游戏是否公平,关键要看是否游戏双方赢的机会是否相等,即判断双方取胜的概率是否相等,或转化为在总情况明确的情况下,判断双方取胜所包含的情况数目是否相等.
树状图,;(分)不公平,理由如下:法一:由树状图可知,,,.所以不公平.法二:从中树状图得知,不是的倍数时,结果是奇数的有种情况,而结果是偶数的有种情况,显然小李胜面大,所以不公平.法三:由于积是的倍数时两人得分相同,所以可直接比较积不是的倍数时,奇数,偶数的概率.,,所以不公平.(分)可将第二道环上的数改为任-奇数;(分)设小军次进入迷宫中心,则解之得.所以小军至少次进入迷宫中心.
本题考查的是游戏公平性的判断.判断游戏公平性就要计算每个事件的概率,概率相等就公平,否则就不公平.用到的知识点为:概率所求情况数与总情况数之比.
4052@@3@@@@游戏公平性@@@@@@271@@Math@@Junior@@$271@@2@@@@概率@@@@@@54@@Math@@Junior@@$54@@1@@@@统计与概率@@@@@@7@@Math@@Junior@@$7@@0@@@@初中数学@@@@@@-1@@Math@@Junior@@$4051@@3@@@@列表法与树状图法@@@@@@271@@Math@@Junior@@$271@@2@@@@概率@@@@@@54@@Math@@Junior@@$54@@1@@@@统计与概率@@@@@@7@@Math@@Junior@@$7@@0@@@@初中数学@@@@@@-1@@Math@@Junior@@
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求解答 学习搜索引擎 | 某学校七年级数学兴趣小组组织一次数学活动.在一座有三道环形路的数字迷宫的每个进口处都标记着一个数,要求进入者把自己当做数"{1}'',进入时必须乘进口处的数,并将结果带到下一个进口,依次累乘下去,在通过最后一个进口时,只有乘积是5的倍数,才可以进入迷宫中心,现让一名5岁小朋友小军从最外环任一个进口进入.(1)小军能进入迷宫中心的概率是多少?请画出树状图进行说明;(2)小组两位组员小张和小李商量做一个小游戏,以猜测小军进迷宫的结果比胜负.游戏规则规完:小军如果能进入迷宫中心,小张和小李各得1分;小军如果不能进入迷宫中心,则他在最后一个进口处所得乘积是奇数时,小张得3分,所得乘积是偶数时,小李得3分,你认为这个游戏公平吗?如果公平,请说明理由;如果不公平,请在第二道环进口处的两个数中改变其中一个数使游戏公平.(3)在(2)的游戏规则下,让小军从最外环进口任意进入10次,最终小张和小李的总得分之和不超过28分,请问小军至少几次进入迷宫中心?小时候没有什么玩的，经常做迷宫给别人玩儿，有一天我发现只要沿着一边走就一定可以找到出口，因为每次画迷宫都是先画一个长方形，标上入口和出口，然后在长方形的边上进行延展，这样一来其实每次走迷宫都只是在原先长方形四条边的延伸上面行走而已，所以一定会环绕长方形走完：&br&&figure&&img src=&https://pic3.zhimg.com/7ee811c6aec010a66a5fec6_b.jpg& data-rawwidth=&640& data-rawheight=&300& class=&origin_image zh-lightbox-thumb& width=&640& data-original=&https://pic3.zhimg.com/7ee811c6aec010a66a5fec6_r.jpg&&&/figure&迷宫经过 &b&收线、拉直&/b& 两步操作，最后会变成两条线，只要沿着一边走就一定能找到出口。。。&br&&br&&br&制作迷宫的事情受到了很大打击，因为你提出了一个难题，但是别人分分钟搞定，这样的挫败感真的很强。&br&所以我发挥聪明才智，制作出了&b&多层迷宫&/b&这种东西：&br&&figure&&img src=&https://pic2.zhimg.com/cb15c160fc2ab75eb8e2a1_b.jpg& data-rawwidth=&460& data-rawheight=&280& class=&origin_image zh-lightbox-thumb& width=&460& data-original=&https://pic2.zhimg.com/cb15c160fc2ab75eb8e2a1_r.jpg&&&/figure&以上是原理图，可惜世界上玩过我亲手制作的多层迷宫的人不超过10个，因为做一个太麻烦了。。。&br&&br&&br&把多层迷宫进行 &b&收线、拉直&/b& 两步操作，最后会变成大概这个样子：&br&&figure&&img src=&https://pic2.zhimg.com/20d246e66bbb3383aad3d_b.jpg& data-rawwidth=&460& data-rawheight=&400& class=&origin_image zh-lightbox-thumb& width=&460& data-original=&https://pic2.zhimg.com/20d246e66bbb3383aad3d_r.jpg&&&/figure&&br&&br&因为多层迷宫间上下联通的关系，很容易出现循环、嵌套、联通的情况，本来你一直在往左走，走着走着走到了右面。。。&br&所以如果制作复杂的多层迷宫，只要圈圈套圈圈，循环又循环，就可以把迷宫变得很复杂。&br&&br&多层迷宫制作完成后，我对自己的成果非常满意，因为我觉得我发现了一个复杂事物的简单原理。&br&&br&只是从此以后，再也没有画迷宫玩过了，就像九连环、孔明锁、魔方一样，曾经觉得有意思的事情，一旦知道了玩法，就再也不会去动它了。。。
小时候没有什么玩的，经常做迷宫给别人玩儿，有一天我发现只要沿着一边走就一定可以找到出口，因为每次画迷宫都是先画一个长方形，标上入口和出口，然后在长方形的边上进行延展，这样一来其实每次走迷宫都只是在原先长方形四条边的延伸上面行走而已，所以一…
翻到了高中画的迷宫。。。。应该是从那个大门开始走，然后找钥匙，钥匙有罗马数字编号，对应不同的门，最后开启宝箱。。。还有个船需要划到另一个岸边。。。哈哈，又重走了一遍&br&和平面迷宫开始画是一样的，后面在加上垂直线改成立体的。&br&&figure&&img src=&https://pic1.zhimg.com/d290d79fc7fc0_b.jpg& data-rawheight=&1172& data-rawwidth=&2112& class=&origin_image zh-lightbox-thumb& width=&2112& data-original=&https://pic1.zhimg.com/d290d79fc7fc0_r.jpg&&&/figure&
翻到了高中画的迷宫。。。。应该是从那个大门开始走，然后找钥匙，钥匙有罗马数字编号，对应不同的门，最后开启宝箱。。。还有个船需要划到另一个岸边。。。哈哈，又重走了一遍 和平面迷宫开始画是一样的，后面在加上垂直线改成立体的。
&p&% 补充了kruskal算法 &/p&&p&高赞答主们大可分为两类，一类是搞程序的，一类是画画的。在我看来用计算机生成随机迷宫的核心就是“遍历”，在没有环路的前提下把所有能走的地方都走一遍，得到的就是迷宫图案，再定个起点和终点就能玩了。而那些高手们自己画的迷宫，隔着屏幕都能感觉到满满的心机，走到无路可走才发现原来最开始忽略的那条路才是正解，把它比作一部推理小说再合适不过了，显然这一点是计算机无论如何都难以做到的，但这也正是人工智能努力的方向。&/p&&p&身为一个耿直的人（没什么心机），一个手残（不会画画），一个程序渣（刚学完C），却是个迷宫的狂热爱好者，参考了&a href=&//link.zhihu.com/?target=http%3A//bbs.9ria.com/thread--1.html& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&三大迷宫生成算法&/a&，并用万能的MATLAB实现了这三个算法：&/p&&p&深度优先：&/p&&figure&&img src=&https://pic1.zhimg.com/7a147eb75dbc_b.png& data-rawwidth=&576& data-rawheight=&514& class=&origin_image zh-lightbox-thumb& width=&576& data-original=&https://pic1.zhimg.com/7a147eb75dbc_r.jpg&&&/figure&&div class=&highlight&&&pre&&code class=&language-matlab&&&span class=&c&&%深度优先算法&/span&
&span class=&n&&L&/span&&span class=&p&&=&/span&&span class=&mi&&51&/span&&span class=&p&&;&/span&
&span class=&c&&%迷宫大小&/span&
&span class=&n&&maze&/span&&span class=&p&&=&/span&&span class=&nb&&ones&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&);&/span&
