# Minimal Forts Function
# Author: Derek Hanely
# Last Updated: March 17, 2024
def minForts(G):
    """
    A brute-force algorithm for producing all minimal forts of a graph.

    INPUT: A simple, undirected graph G.

    OUTPUT: Returns a list of the minimal forts of G.
    """
    V=G.vertices(sort=True)
    forts=[]
    for F in powerset(V): # check if F is a fort of G
        if len(F)<=1: continue
        for u in Set(V).difference(Set(F)):
            neighbors = G.neighbors(u)
            if len(Set(F).intersection(Set(neighbors)))==1: break
        else:
            forts.append(F)
    uni_forts=[]
    for x in forts:
        if x not in uni_forts:
            uni_forts.append(x)

    min_forts=deepcopy(uni_forts)
    for x in uni_forts: # minimality check
        if any((Set(x).issuperset(Set(y)) and y!=x) for y in uni_forts):
            min_forts.remove(x)

    return min_forts

### EXAMPLE ###

# Generate the sequence of minimal forts of the wheel graph containing the center

for n in range(4,20):
    G=graphs.WheelGraph(n)
    min_forts = minForts(G)
    count = len([mf for mf in min_forts if 0 in mf]) # check if center vertex is in the minimal fort
    print('n =',n,': ','min forts w/ cntr: ',count)