【算法总结-回溯法】回溯与八皇后

来源：互联网发布：java能做什么知乎编辑：程序博客网时间：2024/05/18 01:02

<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title> test </title></head><body> <div><?php     /*八皇后问题代码实现      *      *      *      *///根据前几行的放置情况，判断这一行是否合法function attack($n){    global $chess;    for($i=1;$i<=$n-1;$i++){       if($chess[$n]==$chess[$i]+($n-$i)||$chess[$n]==$chess[$i]-($n-$i)||$chess[$n]==$chess[$i]){          return true;       }       }     return false;}//输出每种可能的解function display(){     global $chess;    global $solution;    echo "    solution".sprintf("% 2d",$solution).":";    for($i=1;$i<=8;$i++){       $img = "<img src='../images/$chess[$i].png'/>";       echo $img;     }    echo "</br>";     $solution++;  }//递归放置皇后function putchess($n){      global $chess;    global $solution;    for($i=1;$i<=8;$i++){        $chess[$n] =$i;        if(!attack($n)){//没有冲突           if($n==8){//已经放满，输出               display();   }           else{                              putchess($n+1);                     }                     }//if                 }//for                                }printf("八皇后问题的解如下：<br/>");$solution = 1;//$chess=array(1,2,3,4,5,6,7,8);putchess(1);echo "共有".($solution-1)."种不同的八皇后放置方法";           ?></div></body></html>

效果图：

python版本的解法如下：

def conflict(state,nextX):    nextY = len(state)    for i in range(nextY):        if(abs(state[i]-nextX)) in (0,nextY-i):            return True    return Falsedef queens(num = 8,state = ()):        for pos in range(num):        if not conflict(state,pos):            if len(state) == num-1:                yield (pos,)            else:                for result in queens(num,state+(pos,)):                    yield (pos,)+resultdef prettyprint(solution):    def line(pos,length = len(solution)):        return '. '*(pos) +'X '+'. '*(length-pos-1)    for pos in solution:        print line(pos)import randomprettyprint(random.choice(list(queens(8))))print len(list(queens(8)))

结果：

. . X . . . . . . . . . X . . . . . . . . . X . X . . . . . . . . . . X . . . . . X . . . . . . . . . . . . . X . . . . . X . . 92