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Problem · Array

Min Elements to Remove to Make Almost Sorted Array

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An array of integers is almost sorted if at most one element can be deleted from it to make it perfectly sorted, ascending. For example, arrays [2, 1, 7], [13, 9, 2], and [1, 5, 6] are almost sorted because they have 0 or 1 elements out of place. The arrays [4, 2, 1] and [1, 2, 6, 4, 3] are not because they have more than one element out of place.

Given an array of n unique integers, determine the minimum number of elements to remove so that it becomes almost sorted.

Examples

01 · Example 1

arr = [3, 4, 2, 5, 1]
return = 1

Remove 2 to get arr' = [3, 4, 5, 1] or remove 1 to get arr' = [3, 4, 2, 5], both of which are almost sorted. The minimum number of elements that must be removed in this case is 1.