Sort List of Lists by Lexicographic Value and then Length - Python

In this problem, sorting a list of lists by lexicographic value and then length means arranging the sublists first by their natural order (lexicographically) and then by their size. For example: For the list [[3, 2], [1, 4, 6], [1, 2], [3, 2, 1]], sorting by lexicographic value and then by length would yield [[1, 2], [3, 2], [1, 4, 6], [3, 2, 1]].

Using sort() Twice 

This method first sorts the lists lexicographically and then by length. sort() function is called twice: the first to handle lexicographic sorting and the second to sort by the list length.

li = [[3, 2], [1, 4, 6], [1, 2], [3, 2, 1]]

li.sort()  # lexicographic sort
li.sort(key=len) # length-based sort

print(li) 

[[1, 2], [3, 2], [1, 4, 6], [3, 2, 1]]

Using Lambda Function

This method optimizes the sorting process by calling the sorted() function only once then lambda function is used as the key combining the sorting criteria of length and lexicographic order in a single step.

li = [[1, 4, 3, 2], [5, 4, 1], [1, 4, 6, 7]]

# sorting using lambda function
res = sorted(li, key=lambda x: (len(x), x))

print(res)  

[[5, 4, 1], [1, 4, 3, 2], [1, 4, 6, 7]]

Explanation: The key in sorted() uses a lambda function that generates a tuple (len(x), x) for each sublist x. This ensures sorting by length first and then lexicographically if lengths are the same.

Using cmp_to_key from functools

Instead of sorting directly with a key function we use cmp_to_key() to define a custom sorting behavior that sorts lists first by length and then lexicographically.

from functools import cmp_to_key

li = [[1, 4, 3, 2], [5, 4, 1], [1, 4, 6, 7]]

# Sorting using cmp_to_key, first by length, then lexicographically
res = sorted(li, key=cmp_to_key(lambda a, b: (len(a) - len(b)) or (-1 if a < b else (1 if a > b else 0))))

print(res)

[[5, 4, 1], [1, 4, 3, 2], [1, 4, 6, 7]]

Explanation:

• lambda function works by first comparing the lengths of a and b and if they are different it sorts based on length.
• If the lengths are equal then it compares the lists lexicographically using these notations: -1 (less than), 1 (greater than), or 0 (equal).

Using Heap Sort

This method uses heap data structure to sort the list of lists in which we first convert the lists into a heap and then extract the minimum element one by one, ensuring they are sorted by length and lexicographically.

import heapq

li = [[1, 4, 3, 2], [5, 4, 1], [1, 4, 6, 7]]

# Convert the list into a heap and sort
heapq.heapify(li)
res = [heapq.heappop(li) for _ in range(len(li))]

print(res)

[[1, 4, 3, 2], [1, 4, 6, 7], [5, 4, 1]]

Explanation

• heapq.heapify() transforms the list into a heap ensuring it can be accessed in a sorted order.
• heappop() retrieves the smallest elements based on the sorting rules which ensures the correct order.