LuckySum | Topcoder Archive

Problem Statement

A lucky number is a positive integer such that each of its digits is a 4 or a 7. A lucky sum is the sum of two (not necessarily distinct) lucky numbers. Cat loves lucky sums!

Cat has a String note. Each character in note is either a digit or a question mark. A number matches note if it can be produced from note by changing each question mark to a single digit. Note that the number produced this way must not have any leading zeros: after the changes, note[0] must be between '1' and '9', inclusive.

Find and return the smallest lucky sum that matches note. If there are no lucky sums that match note, return -1.

Definition

Class:: LuckySum
Method:: construct
Parameters:: String
Returns:: long
Method signature:: long construct(String note)
(be sure your method is public)

Constraints

note will contain between 1 and 14 characters, inclusive.
Each character of note will be either a digit ('0'-'9') or a question mark ('?').
The first character of note will not be '0'.
At least one character of note will be '?'.

Examples

```
"?"
```
```
Returns: 8
```
4+4=8, which is the smallest lucky sum.
```
"?1"
```
```
Returns: 11
```
4+7=11
```
"4?8"
```
```
Returns: 448
```
4+444=448
```
"2??"
```
```
Returns: -1
```
The numbers that match this note are the numbers 200 through 299. None of these numbers is a lucky sum.
```
"??????????????"
```
```
Returns: 11888888888888
```

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