💡 Problem Formulation: The task is to determine the indices of a list that would remain after sequentially deleting the smallest elements until the list is empty. For example, given the list [3, 1, 2], the order of deletion would be elements at indices [1, 2, 0], respectively. This article explores five methods to programmatically identify these indices in Python.
Method 1: Using Sorted Index Pairs
This method involves creating a list of tuples, where each tuple contains an element and its original index. By sorting this list and mapping the second elements (the original indices) to a new list, we get the desired index order for the deletions.
Here’s an example:
arr = [3, 1, 2] sorted_index_pairs = sorted(enumerate(arr), key=lambda x: x[1]) indices = [index for index, value in sorted_index_pairs] print(indices)
Output:
[1, 2, 0]
This snippet first creates a list of tuples with enumerate(arr), sorts them by the original list values, and then extracts the indices representing the order of ascending value deletion.
Method 2: Using Argsort from NumPy
For those with NumPy installed, we can take advantage of the argsort() function which returns the indices that would sort the array. This method is efficient and compact, especially for large lists.
Here’s an example:
import numpy as np arr = [3, 1, 2] indices = np.argsort(arr).tolist() print(indices)
Output:
[1, 2, 0]
This code uses NumPy’s argsort() functionality to return a sequence of indices that sort the array in ascending order, which is then converted to a list.
Method 3: Using List Comprehension and Min Function
This method involves repeatedly finding the smallest element and its index, then ‘deleting’ it from the list and updating the remaining indices. It’s a brute-force approach that’s simple to understand.
Here’s an example:
arr = [3, 1, 2]
indices = []
for i in range(len(arr)):
min_index = arr.index(min(arr))
indices.append(min_index)
arr[min_index] = float('inf')
print(indices)Output:
[1, 2, 0]
Here, the min() function finds the smallest element, and index() gets its position. We then simulate deletion by setting the element to infinity, thus excluding it from subsequent calls to min().
Method 4: Using HeapQueue Pop Operation
The heapq module in Python offers a way to efficiently manage a heap queue or priority queue. We can push all elements with their indices into a heap and then pop them out to get the indices in the desired order.
Here’s an example:
import heapq arr = [3, 1, 2] heap = [(value, i) for i, value in enumerate(arr)] heapq.heapify(heap) indices = [heapq.heappop(heap)[1] for _ in range(len(arr))] print(indices)
Output:
[1, 2, 0]
The code above demonstrates creating a min-heap from the array elements and their indices and then popping elements from the heap to get their indices in ascending order.
Bonus One-Liner Method 5: Using Sorted and Lambda Function
This method combines Python’s sorted() function with a lambda to provide a quick one-liner. It’s similar to Method 1 but more succinct, which Pythonistas may appreciate for its brevity.
Here’s an example:
arr = [3, 1, 2] indices = [i for _, i in sorted((val, idx) for idx, val in enumerate(arr))] print(indices)
Output:
[1, 2, 0]
The one-liner utilizes list comprehension, sorted(), and enumerate() to accomplish the same as Method 1 but with a more compact syntax.
Summary/Discussion
- Method 1: Using Sorted Index Pairs. Straightforward and uses native Python. Not the most efficient for large data sets.
- Method 2: Using Argsort from NumPy. Very efficient, especially for large arrays, but requires NumPy, which is an external library.
- Method 3: Using List Comprehension and Min Function. Easy to understand but inefficient for large lists due to its O(n^2) complexity.
- Method 4: Using HeapQueue Pop Operation. Efficient and elegant, suitable for large data sets, but relies on understanding of heap data structures.
- Bonus Method 5: One-Liner Using Sorted and Lambda Function. Concise and pythonic, but one-liners may be less readable to those unfamiliar with lambda functions and comprehensions.