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69 lines
2.6 KiB
Python
69 lines
2.6 KiB
Python
"""Least Common Multiple (LCM) task generator"""
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from dataclasses import dataclass
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from functools import reduce
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from math import lcm
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from random import Random
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from typing import Optional
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from ..factory import ProceduralDataset, register_dataset
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@dataclass
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class LCMConfig:
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"""Configuration for LCM task generation"""
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min_numbers: int = 2 # Minimum numbers to find LCM of
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max_numbers: int = 2 # Maximum numbers to find LCM of
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min_value: int = 1 # Minimum value for each number
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max_value: int = 100 # Maximum value for each number (kept smaller than GCD default since LCM grows fast)
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seed: Optional[int] = None
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size: int = 500 # Virtual dataset size
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def validate(self) -> None:
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"""Validate configuration parameters"""
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assert self.min_numbers >= 2, "min_numbers must be at least 2"
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assert self.max_numbers >= self.min_numbers, "max_numbers must be >= min_numbers"
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assert self.min_value >= 1, "min_value must be positive"
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assert self.max_value > self.min_value, "max_value must be > min_value"
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class LCMDataset(ProceduralDataset):
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"""Generates Least Common Multiple (LCM) tasks"""
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def __init__(self, config: LCMConfig):
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super().__init__(config=config, seed=config.seed, size=config.size)
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def _generate_numbers(self, rng: Random) -> tuple[list[int], int]:
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"""Generate a list of random positive integers and their LCM.
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Will try up to 3 times to find numbers with LCM < product."""
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def calculate_product(nums: list[int]) -> int:
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return reduce(lambda x, y: x * y, nums)
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# Try up to 3 times to get LCM < product
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for _ in range(3):
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num_count = rng.randint(self.config.min_numbers, self.config.max_numbers)
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numbers = [rng.randint(self.config.min_value, self.config.max_value) for _ in range(num_count)]
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result = reduce(lcm, numbers)
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if result < calculate_product(numbers):
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break
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# Return the last generated numbers, whether they met the criteria or not
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return numbers, result
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def __getitem__(self, idx: int) -> dict:
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"""Generate a single LCM task"""
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rng = Random(self.seed + idx)
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numbers, result = self._generate_numbers(rng)
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numbers_str = ", ".join(str(n) for n in numbers)
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return {
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"question": f"Find the Least Common Multiple (LCM) of these numbers: {numbers_str}",
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"answer": str(result),
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"metadata": {"numbers": numbers, "result": result},
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}
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register_dataset("lcm", LCMDataset, LCMConfig)
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