PerfectSequences2 | Topcoder Archive

Problem Statement

A perfect sequence is a sequence such that all of its elements are integers and the product of all of them is equal to their sum. For example {1,2,3} is a perfect sequence because 1+2+3 = 1*2*3, {-1,1,-1,1,6} is a perfect sequence as well, but {4,5,6} is not a perfect sequence because 4*5*6 is not equal to 4+5+6.

You are given a int[] seq. In one move you can choose one element of seq and increase or decrease it by 1. Return the minimum number of moves required to transform seq into a perfect sequence.

Definition

Class:: PerfectSequences2
Method:: minimumMoves
Parameters:: int[]
Returns:: long
Method signature:: long minimumMoves(int[] seq)
(be sure your method is public)

Constraints

seq will contain between 1 and 50 elements, inclusive.
Each element of seq will be between -1,000,000,000 and 1,000,000,000, inclusive.

Examples

```
{-1000000000}
```
```
Returns: 0
```
Any sequence consisting of 1 integer is perfect, so no additional moves are needed.
```
{-1,1}
```
```
Returns: 2
```
There are 2 perfect sequences containing two elements: {0,0} and {2,2}. In order to obtain {0,0} from {-1,1} you need 2 moves, in order to obtain {2,2} you need 4 moves.
```
{4,3}
```
```
Returns: 3
```
This time it is better to obtain {2,2}.
```
{17,95,-79}
```
```
Returns: 33
```
Here the best solution is to transform seq into {0,95,-95}.
```
{10,9,8}
```
```
Returns: 21
```
Decrease each element by 7 to obtain {3,2,1}.
```
{-2,-29,-13}
```
```
Returns: 38
```
```
{-7,-31,2,-14}
```
```
Returns: 48
```

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