HeightRound | Topcoder Archive

Problem Statement

There are several people that will sit around the same table in a circular fashion. Since all these people are very self-conscious about their height, you don't want to sit any short person next to a tall one. To formalize this, we want to minimize the maximum height difference between 2 adjacent persons.

You will be given the heights of the people as a int[]. Return a int[] with the height of each individual in clockwise order of a seating arrangement that follows the above rule. If there are several solutions, return the lexicographically first one.

Definition

Class:: HeightRound
Method:: getBestRound
Parameters:: int[]
Returns:: int[]
Method signature:: int[] getBestRound(int[] heights)
(be sure your method is public)

Constraints

heights will contain between 3 and 50 elements, inclusive.
Each element of heights will be between 1 and 1000, inclusive.

Examples

```
{1,2,3,4}
```
```
Returns: {1, 2, 4, 3 }
```
It's better to separate the tallest and shortest people in the round. All solutions with 1 and 4 separated are equivalent, so we choose the lexicographically first one.
```
{1000,500,1}
```
```
Returns: {1, 500, 1000 }
```
In a round of only 3 persons, everybody is next to everyone else, so we only have to return the lexicographically first representation.
```
{1,3,4,5,7}
```
```
Returns: {1, 3, 5, 7, 4 }
```

{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}

Returns: {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

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