💡 Problem Formulation: Given an array of integers, the task is to find a list where each element is the square of the elements of the original array, sorted in non-decreasing order. For example, from an input array [-4, -1, 0, 3, 10], we want to output a sorted squared array [0, 1, 9, 16, 100].
Method 1: Using a Map and Sort
An efficient way to solve this challenge involves mapping each element to its square and then sorting the resulting list. The map() function applies the square operation to each element, and sorted() ensures the final list is in ascending order.
Here’s an example:
input_list = [-4, -1, 0, 3, 10] squared_sorted_list = sorted(map(lambda x: x**2, input_list)) print(squared_sorted_list)
Output: [0, 1, 9, 16, 100]
This code snippet is straightforward: it first squares each element in the original list using a lambda function inside the map. The sorted() function then returns a new list with all squared elements in ascending order.
Method 2: Using List Comprehension and Sort
List comprehension in Python is a concise and readable way to create lists. By coupling list comprehension with the sort() method, one can efficiently generate and sort a squared list.
Here’s an example:
input_list = [-4, -1, 0, 3, 10] squared_sorted_list = [x ** 2 for x in input_list] squared_sorted_list.sort() print(squared_sorted_list)
Output: [0, 1, 9, 16, 100]
The above snippet squares each item in the input list through list comprehension and then sorts the resulting list in place. This method is very Pythonic and favored for its simplicity and elegance.
Method 3: Using a Heap Queue
Utilizing Python’s heapq module can be a great approach where each squared element is pushed into a heap to keep it always sorted. This can be more efficient for very large lists compared to a full sort.
Here’s an example:
import heapq
input_list = [-4, -1, 0, 3, 10]
heap = []
for num in input_list:
heapq.heappush(heap, num ** 2)
squared_sorted_list = [heapq.heappop(heap) for _ in range(len(heap))]
print(squared_sorted_list)Output: [0, 1, 9, 16, 100]
The code creates a heap and pushes the squared elements onto it. The heap maintains the elements in sorted order, which are then popped out into a list. This is an efficient way to sort as the list is being built.
Method 4: Two-pointer Technique
For a list of sorted integers, the two-pointer technique can be useful. Pointers start from both ends of the list, compare absolute values, square the larger one, and move the pointers inward until they meet.
Here’s an example:
input_list = [-4, -1, 0, 3, 10]
squared_sorted_list = []
left = 0
right = len(input_list) - 1
while left abs(input_list[right]):
squared_sorted_list.append(input_list[left]**2)
left += 1
else:
squared_sorted_list.append(input_list[right]**2)
right -= 1
squared_sorted_list.reverse() # Squares are added in reverse sorted order
print(squared_sorted_list)Output: [0, 1, 9, 16, 100]
This snippet uses two pointers to traverse the list from both ends, always squaring and adding the larger absolute value first. Because it fills the result list from highest to lowest, we reverse it at the end.
Bonus One-Liner Method 5: Using NumPy
NumPy, a powerful numerical computing library in Python, can square and sort an array efficiently, especially for large datasets.
Here’s an example:
import numpy as np input_array = np.array([-4, -1, 0, 3, 10]) squared_sorted_array = np.sort(input_array ** 2) print(squared_sorted_array)
Output: [ 0 1 9 16 100]
This elegant one-liner first squares the whole array using NumPy’s element-wise operation and immediately sorts it. NumPy’s optimized algorithms make this method very fast, particularly suitable for large-scale operations.
Summary/Discussion
- Method 1: Map and Sort. It is simple and has a clear intent. Works efficiently for small to medium-sized lists. However, it could be slightly slower than more optimized methods for larger lists.
- Method 2: List Comprehension and Sort. Offers excellent readability and is Pythonic. Recommended for those who favor comprehension and in-place sorting. It has similar performance considerations as Method 1.
- Method 3: Heap Queue. This is more efficient for larger datasets as it maintains a sorted state while building the list. However, it’s less readable than other methods and can be overkill for small lists.
- Method 4: Two-pointer Technique. Highly efficient for sorted lists, it minimizes operations by handling negative numbers smartly. However, it can be less intuitive and harder to understand at first.
- Bonus Method 5: Using NumPy. Quick and concise, perfect for those working with large numerical datasets regularly. However, it introduces a dependency on NumPy, which may not be necessary for smaller problems.