Compute the value of a game of placing non-attacking kings on an n x n board; see https://math.stackexchange.com/questions/4849448.

Question4849448.java

import java.util.HashMap;
import java.util.Map;

public class Question4849448 {
    final static int d = 8;
    final static int n = d * d;
    
    static long [] moves = new long [n];
    static long [] [] transformedMoves = new long [n] [8];
    
    public static void main(String [] args) {
        // prepare moves and transformed moves
        for (int i = 0;i < d;i++)
            for (int j = 0;j < d;j++) {
                long move = 0;
                for (int k = Math.max (0,i - 1);k < Math.min (d,i + 2);k++)
                    for (int l = Math.max (0,j - 1);l < Math.min (d,j + 2);l++)
                        move |= 1L << (l * d + k);
                moves [j * d + i] = move;
                int k = i;
                int l = j;
                int m = 0;
                for (int r = 0;r < 2;r++) {
                    for (int t = 0;t < 4;t++) {
                        transformedMoves [l * d + k] [m++] = move;
                        // rotate
                        int h = k;
                        k = l;
                        l = d - h - 1;
                    }
                    // reflect
                    k = d - k - 1;
                }
            }
        
        for (int i = 0,m = 0;i < d;i++) {
            for (int j = 0;j < d;j++,m++)
                System.out.print("  " + (wins (transformedMoves [m]) ? '+' : '-'));
            System.out.println();
        }
    }
    
    static Map<Long,Boolean> cache = new HashMap<>();
    
    static boolean wins (long [] state) {
        boolean result = !evaluate (state);
        for (int i = 0;i < 8;i++)
            cache.put(state [i],result);
        return result;
    }
    
    static boolean evaluate (long [] state) {
        long bit = 1;
        long position = state [0];
        for (int i = 0;i < n;i++,bit <<= 1)
            if ((position & bit) == 0) {
                long newPosition = position | moves [i];
                Boolean result = cache.get(newPosition);
                if (result == null) {
                    long [] copy = state.clone();
                    for (int j = 0;j < 8;j++)
                        copy [j] |= transformedMoves [i] [j];
                    result = wins (copy);
                }
                if (result)
                    return true;
            }
        return false;
    }
}