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Minimize Adjacent Squared-Difference Cost with One Insertion

Microsoft● MediumINTERNOA

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Problem statement

The cost of an integer array is the sum of (values[i]-values[i-1])^2 for every adjacent pair.

Insert exactly one integer anywhere, including either end, and return the minimum possible cost. The inserted integer may be any signed 32-bit value.

Function

minimumSquaredDifferenceCost(values: int[]) → long

Examples

Example 1

values = [1,5]return = 8

Inserting 3 changes the cost from 16 to 8.

Example 2

values = [1,2,3]return = 2

Every adjacent gap is one, so insertion cannot reduce the cost.

Example 3

values = []return = 0

Inserting into an empty array leaves no adjacent pair.

Constraints

0 <= values.length <= 100000.
-10^9 <= values[i] <= 10^9.
The answer fits in a signed 64-bit integer.