&span class=&n&&s&/span&&span class=&p&&=[&/span&&span class=&mi&&2&/span& &span class=&mi&&2&/span&&span class=&p&&];&/span&&span class=&c&&%起点&/span&
&span class=&n&&f&/span&&span class=&p&&=[&/span&&span class=&n&&L&/span& &span class=&n&&L&/span&&span class=&p&&];&/span&&span class=&c&&%终点&/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&=&/span&&span class=&n&&s&/span&&span class=&p&&;&/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&last&/span&&span class=&p&&=&/span&&span class=&n&&s&/span&&span class=&p&&;&/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&next&/span&&span class=&p&&=[&/span&&span class=&mi&&2&/span& &span class=&mi&&4&/span&&span class=&p&&;&/span&&span class=&mi&&4&/span& &span class=&mi&&2&/span&&span class=&p&&];&/span&
&span class=&k&&while&/span&&span class=&p&&(&/span&&span class=&o&&~&/span&&span class=&nb&&isempty&/span&&span class=&p&&(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&last&/span&&span class=&p&&))&/span&
&span class=&k&&if&/span&&span class=&p&&(&/span&&span class=&o&&~&/span&&span class=&nb&&isempty&/span&&span class=&p&&(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&next&/span&&span class=&p&&))&/span&
&span class=&c&&%下一步有路走&/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&last&/span&&span class=&p&&=[&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&;&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&last&/span&&span class=&p&&];&/span&
&span class=&p&&[&/span&&span class=&n&&a&/span&&span class=&p&&,&/span&&span class=&n&&b&/span&&span class=&p&&]=&/span&&span class=&nb&&size&/span&&span class=&p&&(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&next&/span&&span class=&p&&);&/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&=&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&next&/span&&span class=&p&&(&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&a&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&),:);&/span&&span class=&c&&%确定下一步&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&))=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&&span class=&c&&%走过抹零&/span&
&span class=&n&&maze&/span&&span class=&p&&((&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&last&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&))&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&,(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&last&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&))&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&next&/span&&span class=&p&&=[];&/span&&span class=&c&&%更新next&/span&
&span class=&k&&for&/span& &span class=&nb&&i&/span&&span class=&p&&=&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&-&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&
&span class=&k&&for&/span& &span class=&nb&&j&/span&&span class=&p&&=&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&-&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&
&span class=&k&&if&/span&&span class=&p&&((&/span&&span class=&nb&&i&/span&&span class=&o&&&&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&nb&&i&/span&&span class=&o&&&&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&nb&&j&/span&&span class=&o&&&&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&nb&&j&/span&&span class=&o&&&&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&c&&...&/span&
&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&last&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&~=&/span&&span class=&nb&&i&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&last&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&~=&/span&&span class=&nb&&j&/span&&span class=&p&&)&/span&&span class=&c&&...&/span&
&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&nb&&i&/span&&span class=&p&&,&/span&&span class=&nb&&j&/span&&span class=&p&&)&/span&&span class=&o&&~=&/span&&span class=&mi&&0&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&c&&...&/span&
