LuckyRemainder | Topcoder Archive

Problem Statement

Little Arthur loves numbers and 9 is his most favorite. When encountering a number, he always calculates its lucky remainder - the remainder after division by 9.

This time Arthur is given a number X of length N which contains no zeros. He is asked to find the supersum of X: super(X).

super(X) is defined as follows. For a given non-full set S of digit positions in X we erase the digits in these positions to obtain a sub-number. For example, if X = 12345 and S = {2, 4} we erase 2nd and 4th digits and obtain a sub-number 135. Supersum of X is simply the sum of sub-numbers for all valid sets S.

For example, if X is 123, then super(X) = 123 + 12 + 13 + 23 + 1 + 2 + 3 = 177.

Calculating super(X) is very difficult for Arthur. However, before getting to work he is wondering if it is possible to quickly tell what the lucky reminder of the supersum of X is. You have to help him.

Given String X, which contains the decimal representation of the number X, return super(X)'s lucky remainder.

Definition

Class:: LuckyRemainder
Method:: getLuckyRemainder
Parameters:: String
Returns:: int
Method signature:: int getLuckyRemainder(String X)
(be sure your method is public)

Constraints

X will contain between 1 and 50 characters, inclusive.
Each character of X will be one of the following: '1', '2', '3', '4', '5', '6', '7', '8', '9'.

Examples

```
"123"
```
```
Returns: 6
```
Example from the problem statement. super(123) = 177, which gives remainder 6 after division by 9.
```
"24816"
```
```
Returns: 3
```
Supersum of 24816 is 43986.
```
"8"
```
```
Returns: 8
```
```
"11235813213455"
```
```
Returns: 7
```
Supersum is 43950094900477.

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