Superking | Topcoder Archive

Problem Statement

We have an infinite chess board, and a new type of chess piece called a "superking". It can perform two types of moves:

Type-1: the normal king move - i.e., a move to a neighboring square in any of the eight directions horizontal, vertical or diagonal.
Type-2: a move two squares to the left, right, up or down.

The superking begins at some square in the infinite board and performs type1 Type-1 moves and type2 Type-2 moves. Return the number of possible squares that the superking can reach after performing these moves.

Definition

Class:: Superking
Method:: squares
Parameters:: int, int
Returns:: long
Method signature:: long squares(int type1, int type2)
(be sure your method is public)

Constraints

type1 and type2 will be between 0 and 100000000 (108), inclusive.

Examples

```
0
```
```
0
```
```
Returns: 1
```
No moves are made, superking remains at the starting square.
```
1
```
```
0
```
```
Returns: 8
```
After one Type-1 move (normal king move), the superking can land in one of the 8 neighboring squares.
```
0
```
```
1
```
```
Returns: 4
```
After one Type-2 move, the superking lands in one of the four squares at a distance of 2 from the starting square (to the left, right, up or down).
```
1
```
```
2
```
```
Returns: 60
```
Let's assume that the superking starts at the red square at the center of the board shown below. After one Type-2 move, the superking can land in one of the blue squares. After the second Type-2 move, the superking can land in one of the red squares. After a final Type-1 move, the superking can land in any square neighboring a red square, i.e., one of the green squares. These are the possible final landing squares for the king after 1 Type-1 and 2 Type-2 moves, 60 in total (note that it is not important in which order we make the moves; here, we first did the two Type-2 moves and then the Type-1 move).
```
31
```
```
17
```
```
Returns: 14713
```
```
24
```
```
45
```
```
Returns: 35881
```

100000000

100000000

Returns: 280000000400000001

The maximum return value.

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