CoolFunction | Topcoder Archive

Problem Statement

The function f: R -> R is called cool if there are integer numbers a₀ <= a₁ <= ... <= a_k-1 (k >= 1) such that f(x) = |x - a₀| + |x - a₁| + ... + |x - a_k-1| for every real value of x.

You will be given a int[] values, containing n elements. You should find a cool function f such that f(i) = values[i] for every i, where 0 <= i < n. Return a int[], containing the values a₀, a₁, ..., a_k-1 for this function. If there are many possible answers, choose the one with the smallest number of elements. If tie still exists, return the lexicographically smallest int[]. Constraints will guarantee that values corresponds to at least one cool function.

Definition

Class:: CoolFunction
Method:: restore
Parameters:: int[]
Returns:: int[]
Method signature:: int[] restore(int[] values)
(be sure your method is public)

Constraints

values will contain between 1 and 50 elements, inclusive.
Each element of values will be between 0 and 50, inclusive.
values will correspond to at least one cool function.

Examples

```
{0}
```
```
Returns: {0 }
```
|x| is acceptable here.
```
{50}
```
```
Returns: {-50 }
```
Here there are two variants with k=1: |x-50| and |x+50|. The second one is lexicographically smaller.
```
{2, 4}
```
```
Returns: {-2, 0 }
```
```
{3, 3}
```
```
Returns: {-2, 1 }
```
```
{5, 1}
```
```
Returns: {1, 1, 1, 2 }
```
The return is not necessarily strictly increasing.
```
{10, 4, 6}
```
```
Returns: {1, 1, 1, 1, 2, 4 }
```

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