PerfectSequences | Topcoder Archive

Problem Statement

A perfect sequence is a sequence such that all of its elements are non-negative integers and the product of all of them is equal to their sum. For example: {2,2}, {1,3,2} and {0,0,0,0} are perfect sequences and {4,5,6} and {0,2,-2} are not perfect sequences (4*5*6 is not equal to 4+5+6, and negative numbers are not allowed by the definition).

You are given a int[] seq. Return "Yes" if it is possible to change exactly one element of seq so that the resulting sequence is perfect. Otherwise, return "No".

Definition

Class:: PerfectSequences
Method:: fixIt
Parameters:: int[]
Returns:: String
Method signature:: String fixIt(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 0 and 1000000000 (10^9), inclusive.

Examples

```
{1,3,4}
```
```
Returns: "Yes"
```
If we change the last element to 2, we have {1,3,2}. 1+3+2 = 1*3*2.
```
{1,2,3}
```
```
Returns: "No"
```
This sequence is already perfect and it is not possible to change exactly one of its elements and keep it perfect.
```
{1,4,2,4,2,4}
```
```
Returns: "No"
```
```
{1000000,1,1,1,1,2}
```
```
Returns: "Yes"
```
It is possible to replace 1000000 with 6 to make the sequence become perfect.
```
{8}
```
```
Returns: "Yes"
```
It is possible to change the first element to any non-negative number and the sequence will stay perfect.
```
{2,0,2}
```
```
Returns: "No"
```
Note that {2,0,-2} is not considered a perfect sequence because negative numbers are not allowed by the definition.

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