289. Game of Life

According to the Wikipedia’s article: “The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970.”

Given a board with m by n cells, each cell has an initial state live (1) or dead (0). Each cell interacts with its eight neighbors (horizontal, vertical, diagonal) using the following four rules (taken from the above Wikipedia article):

Any live cell with fewer than two live neighbors dies, as if caused by under-population.
Any live cell with two or three live neighbors lives on to the next generation.
Any live cell with more than three live neighbors dies, as if by over-population..
Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.
Write a function to compute the next state (after one update) of the board given its current state.

Follow up:
Could you solve it in-place? Remember that the board needs to be updated at the same time: You cannot update some cells first and then use their updated values to update other cells.
In this question, we represent the board using a 2D array. In principle, the board is infinite, which would cause problems when the active area encroaches the border of the array. How would you address these problems?

这个题目的关键就是不允许开辟额外的空间。
参考网上的思路，可以用0，1,10,11来表示题目对应的四种状态。
这样在进行查找周围存活细胞的数量的时候，用%10操作，
只有等于1的才是原本就是存活的状态。
这样在当前进行改变之后，就不会影响后续的判断了。

class Solution {
public:
    int getnum(vector<vector<int>>&map,int x,int y ){
        int ans=0;
        for(int i=x-1;i<=x+1;i++){
            for(int j=y-1;j<=y+1;j++){
                if(i>=0&&i<map.size()&&j>=0&&j<map[0].size()){
                    if(i==x&&j==y)continue;
                    if(map[i][j]%10==1)ans++;
                }
            }
        }
        return ans;
    }
    void gameOfLife(vector<vector<int>>& board) {
        for(int i=0;i<board.size();i++){
            for(int j=0;j<board[0].size();j++){
                int t=getnum(board,i,j);
                if(board[i][j]==0){
                    if(t==3)board[i][j]+=10;
                }
                else if(board[i][j]==1){
                    if(t==2||t==3) 
                        board[i][j]+=10;
                }
            }
        }
        for(int i=0;i<board.size();i++)
            for(int j=0;j<board[0].size();j++)
                board[i][j]/=10;
    }
};