# Copyright (c) OpenAI (https://openai.com)

# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:

# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
# ============================================================================
import itertools
import numpy as np

from typing import *


def estimate_pass_at_k(
        num_samples: Union[int, List[int], np.ndarray],
        num_correct: Union[List[int], np.ndarray],
        k: int
) -> np.ndarray:
    """
    Estimates pass@k of each problem and returns them in an array.
    """

    def estimator(n: int, c: int, k: int) -> float:
        """
        Calculates 1 - comb(n - c, k) / comb(n, k).
        """
        if n - c < k:
            return 1.0
        return 1.0 - np.prod(1.0 - k / np.arange(n - c + 1, n + 1))

    if isinstance(num_samples, int):
        num_samples_it = itertools.repeat(num_samples, len(num_correct))
    else:
        assert len(num_samples) == len(num_correct)
        num_samples_it = iter(num_samples)

    return np.array([estimator(int(n), int(c), k) for n, c in zip(num_samples_it, num_correct)])