使用全排列方法解九宫格问题

使用全排列方法解九宫格问题

下面的方法能解出九宫格，但对于更高阶只有理论可能性，因为耗时太长，不能作为通用解决方案。

输出：
2    7    6    
9    5    1    
4    3    8   

package  com.sitinspring;

public   class  SquarePuzzle{
     /**
     * 阶数
      */
     private   int  n;
    
     /**
     * 方阵数组
      */
     private  Integer[] arr;
    
     /**
     * 平均值
      */
     private   int  average;
    
     public  SquarePuzzle( int  n){
         this .n = n;
        
         //  建立数组并得到平均值
        arr = new  Integer[n * n];
        
        average = 0 ;
         for ( int  i = 1 ;i <= n * n;i ++ ){
            arr[i - 1 ] = i;
            average += i;
        }
        average = average / n;
        
         //  递归查看
        permutation(arr, 0 ,arr.length);
    }
    
     private   void  permutation(Integer[] arr, int  start, int  end){
         if (start < end + 1 ){
            permutation(arr,start + 1 ,end);
            
             for ( int  i = start + 1 ;i < end;i ++ ){
                Integer temp;
                
                temp = arr[start];
                arr[start] = arr[i];
                arr[i] = temp;
                
                permutation(arr,start + 1 ,end);
                
                temp = arr[i];
                arr[i] = arr[start];
                arr[start] = temp;
            }
        }
         else {
             /* for(int i=0;i<end;i++){
                System.out.print(arr[i]);
            }
            System.out.print("\n"); */
            
             int  i,sum = 0 ;
            
             for (i = 0 ;i < n;i ++ ){
                sum += arr[i];
            }
            
             if (sum != average){
                 return ;
            }
            
             //  查看是否纵横对角线值都相等
            checkAndPrint(arr);
        }
    }
    
     private   void  checkAndPrint(Integer[] arr){
        Integer[][] arr2 = new  Integer[n][n];
         int  i,j,sum;
        
         for (i = 0 ;i < n;i ++ ){
             for (j = 0 ;j < n;j ++ ){
                arr2[i][j] = arr[i * n + j];
            }
        }
        
         //  横
         for (i = 0 ;i < n;i ++ ){
            sum = 0 ;
             for (j = 0 ;j < n;j ++ ){
                sum += arr2[i][j];
            }
            
             if (sum != average){
                 return ;
            }
        }
        
         //  纵
         for (i = 0 ;i < n;i ++ ){
            sum = 0 ;
             for (j = 0 ;j < n;j ++ ){
                sum += arr2[j][i];
            }
            
             if (sum != average){
                 return ;
            }
        }
        
         //  对角线
        sum = 0 ;
         for (i = 0 ;i < n;i ++ ){
            sum += arr2[i][i];        
        }
        
         if (sum != average){
             return ;
        }
        
         //  对角线
        sum = 0 ;
         for (i = 0 ;i < n;i ++ ){
            sum += arr2[i][n - i - 1 ];        
        }
        
         if (sum != average){
             return ;
        }
        
         //  最终打印
         for (i = 0 ;i < n;i ++ ){
             for (j = 0 ;j < n;j ++ ){
                System.out.print(arr2[i][j] + " \t " );;
            }
            
            System.out.print( " \n " );;
        }
        System.out.print( " \n " );;
        System.exit( 0 );
    }
    
     public   static   void  main(String[] args){
         new  SquarePuzzle( 3 );
    }
}