Python 有效地删除最大数量的二进制元素，同时将行和列总和保持在一定水平以上

我有以下问题，我很难为它编写优化的程序.

我得到了一个2D二进制数组(所有元素都是0或1，其形状是(n，m))，我需要从数组中删除最大数量的元素，同时保持每行之和大于min_x，每列之和大于min_y的属性.

我已经编写了以下非优化代码，它可以很好地用于小数组:

import numpy as np
from typing import Optional, Tuple
from itertools import product
from tqdm import tqdm

def min_dataset(data, min_x, min_y):
    '''Data is a row-major numpy array of shape (n, m), consisting of only 0s and 1s (a mask).
    min_x and min_y are the minimum number of 1s in each row and column, respectively.
    This function returns a new data array, where each row and column has at least min_x and min_y 1s, respectively, and there are as few 1s as possible.
    '''
    best_solution = data
    score = np.sum(best_solution)
    # format: {matrix.tobytes(): (best_matrix, score)}

    memo = {}

    if np.any(np.sum(data, axis=0) < min_y) or np.any(np.sum(data, axis=1) < min_x):
        return None

    def get_best(data, main=False) -> Tuple[np.ndarray, int]:
        '''Gets the matrix with the lowest score, given the constraints.
        Uses memoization.
        '''
        nonlocal memo
        if data.tobytes() in memo:
            return memo[data.tobytes()]
        
        # Find the rows with more than min_x 1s
        can_remove_rows = np.sum(data, axis=1) > min_x
        # Find the columns with more than min_y 1s
        can_remove_columns = np.sum(data, axis=0) > min_y

        if (not np.any(can_remove_rows)) or (not np.any(can_remove_columns)):
            # If there's no row or column where we can remove a 1, we're done
            ans = (data, np.sum(data))
            memo[data.tobytes()] = (data, np.sum(data))
            return ans
        
        # Try removing each combination of rows and columns where we can remove a 1
        best = data, np.sum(data)
        # print(np.nonzero(can_remove_rows))
        # print(np.nonzero(can_remove_columns))
        iterator = product(np.nonzero(can_remove_rows)[0], np.nonzero(can_remove_columns)[0])
        if main:
            iterator = tqdm(list(iterator))
        for row, col in iterator:
            # print(row, col)
            if data[row, col] == 0:
                continue
            
            # Remove the 1 at (row, col)
            new_data = data.copy()
            new_data[row, col] = 0

            # Check if the new matrix is valid
            if np.any(np.sum(new_data, axis=0) < min_y) or np.any(np.sum(new_data, axis=1) < min_x):
                continue

            # Recurse
            new_best = get_best(new_data)
            if new_best[1] < best[1]:
                best = new_best

        memo[data.tobytes()] = best
        return best

    get_best(data, main=True)
    best = memo[data.tobytes()][0]
    return best

if __name__ == "__main__":
    # Create a random 5x5 binary matrix
    data = np.random.randint(0, 2, (5, 5))
    print(data)
    print("computing")
    ans = min_dataset(data, 1, 1)
    print("Solution:")
    print(ans)
    print("Score (lower is better; None means no solution was found.):")
    print(np.sum(ans))

示例输出:

 [[0 1 0 0 0]
 [1 1 1 1 1]
 [1 1 0 1 1]
 [0 1 1 0 1]
 [0 1 1 0 1]]
computing
100%|█████████████████████████████████████████████████████████████████████████████████| 20/20 [00:02<00:00,  8.27it/s]
Solution:
[[0 1 0 0 0]
 [0 0 0 1 0]
 [1 0 0 0 0]
 [0 0 0 0 1]
 [0 0 1 0 0]]
Score (lower is better; None means no solution was found.):
5

然而，一旦我开始使用10x10矩阵，代码就运行得非常慢，我需要能够运行20000x500矩阵.

我如何才能加速我的代码？