8 Queen question

（ One ） Problem description

（ Two ） Problem analysis

（ 3、 ... and ） Code implementation

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       package 
       
       recursion;
       
       

       
       

       
       /**
       
       
 
       
       * @author Jin
       
       
 
       
       * @ Date 2022 year 07 month 2022/7/1 Japan 23:04
       
       
 
       
       */
       
       

       
       public 
       
       class 
       
       Queen {
       
       
    
       
       /** Define a max It means there are several queens */
       
       
    
       
       int 
       
       max
       
       =
       
       8;
       
       
    
       
       static 
       
       int 
       
       count
       
       =
       
       0;
       
       
    
       
       /** Define an array array, Save where the queen is placed , such as arr={0,4,7,5,2,6,1,3}*/
       
       
    
       
       int[]
       
       array
       
       =
       
       new 
       
       int[
       
       max];
       
       
    
       
       public 
       
       static 
       
       void 
       
       main(
       
       String[] 
       
       args) {
       
       
        
       
       Queen 
       
       queue8
       
       =
       
       new 
       
       Queen();
       
       
        
       
       queue8.
       
       check(
       
       0);
       
       
        
       
       System.
       
       out.
       
       println(
       
       " There are solutions in total : "
       
       +
       
       count
       
       +
       
       " Kind of ");
       
       
    }
       
       
    
       
       /** Method ： Place the second n A queen */
       
       
    
       
       private 
       
       void 
       
       check(
       
       int 
       
       n){
       
       
       
       
       if(
       
       n
       
       ==
       
       max){
       
       
           
       
       print();
       
       
           
       
       return;
       
       
       }
       
       
       
       
       // Put the queen in turn n, And determine if there is a conflict 
       
       
        
       
       for (
       
       int 
       
       i 
       
       = 
       
       0; 
       
       i 
       
       <
       
       max ; 
       
       i
       
       ++) {
       
       
            
       
       // Will be the first n Put queens in the first column of the row 
       
       
            
       
       array[
       
       n]
       
       =
       
       i;
       
       
            
       
       // Judge when placing the n Whether the positions of the Queens conflict 
       
       
            
       
       if(
       
       judge(
       
       n)){
       
       
                
       
       // If the location does not conflict , Start to put the first （n+1） A queen 
       
       
                
       
       check(
       
       n
       
       +
       
       1);
       
       
            }
       
       
            
       
       // If conflict , Will be the first n The queen is placed in the next position of the line , Continue to judge 
       
       
        }
       
       
    }
       
       

       
       
    
       
       /** When placing the first n When I was a queen , Go and check whether the queen conflicts with the queen already placed in front 
       
       
     
       
       *  Be careful ：check It's every recursion , Enter into check There will be  for(int i=0;i<max;i++) , So there will be backtracking 
       
       
     
       
       * */
       
       
    
       
       private 
       
       boolean 
       
       judge(
       
       int 
       
       n){
       
       
        
       
       //n It means the first one n A queen 
       
       
        
       
       for (
       
       int 
       
       i 
       
       = 
       
       0; 
       
       i 
       
       <
       
       n ; 
       
       i
       
       ++) {
       
       
            
       
       /**
       
       
             
       
       *  explain ：
       
       
             
       
       * （1） array[i]==array[n] : It means to judge whether two queens are in the same column 
       
       
             
       
       * （2） Math.abs(n-i)==Math.abs(array[n]-array[i])): It means to judge whether two queens are in the same slash ( Think about )
       
       
             
       
       * （3）  There is no need to judge whether it is on the same line （n Has been increasing ）
       
       
             
       
       * */
       
       
            
       
       if(
       
       array[
       
       i]
       
       ==
       
       array[
       
       n]
       
       ||
       
       Math.
       
       abs(
       
       n
       
       -
       
       i)
       
       ==
       
       Math.
       
       abs(
       
       array[
       
       n]
       
       -
       
       array[
       
       i])){
       
       
                
       
       return 
       
       false;
       
       
            }
       
       
        }
       
       
        
       
       return 
       
       true;
       
       
    }
       
       
    
       
       /** Write a method , You can output the Queen's placement */
       
       
    
       
       private 
       
       void 
       
       print(){
       
       
        
       
       count
       
       ++;
       
       
        
       
       for (
       
       int 
       
       i 
       
       = 
       
       0; 
       
       i 
       
       < 
       
       array.
       
       length; 
       
       i
       
       ++) {
       
       
            
       
       System.
       
       out.
       
       print(
       
       array[
       
       i]
       
       +
       
       " ");
       
       
        }
       
       
        
       
       System.
       
       out.
       
       println();
       
       
    }
       
       
}
       
       

       
       

      
      
      
      

       
       
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