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Approach 1:-
Initialization:
If the array length is less than or equal to 4, we return 0 since we can remove all elements to make the array empty.
Sorting:
We sort the array to simplify finding the minimum difference after removals.
Calculating Minimum Difference:
We consider four possible scenarios:
Removing the first three elements.
Removing the first two elements and the last one.
Removing the first one and the last two.
Removing the last three elements.
We compute the differences for these scenarios and return the minimum difference.
Time and Space Complexity:
Time Complexity:
Sorting the array: O(n log n), where n is the length of the array.
Calculating the minimum difference: O(1) constant time.
Overall time complexity: O(n log n).
Space Complexity:
The space used for the sorted list: O(n).
Overall space complexity: O(n).
Approach 2:-
Initialization:
If the array length is less than or equal to 4, return 0 since we can remove all elements to make the array empty.
Using Priority Queues:
Two priority queues (max-heap and min-heap) are used to keep track of the smallest and largest elements.
Elements are added to the priority queues, and the size is maintained at 4 for optimization.
Calculating Minimum Difference:
Adjust the array elements using values from the priority queues.
Calculate the minimum difference using four possible scenarios and return the minimum.
Time and Space Complexity:
Time Complexity:
Sorting the elements using priority queues: O(n log 4) which simplifies to O(n).
Calculating the minimum difference: O(1) constant time.
Overall time complexity: O(n).
Space Complexity:
Space used by the priority queues: O(4) which simplifies to O(1).
Space used by the auxiliary list: O(n).
Overall space complexity: O(n).
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