[回溯法_八皇后]堆栈实现的非递归版本

[回溯法_八皇后]堆栈实现的非递归版本

                                                                                                                By EmilMatthew

                                                                                                                              05/11/9

 

       其实,用递归或while循环实现N皇后问题效果挺好的(请参考: http://blog.youkuaiyun.com/EmilMatthew/archive/2005/09/15/481411.aspx ),而且思路也很清楚,为什么还要去多加一个栈呢?原因在于,为了更好的训练算法及数据结构的应用,达到融会贯通的目的.做些递归与非递归程序间的转换是起码的要求.(水平菜就得这样来)

       算法陈述:

       用一个数组arr来表示皇后在行间或位置

depth表示下一步探索的深度

Stack作为上层跳转下来时上层位置的中间纪录.*

       Size表示问题的规模.

      

       NQueensProblem Stack Version

压首行首列元素0进栈.

       depth置1

       do

{

       If     depth达到size

                     则跳出并输出结果

              Else

              {

                     If(当前层[depth-1]达到了底部)

                                   将搜索层上跳一层并压栈*

                     Else

                     {

       搜索层(depth)试探同层的下一个位置i

       if这个位置有冲突并且i没有超出问题规模

       {

              将i置于同层的下一个位置.

       }

else if 这个位置有冲突并且i已超出问题规模

       {

              返回到上层的跳下来的位置,借助堆栈(先弹出,然后压新位置)*

              探索层仍为depth

}

Else 当前位置没有冲突

{    

当前位置压栈

       Depth下跳一层(depth++)

}

}           

}

}

 

下面给出算法的C程序实现:

void NQueensProblemStack(int size,FILE* outputFile)

{

       //extern int partFinished(int* arr,int len);

       int depth;

       int i;

       int* arr;

       PSeqStack myStack;

       int flag;

 

 

       assertF(outputFile!=NULL,"in NQueensProblemStack, outputFile is null/n");

      

       myStack=createNullSeqStack();

       arr=(int*)malloc(sizeof(int)*size);

       assertF(arr!=NULL,"in NQueensProblemStack,mem apply failure/n");

      

       //data init

       seqPush(myStack,0);

       i=0;

       depth=1;

       arr[0]=0;

       flag=0;

       while(!isNullSeqStack(myStack))

       {

              if(depth==size)

              {

                     fprintf(outputFile,"Answer of%dQueens Problem:/r/n",size);

                     outputListArrInt(arr,0,size,outputFile);

                     outputQueensAns0(arr,size,outputFile);

                     flag=1;

                     break;

              }

              else

              {

      

                     if(arr[depth-1]==size)//previous has reach to end.

                     {

                            seqPop(myStack);

                            depth-=2;//return to previous level

                            arr[depth]=seqPop(myStack)+1;

                            seqPush(myStack,arr[depth]);

                            depth++;//set current search level

                            i=0;

                     }

                     else

                     {

                            arr[depth]=i;//next level's possible pos

                            printf("%d/t",arr[depth]);

             

                            if(!partFinished(arr,depth+1)&&i<size-1)         

//collide: next level parallel search

                                   i++;

                            else if(!partFinished(arr,depth+1)&&i==size-1)

//collide: return to the pre level

                            {

                                   depth--;//return to previous level

                                   arr[depth]=seqPop(myStack)+1;

                                   seqPush(myStack,arr[depth]);

                                   depth++;//set current search level

                                   i=0;

                            }

                            else//no collide,branching to next level

                            {

                                   seqPush(myStack,arr[depth]);//save current

                                   depth++;

                                   i=0;

                            }

                     }

              }

       }

 

       printf("/ndepth%d/n",depth);

       if(flag==1)

              printf("resolve successfully/n");

       else

              printf("no resolve/n");

}

 

/*aid fun*/

int checkXiePos(int r1,int r2,int c1,int c2)

{

 

       return !(fabs(r1-r2)==fabs(c1-c2));

}

 

int checkVPos(int* arr,int len)

{

       int flag=1;

       int i,j;

       assertF(arr!=NULL,"in checkVPos,arr is null/n");

       for(i=0;i<len-1;i++)

              for(j=i+1;j<len;j++)

                     if(arr[i]==arr[j])

                     {

                            flag=0;

                            break;

                     }

       return flag;

}

 

int partFinished(int* arr,int len)

{

       int flag=1;

       int i,j;

       assertF(arr!=NULL,"in partFinished,arr is null/n");

       flag=flag&&checkVPos(arr,len);

       for(i=0;i<len-1;i++)

              for(j=i+1;j<len;j++)

              {

                     flag=flag&&checkXiePos(i,j,arr[i],arr[j]);

                     if(!flag)goto out;

              }

       out:

       return flag;

}