分治算法：Tromino谜题，L型覆盖

  1 public class Tromino {
  2
  3     static int num = 2;
  4     //x 对应 第二维
  5     //y 对应 第一维
  6     static int[][] panel = {
  7         {0,0,0,0,0,0,0,0},
  8         {0,0,0,0,0,0,0,0},
  9         {0,0,0,0,0,0,1,0},
 10         {0,0,0,0,0,0,0,0},
 11         {0,0,0,0,0,0,0,0},
 12         {0,0,0,0,0,0,0,0},
 13         {0,0,0,0,0,0,0,0},
 14         {0,0,0,0,0,0,0,0}
 15     };
 16     /*static int[][] panel ={
 17         {0,0},{0,1}
 18     };*/
 19     /*
 20      * 棋盘大小 2^n * 2^n
 21      * 缺失方块的位置  (x, y)
 22      * 棋盘的开始位置x0, y0
 23      */
 24     public static void cover(int x0, int y0, int x, int y, int size){
 25         int cx = x0 + size / 2 - 1;
 26         int cy = y0 + size / 2 - 1;
 27         if(size == 2){
 28             if(x0 == x && y0 == y){//左上
 29                 panel[y0][x0+1] = num;
 30                 panel[y0+1][x0+1] = num;
 31                 panel[y0+1][x0] = num;
 32                 num++;
 33             }
 34             if(x0+1 == x && y == y0){//右上
 35                 panel[y0][x0] = num;
 36                 panel[y0+1][x0+1] = num;
 37                 panel[y0+1][x0] = num;
 38                 num++;
 39             }
 40             if(x0 == x && y == y0 + 1){//左下
 41                 panel[y0][x0] = num;
 42                 panel[y0+1][x0+1] = num;
 43                 panel[y0][x0+1] = num;
 44                 num++;
 45             }
 46             if(x0+1 == x && y == y0 + 1){//右下
 47                 panel[y0][x0] = num;
 48                 panel[y0][x0+1] = num;
 49                 panel[y0+1][x0] = num;
 50                 num++;
 51             }
 52             print();
 53             return;
 54         }
 55
 56         if( x <= cx && y <= cy){
 57             //左上
 58             panel[cy][cx+1] = num;
 59             panel[cy+1][cx] = num;
 60             panel[cy+1][cx+1] = num;
 61             num++;
 62             print();
 63             cover(x0, y0, x, y, size/2);//递归左上
 64             cover(cx+1, y0, cx+1, cy, size/2);//递归右上
 65             cover(x0, cy+1, cx, cy+1, size/2);//递归左下
 66             cover(cx+1, cy+1, cx+1, cy+1, size/2);//递归右下
 67         }
 68         if( x > cx && y > cy){
 69             //右下
 70             panel[cy][cx] = num;
 71             panel[cy+1][cx] = num;
 72             panel[cy][cx+1] = num;
 73             num++;
 74             print();
 75             cover(x0, y0, cx, cy, size/2);//递归左上
 76             cover(cx+1, y0, cx+1, cy, size/2);//递归右上
 77             cover(x0, cy+1, cx, cy+1, size/2);//递归左下
 78             cover(cx+1, cy+1, x, y, size/2);//递归右下
 79         }
 80         if( x > cx && y <= cy){
 81             //右上
 82             panel[cy][cx] = num;
 83             panel[cy+1][cx] = num;
 84             panel[cy+1][cx+1] = num;
 85             num++;
 86             print();
 87             cover(x0, y0, cx, cy, size/2);//递归左上
 88             cover(cx+1, y0, x, y, size/2);//递归右上
 89             cover(x0, cy+1, cx, cy+1, size/2);//递归左下
 90             cover(cx+1, cy+1, cx+1, cy+1, size/2);//递归右下
 91         }
 92         if( x <= cx && y > cy){
 93             //左下
 94             panel[cy][cx] = num;
 95             panel[cy][cx+1] = num;
 96             panel[cy+1][cx+1] = num;
 97             num++;
 98             print();
 99             cover(x0, y0, cx, cy, size/2);//递归左上
100             cover(cx+1, y0, cx+1, cy, size/2);//递归右上
101             cover(x0, cy+1, x, y, size/2);//递归左下
102             cover(cx+1, cy+1, cx+1, cy+1, size/2);//递归右下
103         }
104     }
105     public static void print(){
106         for(int i = 0; i < panel.length; i++){
107             for(int j = 0; j < panel[i].length; j++){
108                 System.out.printf("%3d", panel[i][j]);
109             }
110             System.out.println();
111         }
112         System.out.println();
113     }
114     public static void main(String[] args) {
115         cover(0, 0, 6, 2, 8);
116         //cover(0, 0, 1, 0, 2);
117         print();
118     }
119 }