Discussion on Chessboard Game, Again! Challenge

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2 years ago+ 0 comments

Too difficult for me

2 years ago+ 1 comment

A good one . If You understand grandy theorem of game theory , then it is very easy for you to solve recursively .When our possible moves from a co-ordinate of chess-board has been given .We can compute grandy-value recursively using the help of memoization .

My full solution here https://github.com/joy-mollick/Game-Theory-Problems/blob/master/HackerRank-Chessboard%20Game%2C%20Again!.cpp

Here is the part of my code to compute grandy value of every co-ordinate by given input .

int sg(int x,int y)
{
    if((x==1&&y==1))
    {
        return 0;
/// (1,1) it is base case ,because from here there is no move,so grandy value of this state is zero
    }
    if(grandy_value[x][y]!=-1) /// if grandy value is already computed just return it , no need to calculate it
    {
        return grandy_value[x][y];
    }
    set<int>s;
    for(int i=0;i<4;i++)
    {
        int newx=x+dx[i];
        int newy=y+dy[i];
        if(newx>=1&&newy>=1&&newx<=15&&newy<=15)///if newx and newy is beyond (1,1) then this recursion will be recursively run ,there is no end .So (1,1) should be the terminal point
        {
            s.insert(sg(newx,newy));
        }
    }
    int mex=0;
    while(s.find(mex)!=s.end()) mex++;
    grandy_value[x][y]=mex;///assigning mex [not included minimum element in the set of grandy value of possible co-ordinates]
    return grandy_value[x][y];/// return grandy_value
}

3 years ago+ 0 comments

What? A cell can contain more than one coin. Ok, when can not a player make a new move?

3 years ago+ 0 comments

this question is full of ambiguities.. who plays first? how can I know that?

3 years ago+ 0 comments

Created board using Grundy -- Time taking solution. But Works!

     static int[][] chess= {
            {0,0,1,1,0,0,1,1,0,0,1,1,0,0,1},
            {0,0,2,1,0,0,1,1,0,0,1,1,0,0,1},
            {1,2,2,2,3,2,2,2,3,2,2,2,3,2,1},
            {1,1,2,1,4,3,2,3,3,3,2,3,3,3,1},
            {0,0,3,4,0,0,1,1,0,0,1,1,0,0,1},
            {0,0,2,3,0,0,2,1,0,0,1,1,0,0,1},
            {1,1,2,2,1,2,2,2,3,2,2,2,3,2,1},
            {1,1,2,3,1,1,2,1,4,3,2,3,3,3,1},
            {0,0,3,3,0,0,3,4,0,0,1,1,0,0,1},
            {0,0,2,3,0,0,2,3,0,0,2,1,0,0,1},
            {1,1,2,2,1,1,2,2,1,2,2,2,3,2,1},
            {1,1,2,3,1,1,2,3,1,1,2,1,4,3,1},
            {0,0,3,3,0,0,3,3,0,0,3,4,0,0,1},
            {0,0,2,3,0,0,2,3,0,0,2,3,0,0,2},
            {1,1,1,1,1,1,1,1,1,1,1,1,1,2,1}
            
    };
    static String chessboardGame(int[][] coins) {        
        int xor = 0;
        for (int[] Y : coins) {
            int x = Y[0]-1;
            int y = Y[1]-1;
         
                xor^=chess[x][y];
        }
        if (xor == 0)
            return "Second";
        return "First";
     }

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