&span class=&p&&(&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&-&/span&&span class=&nb&&i&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&-&/span&&span class=&nb&&j&/span&&span class=&p&&)&/span&&span class=&o&&==&/span&&span class=&mi&&2&/span&&span class=&p&&))&/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&next&/span&&span class=&p&&=[&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&next&/span&&span class=&p&&;[&/span&&span class=&nb&&i&/span& &span class=&nb&&j&/span&&span class=&p&&]];&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&else&/span&
&span class=&c&&%下一步没路走&/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&=&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&last&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&,:);&/span&&span class=&c&&%退回 &/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&last&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&,:)=[];&/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&next&/span&&span class=&p&&=[];&/span&&span class=&c&&%更新next&/span&
&span class=&k&&for&/span& &span class=&nb&&i&/span&&span class=&p&&=&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&-&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&
&span class=&k&&for&/span& &span class=&nb&&j&/span&&span class=&p&&=&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&-&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&
&span class=&k&&if&/span&&span class=&p&&((&/span&&span class=&nb&&i&/span&&span class=&o&&&&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&nb&&i&/span&&span class=&o&&&&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&nb&&j&/span&&span class=&o&&&&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&nb&&j&/span&&span class=&o&&&&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&c&&...&/span&
&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&nb&&i&/span&&span class=&p&&,&/span&&span class=&nb&&j&/span&&span class=&p&&)&/span&&span class=&o&&~=&/span&&span class=&mi&&0&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&c&&...&/span&
&span class=&p&&(&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&-&/span&&span class=&nb&&i&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&temp&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&-&/span&&span class=&nb&&j&/span&&span class=&p&&)&/span&&span class=&o&&==&/span&&span class=&mi&&2&/span&&span class=&p&&))&/span&
&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&next&/span&&span class=&p&&=[&/span&&span class=&n&&start&/span&&span class=&p&&.&/span&&span class=&n&&next&/span&&span class=&p&&;[&/span&&span class=&nb&&i&/span& &span class=&nb&&j&/span&&span class=&p&&]];&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&/code&&/pre&&/div&&br&&p&递归分割：&/p&&figure&&img src=&https://pic3.zhimg.com/86a9ab0c472aea_b.png& data-rawwidth=&576& data-rawheight=&514& class=&origin_image zh-lightbox-thumb& width=&576& data-original=&https://pic3.zhimg.com/86a9ab0c472aea_r.jpg&&&/figure&&div class=&highlight&&&pre&&code class=&language-matlab&& &span class=&c&&%递归分割算法&/span&
&span class=&n&&L&/span&&span class=&p&&=&/span&&span class=&mi&&51&/span&&span class=&p&&;&/span&
&span class=&c&&%迷宫大小&/span&
&span class=&k&&global&/span& &span class=&n&&maze&/span&
&span class=&n&&maze&/span&&span class=&p&&=&/span&&span class=&nb&&ones&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&);&/span& &span class=&c&&%一片空地&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)=&/span&&span class=&nb&&zeros&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&p&&);&/span&
&span class=&n&&dvd&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&);&/span&
&span class=&c&&%递归分割&/span&
&span class=&n&&image&/span&&span class=&p&&(&/span&&span class=&mi&&50&/span&&span class=&o&&*&/span&&span class=&n&&maze&/span&&span class=&p&&);&/span&
&span class=&k&&function&/span&&span class=&w&& &/span&&span class=&nf&&dvd&/span&&span class=&p&&(&/span&x1,x2,y1,y2&span class=&p&&)&/span&&span class=&w&&&/span&
&span class=&k&&global&/span& &span class=&n&&maze&/span&
&span class=&n&&x&/span&&span class=&p&&=[];&/span&
&span class=&n&&y&/span&&span class=&p&&=[];&/span&
