SpiralNumbers | Topcoder Archive

Problem Statement

Consider all positive integers written in the following manner (you can imagine an infinite spiral).

                 21  22  23  24  25  26
                 20   7   8   9  10 ...
                 19   6   1   2  11 ...
                 18   5   4   3  12 ...
                 17  16  15  14  13 ...

You task is to determine the position (row,column) of a given number N, assuming that the center (number 1) has position (0,0). Rows are numbered from top to bottom, columns are numbered from left to right (for example, number 3 is at (1,1)). Your method should return a string containing the position of N in form (R,C) where R is the row and C is the column. R and C must not contain any leading zeroes.

Definition

Class:: SpiralNumbers
Method:: getPosition
Parameters:: int
Returns:: String
Method signature:: String getPosition(int N)
(be sure your method is public)

Constraints

N will be between 1 and 2,147,483,647, inclusive.

Examples

```
2
```
```
Returns: "(0,1)"
```
```
3
```
```
Returns: "(1,1)"
```
```
7
```
```
Returns: "(-1,-1)"
```
```
17
```
```
Returns: "(2,-2)"
```
```
24
```
```
Returns: "(-2,1)"
```
```
830
```
```
Returns: "(-14,3)"
```
```
765409
```
```
Returns: "(-437,221)"
```

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