shortest-subarray-to-be-removed-to-make-array-sorted

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1574. Shortest Subarray to be Removed to Make Array Sorted (Medium)

Given an integer array arr, remove a subarray (can be empty) from arr such that the remaining elements in arr are non-decreasing.

Return the length of the shortest subarray to remove.

A subarray is a contiguous subsequence of the array.

 

Example 1:

Input: arr = [1,2,3,10,4,2,3,5]
Output: 3
Explanation: The shortest subarray we can remove is [10,4,2] of length 3. The remaining elements after that will be [1,2,3,3,5] which are sorted.
Another correct solution is to remove the subarray [3,10,4].

Example 2:

Input: arr = [5,4,3,2,1]
Output: 4
Explanation: Since the array is strictly decreasing, we can only keep a single element. Therefore we need to remove a subarray of length 4, either [5,4,3,2] or [4,3,2,1].

Example 3:

Input: arr = [1,2,3]
Output: 0
Explanation: The array is already non-decreasing. We do not need to remove any elements.

 

Constraints:

• 1 <= arr.length <= 105
• 0 <= arr[i] <= 109

Related Topics

[Array] [Two Pointers] [Binary Search] [Stack] [Monotonic Stack]

Hints

Hint 1

The key is to find the longest non-decreasing subarray starting with the first element or ending with the last element, respectively.

Hint 2

After removing some subarray, the result is the concatenation of a sorted prefix and a sorted suffix, where the last element of the prefix is smaller than the first element of the suffix.