VectorSet | Topcoder Archive

Problem Statement

You are given a set of two-dimensional vectors in two int[]s - x and y (the i-th elements of x and y represent x and y coordinates of the i-th vector). Find a subset of the vectors such that the sum of all vectors in the subset has the maximum possible length. Return this length.

Definition

Class:: VectorSet
Method:: maxLength
Parameters:: int[], int[]
Returns:: double
Method signature:: double maxLength(int[] x, int[] y)
(be sure your method is public)

Notes

The sum of vectors (x1, y1) and (x2, y2) is the vector (x1+x2, y1+y2).
The length of vector (x, y) is the value sqrt(x * x + y * y).
The returned value must be accurate to within a relative or absolute value of 1E-9.
The input (as well as the resulting subset) can contain equal vectors (see example 1).
Consider the entire set to be a subset.

Constraints

x will contain between 1 and 50 elements, inclusive.
x and y will contain the same number of elements.
Each element of x will be between -1000 and 1000, inclusive.
Each element of y will be between -1000 and 1000, inclusive.

Examples

```
{0,0}
```
```
{1,-1}
```
```
Returns: 1.0
```
Choose any one vector.
```
{0, 0}
```
```
{1, 1}
```
```
Returns: 2.0
```
Choose two vectors. The sum is (0, 2).

{0, 0, 1, -1}

{1, -1, 0, 0}

Returns: 1.4142135623730951

```
{0, 0, 0, 0}
```
```
{1, 2, -1, -2}
```
```
Returns: 3.0
```

{17,8,-5,-8,-8,-11,-3,2,19,4,22,15,20,13,-7,15,-23,17,-9,-10,17,24,20,-22,-1,-7,-19,18,-17}

{7,-5,-2,18,-9,-24,14,9,-21,14,-23,7,14,23,23,17,17,22,-3,-21,-10,1,24,-17,25,12,-21,12,13}

Returns: 289.4563870430224

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