BishopOnTheBoard | Topcoder Archive

Problem Statement

A bishop is a chess piece that can move any number of squares in any diagonal direction (see diagram below).

The chess board has dimensions xSize * ySize, where the top-left corner of the board has coordinates (0, 0), and the bottom-right corner has coordinates (xSize - 1, ySize -1). The bishop is initially at coordinates (x, y). Find the total number of squares reachable by this bishop in k or less moves. Note, that initial square is always counted as reachable.

Definition

Class:: BishopOnTheBoard
Method:: countReachableCells
Parameters:: int, int, int, int, int
Returns:: int
Method signature:: int countReachableCells(int xSize, int ySize, int x, int y, int k)
(be sure your method is public)

Constraints

xSize will be between 2 and 50000, inclusive.
ySize will be between 2 and 50000, inclusive.
x will be between 0 and xSize - 1, inclusive.
y will be between 0 and ySize - 1, inclusive.
k will be between 1 and 50000, inclusive.

Examples

```
8
```
```
8
```
```
0
```
```
0
```
```
2
```
```
Returns: 32
```
Reachable cells are marked by 'X' on the picture:
```
8
```
```
4
```
```
0
```
```
0
```
```
2
```
```
Returns: 12
```
Reachable cells are marked by 'X' on the picture:
```
2
```
```
2
```
```
0
```
```
0
```
```
1
```
```
Returns: 2
```
Reachable cells are marked by 'X' on the picture:
```
11
```
```
5
```
```
0
```
```
1
```
```
2
```
```
Returns: 17
```
Reachable cells are marked by 'X' on the picture:
```
278
```
```
17
```
```
37
```
```
11
```
```
5
```
```
Returns: 912
```

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