💡 Problem Formulation: Imagine you have a list of integers and you want to remove all elements that are less than ‘k’ differences away from each other. For instance, given a list [1, 3, 4, 9, 10] and ‘k’ equal to 2, you want the output to be [1, 9] because ‘3’ and ‘4’ are less than ‘2’ units away from each other, and so is ‘9’ and ’10’.
Method 1: Naive Iterative Approach
The naive iterative approach involves iterating over the sorted list and comparing each element with the next, if they are less than ‘k’ apart, the latter element is removed. This method is straightforward but not optimized for performance with large lists.
Here’s an example:
def remove_close_elements(lst, k):
lst.sort()
i = 0
while i < len(lst) - 1:
if lst[i + 1] - lst[i] < k:
del lst[i + 1]
else:
i += 1
return lst
# Example usage:
my_list = [1, 3, 4, 9, 10]
distance = 2
print(remove_close_elements(my_list, distance))
The output of this code snippet:
[1, 9]
This code snippet sorts the original list and then iteratively compares adjacent elements. If the difference between the two is less than k, the latter element is removed. The process is repeated until the end of the list is reached, resulting in a list with elements that are all ‘k’ or more differences apart.
Method 2: Using List Comprehension
A more Pythonic approach is to use list comprehension to create a new list. This method combines filtering and list construction in a concise and readable one-liner, but requires a prior understanding of list comprehension syntax and also creates a new list rather than modifying the original in-place.
Here’s an example:
def remove_close_elements_list_comprehension(lst, k):
lst.sort()
return [lst[i] for i in range(len(lst)) if i == 0 or lst[i] - lst[i-1] >= k]
# Example usage:
my_list = [1, 3, 4, 9, 10]
distance = 2
print(remove_close_elements_list_comprehension(my_list, distance))
The output of this code snippet:
[1, 9]
This code uses a list comprehension to rebuild the list from scratch, including only those elements where the difference from the previous element is greater than or equal to k. It assumes the list is already sorted, and also keeps the first element unconditionally.
Method 3: Filter with Lambda Function
For those familiar with functional programming, Python’s filter function can be used alongside a lambda to exclude close elements. This method is succinct and expressive for filtering logic but requires understanding of functional programming concepts.
Here’s an example:
def remove_close_elements_filter(lst, k):
lst.sort()
result = [lst[0]] + list(filter(lambda x, lst=lst: x - lst[lst.index(x)-1] >= k, lst[1:]))
return result
# Example usage:
my_list = [1, 3, 4, 9, 10]
distance = 2
print(remove_close_elements_filter(my_list, distance))
The output of this code snippet:
[1, 9]
This solution sorts the list and then applies a filter function to keep only those elements where the difference to the previous element (found by index look-up) is at least k. The first element is kept by default and appended to the filtered result of the rest of the list.
Method 4: Using a Queue
Involving data structure, a queue can help track elements as they’re evaluated. This method uses queues for a clearer logic flow when dealing with sequential removals. It’s especially strong when you need to maintain original order without sorting, but can be slightly more complex and have higher space complexity.
Here’s an example:
from collections import deque
def remove_close_elements_queue(lst, k):
if not lst: # guard against empty list
return []
sorted_lst = sorted(lst)
q = deque([sorted_lst[0]])
for elem in sorted_lst[1:]:
if elem - q[-1] >= k:
q.append(elem)
return list(q)
# Example usage:
my_list = [1, 3, 4, 9, 10]
distance = 2
print(remove_close_elements_queue(my_list, distance))
The output of this code snippet:
[1, 9]
The deque data structure is used to efficiently append and discard elements while iterating through the sorted list. This prevents modification of the list during iteration and allows for clear, efficient queue-based logic.
Bonus One-Liner Method 5: Using Set Operations
This one-liner relies on set operations to remove close elements: converting the list to a set, iterating over a sorted copy, and discarding elements from the set that are too close to their predecessors.
Here’s an example:
def remove_close_elements_set(lst, k):
s, prev = set(lst), float('inf')
return sorted([prev := x for x in sorted(s) if (x - prev) >= k or prev is float('inf')])
# Example usage:
my_list = [1, 3, 4, 9, 10]
distance = 2
print(remove_close_elements_set(my_list, distance))
The output of this code snippet:
[1, 9]
This one-liner uses an assignment expression within a list comprehension, taking advantage of the fact that set operations discard duplicates and sorted() returns a list, to ensure elements are only added when the difference with the previous element is k or more.
Summary/Discussion
- Method 1: Naive Iterative Approach. Strength: Easy to understand. Weakness: Doesn’t handle large lists well due to inefficient in-place deletions.
- Method 2: List Comprehension. Strength: Pythonic and concise. Weakness: Requires extra space for the new list and prior knowledge of list comprehensions.
- Method 3: Filter with Lambda Function. Strength: Expressive and functional. Weakness: Lower readability for those unfamiliar with lambda expressions.
- Method 4: Using a Queue. Strength: Maintains order and clear logic. Weakness: Higher space complexity due to additional data structure.
- Method 5: One-Liner with Set Operations. Strength: Compact and elegant. Weakness: Higher cognitive load to understand set operations and assignment expressions.