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104 lines
3.7 KiB
Python
104 lines
3.7 KiB
Python
"""Least Common Multiple (LCM) task generator"""
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from dataclasses import dataclass
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from random import Random
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from typing import List, Optional, Tuple
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from math import lcm
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from functools import reduce
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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):
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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:
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"""Generates Least Common Multiple (LCM) tasks"""
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def __init__(self, config: LCMConfig):
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self.config = config
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self.config.validate()
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self.seed = config.seed if config.seed is not None else Random().randint(0, 2**32)
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def __len__(self) -> int:
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return self.config.size
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def __iter__(self):
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self._current_idx = 0
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return self
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def __next__(self):
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if self._current_idx >= self.config.size:
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raise StopIteration
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item = self[self._current_idx]
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self._current_idx += 1
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return item
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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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for _ in range(3): # Try up to 3 times to get LCM < product
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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)
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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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return numbers, result
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# If we failed to find LCM < product after 3 tries, generate one final set
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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)
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for _ in range(num_count)]
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result = reduce(lcm, numbers)
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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": {
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"numbers": numbers,
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"result": result
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}
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}
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def lcm_dataset(
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min_numbers: int = 2,
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max_numbers: int = 2,
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min_value: int = 1,
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max_value: int = 100,
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seed: Optional[int] = None,
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size: int = 500,
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) -> LCMDataset:
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"""Create a LCMDataset with the given configuration."""
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config = LCMConfig(
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min_numbers=min_numbers,
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max_numbers=max_numbers,
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min_value=min_value,
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max_value=max_value,
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seed=seed,
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size=size,
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)
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return LCMDataset(config)
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