MakingRightyTriangle | Topcoder Archive

Problem Statement

There is a 2-D plane and there are N points. i-th point is located at (X[i], Y[i]). You are going to choose 3 distinct points from them. Then, we calculate:

longest = the longest distance between two of the three points
shortest = the shortest distance between two of the three points

You want to pick the three points that minimize the value, longest/shortest. Given int[] X and int[] Y, return this smallest value.

Definition

Class:: MakingRightyTriangle
Method:: best
Parameters:: int[], int[]
Returns:: double
Method signature:: double best(int[] X, int[] Y)
(be sure your method is public)

Constraints

The number of elements in X will be between 3 and 200, inclusive.
The number of elements in Y will be between 3 and 200, inclusive.
X and Y will have the same number of elements.
Each element in X will be between -1,000 and 1,000 inclusive.
Each element in Y will be between -1,000 and 1,000 inclusive.
(X[i], Y[i]) will be pairwise distinct.

Examples

{0,0,1,1}

{0,1,0,1}

Returns: 1.4142135623730951

```
{0,0,0}
```
```
{0,1,2}
```
```
Returns: 2.0
```
It is possible to choose 3 points that are in a straight line.

{114,514,-810,893,364,334}

{-134,22,482,103,276,-912}

Returns: 1.433199134719805

{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

{3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4}

Returns: 1.0749676997731399

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