate_expression(self, rng: Random, num_terms: int) -> tuple[sympy.Expr, list[int], list[Symbol]]:
        """Generate a candidate expression with random numbers and operators

        Args:
            rng: Random number generator
            num_terms: Number of terms to include

        Returns:
            Tuple of (sympy expression, list of numbers, list of symbols)
        """
        # Generate random numbers
        numbers = [rng.randint(self.config.min_value, self.config.max_value) for _ in range(num_terms)]

        # Create symbols for building expression
        syms = symbols(f"x:{num_terms}")

        # Build random expression
        expr = syms[0]

        for i in range(1, num_terms):
            op = rng.choice(self.config.operators)
            if op == "+":
                expr = expr + syms[i]
            elif op == "-":
                expr = expr - syms[i]
            elif op == "*":
                expr = expr * syms[i]
            else:  # division
                # Handle division carefully to ensure integer results
                if numbers[i] != 0:  # Avoid division by zero
                    # Get current value after substituting previous numbers
                    current = int(expr.subs({sym: num for sym, num in zip(syms[:i], numbers[:i])}))
                    # Try each remaining number to find one that divides evenly
                    remaining = [n for n in numbers[i:] if n != 0]
                    rng.shuffle(remaining)  # Randomize order for variety
                    found_divisor = False
                    for div in remaining:
                        if current % div == 0:  # Check if divides evenly
                            numbers[i] = div
                            expr = expr / syms[i]
                            found_divisor = True
                            break
                    if not found_divisor:
                        # If no number divides evenly, fallback to subtraction
                        expr = expr - syms[i]
                else:
                    # Fallback to addition for zero
                    expr = expr + syms[i]

        return expr, numbers, syms

    def _generate_expression(self, rng: Random) -> tuple[str, list[int], int]:
        """Generate a valid expression and its result

        Returns:
            Tuple of (expression string, list of numbers used, target value)
        """
        num_terms = rng.randint(self.config.min_numbers, self.config.max_numbers)

        max_attempts = 100
        for attempt in range(max_attempts):
            try:
                expr, numbers, syms = self._generate_candidate_expression(rng, num_terms)

                # Substitute actual numbers to get target
                subs = {sym: num for sym, num in zip(syms, numbers)}
                target = int(expr.subs(subs))

                # Convert to string expression
                expr_str = str(expr)
                for i, sym in enumerate(syms):
                    expr_str = expr_str.replace(str(sym), str(numbers[i]))

                # Ensure target is within bounds
                if self.config.min_target <= target <= self.config.max_target:
                    return expr_str, numbers, target

            except (ValueError, ZeroDivisionError):
                continue

        raise ValueError(f"Failed to generate valid expression after {max_attempts} attempts")

    def score_answer(self, answer: Optional[str], entry: dict[str, Any]) -> float:
        """Determine if the solution provided solves the problem"""
        reward = 0.0
        metadata = entry["metadata"]
        if answer is not None:
            try:
                user_answer = int(parse_expr(answer))
                solved = user_answer == metadata["target"]
                if solved:
                    reward = 1.0
                elif len(answer.strip()) > 0:  # encourage partial solutions
                    reward = 0.05
                else:
                    reward = 0.01
            except:
                reward = 0.01
        return reward


# Register the dataset
register_dataset("countdown", CountdownDataset, CountdownConfig)