PrimePairs | Topcoder Archive

Problem Statement

You wish to group a list of numbers into pairs such that the sum of each pair is prime. For example, given the numbers { 1, 4, 7, 10, 11, 12 }, you could group them as follows:

1 + 4 = 5
7 + 10 = 17
11 + 12 = 23

or:

1 + 10 = 11
4 + 7 = 11
11 + 12 = 23

Given a int[] numbers, return a int[] of all the elements in numbers that could be paired with numbers[0] successfully as part of a complete pairing, sorted in ascending order. Note that in the example above, even though 1 + 12 is prime, there would be no way to pair the remaining 4 numbers. So the answer for the example above would be { 4, 10 }.

Definition

Class:: PrimePairs
Method:: matches
Parameters:: int[]
Returns:: int[]
Method signature:: int[] matches(int[] numbers)
(be sure your method is public)

Notes

A prime number is a number divisible only by 1 and itself.

Constraints

numbers will contain an even number of elements, between 2 and 50, inclusive.
Each element of numbers will be between 1 and 1000, inclusive.
Each element of numbers will be distinct.

Examples

```
{ 1, 4, 7, 10, 11, 12 }
```
```
Returns: {4, 10 }
```
This is the example from the problem statement.
```
{ 11, 1, 4, 7, 10, 12 }
```
```
Returns: {12 }
```
The same numbers, but in a different order. In both of the 2 possible complete pairings, the 11 is paired with the 12.
```
{ 8, 9, 1, 14 }
```
```
Returns: { }
```
No complete pairings are possible because none of the numbers can be paired with 1.

{ 34, 39, 32, 4, 9, 35, 14, 17 }

Returns: {9, 39 }

{ 941, 902, 873, 841, 948, 851, 945, 854, 815, 898,
  806, 826, 976, 878, 861, 919, 926, 901, 875, 864 }

Returns: {806, 926 }

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