💡 Problem Formulation: Imagine you have a list of numbers and you need to analyze every ‘window’ or segment of size k to ensure that each number within that window is unique. For example, given the list [1, 2, 3, 4, 2, 5] and a window size k = 4, we want to find which 4-number segments contain all unique elements. The desired output would be a list of the start indices of the windows where this condition holds true.
Method 1: Using Loops and Sets
This classical approach checks each window sequentially, converts it into a set, and compares its size to k to ensure all elements are unique. If they are, the starting index of the window is added to the result list.
Here’s an example:
def find_unique_windows(lst, k):
unique_starts = []
for i in range(len(lst) - k + 1):
window = lst[i:i+k]
if len(window) == len(set(window)):
unique_starts.append(i)
return unique_starts
# Example usage:
print(find_unique_windows([1, 2, 3, 4, 2, 5], 4))Output: [0, 1]
By converting the window to a set, we are ensuring all elements are unique since sets cannot contain duplicates. The code iterates over every possible window in the list and appends the index to unique_starts if the set size matches the window size, indicating all elements are unique.
Method 2: Sliding Window and Dictionary
This method uses a dictionary to keep track of element counts within the window. It slides the window across the list while updating the counts and checks for uniqueness at each step.
Here’s an example:
from collections import defaultdict
def find_unique_windows(lst, k):
unique_starts = []
counts = defaultdict(int)
for i, num in enumerate(lst):
if i >= k:
counts[lst[i-k]] -= 1
counts[num] += 1
if i >= k-1 and all(count == 1 for count in counts.values()):
unique_starts.append(i-k+1)
return unique_starts
# Example usage:
print(find_unique_windows([1, 2, 3, 4, 2, 5], 4))Output: [0, 1]
This snippet uses a sliding window technique for efficiency. At every step, it updates the count of the entering and exiting elements. If the counts are all one (indicating all elements are unique within the window), the start index is recorded.
Method 3: Optimized Sliding Window with Set
This optimized version of the sliding window method uses a set to quickly check if a new number is already in the current window, potentially reducing the overall runtime.
Here’s an example:
def find_unique_windows(lst, k):
unique_starts = []
current_set = set()
for i in range(len(lst)):
if i >= k:
current_set.remove(lst[i - k])
if lst[i] not in current_set:
current_set.add(lst[i])
if i >= k - 1:
unique_starts.append(i - k + 1)
else:
current_set.clear() # Reset if a duplicate is found
return unique_starts
# Example usage:
print(find_unique_windows([1, 2, 3, 4, 2, 5], 4))Output: [0, 1]
In this strategy, we use a set current_set to keep track of the unique elements in the current sliding window. If a duplicate is encountered, the set is cleared. Only when a window satisfies the uniqueness condition, the starting index is noted.
Method 4: Using itertools and islice
The itertools library can be used to efficiently generate sliding windows, combined with islice to provide the desired window size. This method may have easier readability for some Python users.
Here’s an example:
from itertools import islice
def find_unique_windows(lst, k):
unique_starts = []
for start_idx in range(len(lst) - k + 1):
window = islice(lst, start_idx, start_idx + k)
if len(set(window)) == k:
unique_starts.append(start_idx)
return unique_starts
# Example usage:
print(find_unique_windows([1, 2, 3, 4, 2, 5], 4))Output: [0, 1]
This code utilizes islice from the itertools module to create the windows, checks for uniqueness through a set and appends the index to the result list if the criterion is met.
Bonus One-Liner Method 5: List Comprehension with Sets
This concise method uses list comprehension together with set uniqueness checking to create a one-liner solution.
Here’s an example:
find_unique_windows = lambda lst, k: [i for i in range(len(lst) - k + 1) if len(set(lst[i:i+k])) == k] # Example usage: print(find_unique_windows([1, 2, 3, 4, 2, 5], 4))
Output: [0, 1]
This one-liner leverages Python’s list comprehension to iteratively build the result list, inserting the index only when the set built from a window has a length equal to k, ensuring uniqueness within that window.
Summary/Discussion
- Method 1: Loop and Set. Straightforward and easy to understand. Performance can degrade for large lists due to repeated conversions to sets.
- Method 2: Sliding Window and Dictionary. More efficient than method 1 but slightly more complex. Uses a constant number of element checks for uniqueness regardless of window size.
- Method 3: Optimized Sliding Window with Set. Offers good performance and is easy to understand. Resets the state when a duplicate is found, which may lead to slightly more work in some cases.
- Method 4: Itertools and Islice. Leverages Python’s standard library for clean and concise code. May not always offer performance benefits depending on implementation details of itertools.
- Bonus Method 5: List Comprehension with Sets. Offers a quick, readable one-liner for simple use-cases. Can still suffer from performance issues with large lists and does not reveal intent as clearly as other methods.