What is the time complexity of Shortest Subarray to be Removed to Make Array Sorted?

The optimal solution for Shortest Subarray to be Removed to Make Array Sorted runs in O(n) time and uses O(1) space. The time complexity is O(n) because we only traverse the array a few times. The space complexity is O(1) since we only use a few variables to keep track of indices.

What is the brute force solution for Shortest Subarray to be Removed to Make Array Sorted?

The brute force approach for Shortest Subarray to be Removed to Make Array Sorted is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking all possible subarrays to see which one can be removed to make the remaining array sorted. This method is straightforward but inefficient as it examines every possible combination. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Shortest Subarray to be Removed to Make Array Sorted?

Always clarify the problem statement and constraints before jumping into coding. Think about edge cases and how they might affect your solution. Explain your thought process clearly during the interview to show your understanding.

What are common mistakes when solving Shortest Subarray to be Removed to Make Array Sorted?

Not considering edge cases where the array is already sorted. Failing to correctly manage the indices when checking the prefix and suffix.

#1574

Shortest Subarray to be Removed to Make Array Sorted

Medium

ArrayTwo PointersBinary SearchStackMonotonic StackTwo PointersSliding WindowArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution leverages the idea of finding the longest non-decreasing prefix and suffix. By identifying these two segments, we can determine the shortest subarray to remove by ensuring the end of the prefix is less than the start of the suffix.

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Algorithm

3 steps

1Step 1: Identify the longest non-decreasing prefix from the start of the array.
2Step 2: Identify the longest non-decreasing suffix from the end of the array.
3Step 3: Use two pointers to find the minimum length of the subarray to remove by checking the conditions between the prefix and suffix.

solution.py17 lines

1def find_length_of_shortest_subarray(arr):
2    n = len(arr)
3    left = 0
4    while left < n - 1 and arr[left] <= arr[left + 1]:
5        left += 1
6    if left == n - 1:
7        return 0
8    right = n - 1
9    while right > 0 and arr[right - 1] <= arr[right]:
10        right -= 1
11    min_length = min(n - left - 1, right)
12    for i in range(left + 1):
13        while right < n and arr[i] > arr[right]:
14            right += 1
15        min_length = min(min_length, right - i - 1)
16    return min_length
17

ℹ

Complexity note: The time complexity is O(n) because we only traverse the array a few times. The space complexity is O(1) since we only use a few variables to keep track of indices.

1Identifying the longest non-decreasing prefix and suffix is crucial for optimizing the solution.
2Using two pointers allows us to efficiently find the minimum subarray to remove.

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