Board coverage issues

In a checkerboard consisting of a 2^k * 2^k, there is a square that is different from the other, and how to cover the other squares of this particular square, using the following four kinds of L-shaped dominoes.

Four L-type dominoes such as 1



Figure 1

Special squares in the chessboard 2



Figure 2

The basic principle of the implementation is to divide the chessboard of the 2^k * 2^k into four 2^ (k-1) * 2^ (K-1), the special squares must be in one of the sub-chessboard, if the special squares in a certain sub-chessboard, continue to recursively process the sub-chessboard, until only one square in this sub-chessboard if the special party Lattice is not in a certain sub-chessboard, the corresponding position in the sub-chessboard is set to bone grade, the non-special grid of the Board into a special box of the sub-chessboard, and then recursively processing the sub-chessboard. The above principle is shown in 3.



Figure 3

Java implementation with bug version:

1  Public classChessboard {2     3      Public Static intI=0;4      Public Static intsize=10;5      Public Static intBoard[][] =New int[size][size];6     7      Public Static voidChessboard (intTrintTcintDrintdcintsize) {8         if(size==1)return;//the chessboard is no longer overwritten when there is only one lattice9         intS=SIZE/2;//Split BoardTen         intt=++i; One          A         //overlay the upper left corner of the chessboard -         if(dr<tr+s&&dc<tc+s) -             //Special squares in this chessboard the chessboard (tr,tc,dr,dc,s); -         Else{//there are no special squares in this chessboard -             //overwrite the lower right corner -board[tr+s-1][tc+s-1]=T; +             //cover the remaining squares -Chessboard (tr,tc,tr+s-1,dc+s-1, s); +         } A          at         //overlay Right-hand corner checkerboard -         if(dr<tr+s&&dc>=tc+s) -             //Special squares in this chessboard -Chessboard (tr,tc+s,dr,dc,s); -         Else{//there are no special squares in this chessboard -             //overwrite the lower left corner inboard[tr+s-1][tc+s]=T; -             //cover the remaining squares toChessboard (tr,tc+s,tr+s-1,tc+s,s); +         } -          the         //overlay The lower left corner of the chessboard *         if(dr>=tr+s&&dc<tc+s) $             //Special squares in this chessboardPanax NotoginsengChessboard (tr+s,tc,dr,dc,s); -         Else{//there are no special squares in this chessboard the             //overwrite the upper right corner +board[tr+s][tc+s-1]=T; A             //cover the remaining squares theChessboard (tr+s,tc,tr+s,tc+s-1, s); +         } -          $         //Overlay Right bottom corner chessboard $         if(dr>=tr+s&&dc>=tc+s) -             //Special squares in this chessboard -Chessboard (tr+s,tc+s,dr,dc,s); the         Else{//there are no special squares in this chessboard -             //overwrite upper left cornerWuyiboard[tr+s][dc+s]=T; the             //cover the remaining squares -Chessboard (tr,tc,tr+s,dc+s,s); Wu         } -          About     } $      -      Public Static voidMain (string[] args) { -Chessboard (0, 0, 2, 2, 4); -          for(inti=0;i<4;i++) A              for(intj=0;j<4;j++) +             { the                 if(j==0) - System.out.println (); $System.out.print ("" +board[i][j]); the             } the     } the  the}

There is no guarantee that the sub-chessboard with no special squares in the chessboard function is properly overwritten.

Board coverage issues