Shuffling sequences in a list

I have a list containing sequences of various lengths. The pattern of a sequence is as follows:

x_k, y_k, ..., x_k_i, y_k_i, ... z_k

For example, a list having 4 sequences with lengths: 3, 3, 5, and 7 is as follows:

input_list = ['x_1', 'y_1', 'z_1', 
              'x_2', 'y_2', 'z_2', 
              'x_3_1', 'y_3_1', 'x_3_2', 'y_3_2', 'z_3', 
              'x_4_1', 'y_4_1', 'x_4_2', 'y_4_2', 'x_4_3', 'y_4_3', 'z_4']

I need to shuffle the list, such that the order of sequences is shuffled, but the entries within a sequence is not shuffled.

For example, a candidate output would be as follows:

shuffled_list = ['x_3_1', 'y_3_1', 'x_3_2', 'y_3_2', 'z_3', 
                 'x_1', 'y_1', 'z_1',
                 'x_4_1', 'y_4_1', 'x_4_2', 'y_4_2', 'x_4_3', 'y_4_3', 'z_4',
                 'x_2', 'y_2', 'z_2']

One way to achieve this would be by saving each sequence as a separate list, and then having a nested list represent all the sequences. Then, one by one randomly removing a list (i.e., a sequence) from the nested list and appending the removed list's elements in the final shuffled list.

Is there a more efficient way to achieve the same?

You can group your items on the first index, with the use of itertools.groupby:

from itertools import groupby

input_list = ['x_1', 'y_1', 'z_1', 
              'x_2', 'y_2', 'z_2', 
              'x_3_1', 'y_3_1', 'x_3_2', 'y_3_2', 'z_3', 
              'x_4_1', 'y_4_1', 'x_4_2', 'y_4_2', 'x_4_3', 'y_4_3', 'z_4']

def key(x):
    return x.split('_')[1]

group_dic = {k:list(g) for k,g in groupby(input_list, key=key)}

{'1': ['x_1', 'y_1', 'z_1'],
 '2': ['x_2', 'y_2', 'z_2'],
 '3': ['x_3_1', 'y_3_1', 'x_3_2', 'y_3_2', 'z_3'],
 '4': ['x_4_1', 'y_4_1', 'x_4_2', 'y_4_2', 'x_4_3', 'y_4_3', 'z_4']}

Of course you don't HAVE to make a dictionary; you can use the results however you want.

Now on to the shuffling part:

from random import shuffle

order = list(group_dic.keys())
shuffle(order)

output_list = [entry for i in order for entry in group_dic[i]]

Example output:

['x_1', 'y_1', 'z_1', 'x_4_1', 'y_4_1', 'x_4_2', 'y_4_2', 'x_4_3', 'y_4_3', 'z_4', 'x_2', 'y_2', 'z_2', 'x_3_1', 'y_3_1', 'x_3_2', 'y_3_2', 'z_3']

Edit: following on @Timus' idea, if you have a list of lengths of the subgroups, you can make a list of corresponding ranges, shuffle it, then build the output_list from the shuffled ranges; for example:

from itertools import accumulate, pairwise
from random import shuffle

lengths =  [3, 3, 5, 7]
ranges = [slice(*pair) for pair in pairwise(accumulate(lengths, initial=0))]
shuffle(ranges)
output_list = sum((input_list[range] for range in ranges), start=[])

# ['x_1', 'y_1', 'z_1', 'x_4_1', 'y_4_1', 'x_4_2', 'y_4_2', 'x_4_3', 'y_4_3', 'z_4', 'x_2', 'y_2', 'z_2', 'x_3_1', 'y_3_1', 'x_3_2', 'y_3_2', 'z_3']

If the format of entries is strictly as shown in the example, then following @Swifty's comment, the list can be shuffled using itertools.groupby.

import itertools
import random

input_list = ['x_1', 'y_1', 'z_1', 
              'x_2', 'y_2', 'z_2', 
              'x_3_1', 'y_3_1', 'x_3_2', 'y_3_2', 'z_3', 
              'x_4_1', 'y_4_1', 'x_4_2', 'y_4_2', 'x_4_3', 'y_4_3', 'z_4']

# Grouping the entries by their sequence
sequences = [list(g) for k, g in itertools.groupby(input_list, lambda x: x.split('_')[1] if '_' in x else x)]

random.shuffle(sequences)

# Flattening the shuffled list
shuffled_list = list(itertools.chain(*sequences))