GameOfLifeDivTwo | Topcoder Archive

Problem Statement

Cat Taro and Rabbit Hanako invented a new variation of "Game Of Life".

N cells are arranged around a circle. The cells are numbered from 0 to N-1. For each i between 0 and N-2, inclusive, the i-th cell and the (i+1)-th cell are adjacent to each other. The (N-1)-th cell and the 0-th cell are adjacent to each other. Each cell has exactly two adjacent cells. Each cell has a state: "live" or "die".

Taro and Hanako can decide the states of the cells at time 0. For time t > 0, the states are determined as follows:

Consider three cells: the i-th cell and the two cells that are adjacent to the i-th cell.
If at least two of the three cells are "live" at time t-1, the state of the i-th cell at time t will be "live".
If at least two of the three cells are "die" at time t-1, the state of the i-th cell at time t will be "die".

You are given a String init. The number of cells in the game (N) is equal to the number of characters in init. The i-th character of init represents the state they assign to the i-th cell at time 0. '1' means "live" and '0' means "die". Return a string that describes the states at time T using the same encoding.

Definition

Class:: GameOfLifeDivTwo
Method:: theSimulation
Parameters:: String, int
Returns:: String
Method signature:: String theSimulation(String init, int T)
(be sure your method is public)

Constraints

init will contain between 3 and 50 characters, inclusive.
Each character in init will be '0' (zero) or '1' (one).
T will be between 0 and 1,000, inclusive.

Examples

```
"01010"
```
```
2
```
```
Returns: "00000"
```
At time 0, Taro and Hanako set the state to "01010". At time 1, the state becomes "00100". At time 2, the state becomes "00000".
```
"010101"
```
```
5
```
```
Returns: "101010"
```
The state alternates between "010101" and "101010" repeatedly.
```
"111010"
```
```
58
```
```
Returns: "111111"
```
```
"111111111"
```
```
511
```
```
Returns: "111111111"
```
The state never changes.

"110010000010111110010100001001"

Returns: "110000000001111110000000000001"

```
"00101110011"
```
```
0
```
```
Returns: "00101110011"
```

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