💡 Problem Formulation: Given a list of integers, the goal is to split it into multiple sublists where each sublist is strictly increasing and has a size greater than a specified value k. For example, given the input list [1, 2, 3, 2, 4, 6] and k = 2, the desired output would be [[1, 2, 3], [4, 6]].
Method 1: Iterative Approach
This method involves iterating over the input list elements and maintaining a current sublist. We append to the current sublist if the next number is greater than the last number in the current sublist. Once an element is smaller or equal, we check if the current sublist is of size greater than k, then start a new sublist. This method ensures that we have strictly increasing sequences, and discards sequences that do not meet the size threshold.
Here’s an example:
def split_into_sublists(lst, k):
sublists, current = [], []
for number in lst:
if not current or number > current[-1]:
current.append(number)
else:
if len(current) > k:
sublists.append(current)
current = [number]
if len(current) > k:
sublists.append(current)
return sublists
print(split_into_sublists([1, 2, 3, 2, 4, 6], 2))Output:
[[1, 2, 3], [4, 6]]
The function split_into_sublists() takes a list and a threshold k, iterating through the list and constructing sublists. When the current element is no longer increasing, it checks if the current sublist’s length exceeds k, appends it to the result if it does, and resets the current sublist.
Method 2: Using GroupBy from itertools
The itertools.groupby function is a powerful utility that can be used to group elements of a list based on a certain condition. For splitting into increasing sublists, a custom key function can be used to identify when the sequence increases, combined with a filtering step to disregard sublists of insufficient size. This method is succinct and leverages Python’s standard library.
Here’s an example:
from itertools import groupby
def key_func(pair):
return pair[0] k:
sublists.append(sublist)
return sublists
print(split_into_sublists([1, 2, 3, 2, 4, 6], 2))Output:
[[1, 2, 3], [4, 6]]
The provided example uses groupby to create iterators for strictly increasing sequences based on a custom key function that compares adjacent elements. Sublists are then materialized and checked against the size threshold k before being added to the result.
Method 3: Recursive Approach
The recursive approach is a divide-and-conquer strategy that splits the list upon finding a non-increasing element, recursively applies the same logic to the remaining list elements, and keeps track of the size to ensure that sublists are longer than k. This approach is intuitive for those who think recursively and is elegant for complex splitting criteria.
Here’s an example:
def split_into_sublists(lst, k, start=0, current=None):
if current is None:
current = []
if start >= len(lst):
return [current] if len(current) > k else []
if not current or lst[start] > current[-1]:
current.append(lst[start])
return split_into_sublists(lst, k, start+1, current)
else:
return ([current] if len(current) > k else []) + split_into_sublists(lst, k, start+1, [lst[start]])
print(split_into_sublists([1, 2, 3, 2, 4, 6], 2))Output:
[[1, 2, 3], [4, 6]]
This recursive method split_into_sublists() works by adding elements to a sublist as long as they are increasing and recursing with a sliced list once they are not. The base case ensures only sublists of size greater than k are returned.
Method 4: Using Zip and List Comprehensions
Python’s list comprehensions provide a concise way to create lists. Combined with the zip function, we can compare adjacent elements to determine where to split the list. This method is Pythonic and leverages list comprehensions for their readability and expressiveness.
Here’s an example:
def split_into_sublists(lst, k):
indices = [i for i, (x, y) in enumerate(zip(lst, lst[1:]+[float('inf')]), 1) if y k]
print(split_into_sublists([1, 2, 3, 2, 4, 6], 2))Output:
[[1, 2, 3], [4, 6]]
The example shows how zip is used to pair each element with its successor, then list comprehensions are utilized to find splitting points and generate the strictly increasing sublists if they’re larger than k.
Bonus One-Liner Method 5: Using NumPy
For those who are comfortable with numerical computing, using NumPy can be a very effective way to perform operations on arrays that include splitting based on conditions. The one-liner might be slightly more opaque but incredibly performant for large datasets. This method showcases the power of NumPy’s array operations.
Here’s an example:
import numpy as np
def split_into_sublists(lst, k):
lst = np.array(lst)
return [list(sub) for sub in np.split(lst, np.where(np.diff(lst) k]
print(split_into_sublists([1, 2, 3, 2, 4, 6], 2))Output:
[[1, 2, 3], [4, 6]]
The code utilizes NumPy’s diff function to find where the list stops increasing. It then splits the array at these points and filters out any subarrays that do not satisfy the size constraint k.
Summary/Discussion
- Method 1: Iterative Approach. Strengths: Straightforward, no extra libraries needed. Weaknesses: Imperative and might not be the most efficient.
- Method 2: Using GroupBy from itertools. Strengths: Clean code using standard library functions. Weaknesses: May be less intuitive for those unfamiliar with
groupby. - Method 3: Recursive Approach. Strengths: Intuitive divide-and-conquer logic. Weaknesses: Potentially high space complexity due to stack usage.
- Method 4: Using Zip and List Comprehensions. Strengths: Pythonic and concise. Weaknesses: Can be less readable for beginners.
- Method 5: Using NumPy. Strengths: Very efficient for large datasets. Weaknesses: Requires NumPy, which may be an unnecessary dependency for some applications.