ILike5 | Topcoder Archive

Problem Statement

You have certainly seen many tasks that start with some ridiculous made-up story. Well, this one is nothing like that.

Ivan A. is a smart boy. He just got a sequence of nonnegative integers as a birthday present. You are given this sequence in the int[] X.

Ivan A. adores the number 5. He thinks that a sequence is pretty if the product of all its elements ends with the digit 5. He now wants to change X into a pretty sequence. In each step he can choose an element of X and replace one of its digits by any other digit. For example, in a single step Ivan A. can change the number 1234 into the number 1734.

Compute and return the minimal number of steps needed to change X into a pretty sequence.

Definition

Class:: ILike5
Method:: transformTheSequence
Parameters:: int[]
Returns:: int
Method signature:: int transformTheSequence(int[] X)
(be sure your method is public)

Notes

It can be shown that any sequence X can be transformed into a pretty sequence in finitely many steps.
It is allowed to change the leading digit of a number into a zero, but this is never needed in the optimal solution.

Constraints

X will contain between 1 and 50 numbers, inclusive.
Each element of X will be between 0 and 10^6, inclusive.

Examples

```
{5, 2, 8, 12}
```
```
Returns: 3
```
One optimal solution looks as follows: Ivan A. changes the 2 to a 1. Ivan A. changes the 8 to a 9. Ivan A. changes the last digit of the number 12 from 2 to 9. After these three steps he will have the sequence {5, 1, 9, 19}. The product of its elements is 5 * 1 * 9 * 19 = 855, so this sequence is pretty.
```
{1555}
```
```
Returns: 0
```
The number already ends in a 5.
```
{0, 10, 100, 1000, 10000}
```
```
Returns: 5
```
Clearly, Ivan A. must change the last digit in each of these numbers, otherwise the product would end in a 0. One optimal solution is to change this sequence into {7, 13, 105, 1005, 10003}.

{1, 2, 2, 3, 3, 3, 4, 4, 4, 4}

Returns: 6

{7890, 4861, 65773, 3769, 4638, 46000, 548254, 36185, 115}

Returns: 4

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