There is a publicly available library for DLX algorithm (also known as 'Algorithm X' or 'Dancing Links' algorithm) available at https://pypi.org/project/dlx/

exampleDLX.py

from dlx import DLX

def genInstance(labels, rows) :
    columns = []
    indices_l = {}
    for i in range(len(labels)) :
        label = labels[i]
        indices_l[label] = i
        columns.append(tuple([label,0]))
    return labels, rows, columns, indices_l

def solveInstance(instance) :
    labels, rows, columns, indices_l = instance
    instance = DLX(columns)
    indices = {}
    for l, i in zip(rows, range(len(rows))) :
        h = instance.appendRow(l, 'r'+str(i))
        indices[str(hash(tuple(sorted(l))))] = i
    sol = instance.solve()
    lst = list(sol)
    selected = []
    for i in lst[0] :
        l = instance.getRowList(i)
        l2 = [indices_l[label] for label in l]
        idx = indices[str(hash(tuple(sorted(l2))))]
        selected.append(idx)
    return selected

def printColumnsPerRow(instance, selected) :
    labels, rows, columns, indices_l = instance
    print 'covered columns per selected row'
    for s in selected :
        A = []
        for z in rows[s-1] :
            c, _ = columns[z]
            A.append(c)
        print s, A

def printInstance(instance) :
    labels, rows, columns, indices_l = instance
    print 'columns'
    print labels
    print 'rows'
    print rows



'''
example instance #1
source: https://www.cs.mcgill.ca/~aassaf9/python/algorithm_x.html

   A B C D E F G
0  1 0 0 1 0 0 1  (0, 3, 6)
1  1 0 0 1 0 0 0  (0, 3)
2  0 0 0 1 1 0 1  (3, 4, 6)
3  0 0 1 0 1 1 0  (2, 4, 5)
4  0 1 1 0 0 1 1  (1, 2, 5, 6)
5  0 1 0 0 0 0 1  (1, 6)

expected solution: 1, 3, 5

   A B C D E F G
1  1 _ _ 1 _ _ _  (0, 3)
3  _ _ 1 _ 1 1 _  (2, 4, 5)
5  _ 1 _ _ _ _ 1  (1, 6)
'''

labels = ['A', 'B', 'C', 'D', 'E', 'F', 'G']
print 'instance #1'
rows = [[0,3,6],[0,3],[3,4,6],[2,4,5],[1,2,5,6],[1,6]]
instance = genInstance(labels, rows)
selected = solveInstance(instance)
printInstance(instance)
printColumnsPerRow(instance, selected)
print ''

'''
example instance #2
source: https://lanl.arxiv.org/pdf/cs/0011047

   A B C D E F G
0  0 0 1 0 1 1 0  (2, 4, 5)
1  1 0 0 1 0 0 1  (0, 3, 6)
2  0 1 1 0 0 1 0  (1, 2, 5)
3  1 0 0 1 0 0 0  (0, 3)
4  0 1 0 0 0 0 1  (1, 6)
5  0 0 0 1 1 0 1  (3, 4, 6)

expected solution: 0, 3, 4

   A B C D E F G
0  _ _ 1 _ 1 1 _  (2, 4, 5)
3  1 _ _ 1 _ _ _  (0, 3)
4  _ 1 _ _ _ _ 1  (1, 6)
'''

print 'instance #2'
rows = [[2, 4, 5], [0, 3, 6], [1, 2, 5], [0, 3], [1, 6], [3, 4, 6]]
instance = genInstance(labels, rows)
selected = solveInstance(instance)
printInstance(instance)
printColumnsPerRow(instance, selected)

output.txt

instance #1
columns
['A', 'B', 'C', 'D', 'E', 'F', 'G']
rows
[[0, 3, 6], [0, 3], [3, 4, 6], [2, 4, 5], [1, 2, 5, 6], [1, 6]]
covered columns per selected row
1 ['A', 'D', 'G']
3 ['D', 'E', 'G']
5 ['B', 'C', 'F', 'G']

instance #2
columns
['A', 'B', 'C', 'D', 'E', 'F', 'G']
rows
[[2, 4, 5], [0, 3, 6], [1, 2, 5], [0, 3], [1, 6], [3, 4, 6]]
covered columns per selected row
3 ['B', 'C', 'F']
0 ['D', 'E', 'G']
4 ['A', 'D']