```{code-cell} ipython3

sol_found = []

cost = []

rng = np.random.default_rng()

# simulate 1000 times

for i in range(1000):

np.random.shuffle(arr)

rng.shuffle(arr)

res_shuffle = linprog(C_vec, A_eq=A[arr], b_eq=b[arr])

# if find a new solution

def build_nodes_of_one_type(group='p', n=100, seed=123):

nodes = []

np.random.seed(seed)

rng = np.random.default_rng(seed)

for i in range(n):

if group == 'p':

m = 1/n

x = np.random.uniform(-2, 2)

y = np.random.uniform(-2, 2)

x = rng.uniform(-2, 2)

y = rng.uniform(-2, 2)

else:

m = betabinom.pmf(i, n-1, 2, 2)

x = 0.6 * np.random.uniform(-1.5, 1.5)

y = 0.6 * np.random.uniform(-1.5, 1.5)

x = 0.6 * rng.uniform(-1.5, 1.5)

y = 0.6 * rng.uniform(-1.5, 1.5)

name = group + str(i)

nodes.append(Node(x, y, m, group, name))