CorrectMultiplication | Topcoder Archive

Problem Statement

Krolik found a sheet of paper with an equation containing three positive integers: "a * b = c". This equation might be wrong, so Krolik is trying to make it correct by adjusting the numbers a, b, and c.

You are given three ints a, b, and c. Return a long containing the minimum value of |A - a| + |B - b| + |C - c|, where A, B, and C are positive integers satisfying A * B = C.

Definition

Class:: CorrectMultiplication
Method:: getMinimum
Parameters:: int, int, int
Returns:: long
Method signature:: long getMinimum(int a, int b, int c)
(be sure your method is public)

Notes

|x| is the absolute value of x (which is x for non-negative x and (-x) for negative x).

Constraints

a, b, and c will each be between 1 and 1,000,000,000, inclusive.

Examples

```
19
```
```
28
```
```
522
```
```
Returns: 2
```
By assigning A = 18, B = 29, and C = 522 the value of |A - a| + |B - b| + |C - c| is minimized.
```
10
```
```
30
```
```
500
```
```
Returns: 11
```
```
11111
```
```
11111
```
```
123454321
```
```
Returns: 0
```
```
1000
```
```
100
```
```
10
```
```
Returns: 1089
```
Note that A, B, and C must be positive integers.
```
399
```
```
522
```
```
199999
```
```
Returns: 24
```

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