&span class=&k&&for&/span& &span class=&nb&&i&/span&&span class=&p&&=&/span&&span class=&n&&x1&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&x2&/span&&span class=&o&&-&/span&&span class=&mi&&2&/span&
&span class=&k&&if&/span&&span class=&p&&((&/span&&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&nb&&i&/span&&span class=&p&&,&/span&&span class=&n&&y1&/span&&span class=&p&&)&/span&&span class=&o&&~=&/span&&span class=&mi&&0&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&nb&&i&/span&&span class=&p&&,&/span&&span class=&n&&y2&/span&&span class=&p&&)&/span&&span class=&o&&~=&/span&&span class=&mi&&0&/span&&span class=&p&&))&/span&
&span class=&n&&x&/span&&span class=&p&&=[&/span&&span class=&n&&x&/span& &span class=&nb&&i&/span&&span class=&p&&];&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&for&/span& &span class=&nb&&j&/span&&span class=&p&&=&/span&&span class=&n&&y1&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&y2&/span&&span class=&o&&-&/span&&span class=&mi&&2&/span&
&span class=&k&&if&/span&&span class=&p&&((&/span&&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&x1&/span&&span class=&p&&,&/span&&span class=&nb&&j&/span&&span class=&p&&)&/span&&span class=&o&&~=&/span&&span class=&mi&&0&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&x2&/span&&span class=&p&&,&/span&&span class=&nb&&j&/span&&span class=&p&&)&/span&&span class=&o&&~=&/span&&span class=&mi&&0&/span&&span class=&p&&))&/span&
&span class=&n&&y&/span&&span class=&p&&=[&/span&&span class=&n&&y&/span& &span class=&nb&&j&/span&&span class=&p&&];&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&if&/span&&span class=&p&&(&/span&&span class=&o&&~&/span&&span class=&nb&&isempty&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&p&&)&/span&&span class=&o&&&&~&/span&&span class=&nb&&isempty&/span&&span class=&p&&(&/span&&span class=&n&&y&/span&&span class=&p&&))&/span&
&span class=&c&&%可以画&/span&
&span class=&n&&m&/span&&span class=&p&&=&/span&&span class=&n&&x&/span&&span class=&p&&(&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&nb&&length&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&p&&),&/span&&span class=&mi&&1&/span&&span class=&p&&));&/span&
&span class=&n&&n&/span&&span class=&p&&=&/span&&span class=&n&&y&/span&&span class=&p&&(&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&nb&&length&/span&&span class=&p&&(&/span&&span class=&n&&y&/span&&span class=&p&&),&/span&&span class=&mi&&1&/span&&span class=&p&&));&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&y1&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&:&/span&&span class=&n&&y2&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&)=&/span&&span class=&mi&&1&/span&&span class=&p&&;&/span&
&span class=&c&&%画墙&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&x1&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&:&/span&&span class=&n&&x2&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&n&&n&/span&&span class=&p&&)=&/span&&span class=&mi&&1&/span&&span class=&p&&;&/span&
&span class=&k&&switch&/span& &span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&mi&&4&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&
&span class=&c&&%开三个门&/span&
&span class=&k&&case&/span& &span class=&mi&&1&/span&
&span class=&c&&%maze(m,y1+randperm(n-y1-1,1))=0;&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&n&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&y2&/span&&span class=&o&&-&/span&&span class=&n&&n&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&))=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&x1&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&o&&-&/span&&span class=&n&&x1&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&n&&n&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&x2&/span&&span class=&o&&-&/span&&span class=&n&&m&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&n&&n&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&k&&case&/span& &span class=&mi&&2&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&y1&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&n&/span&&span class=&o&&-&/span&&span class=&n&&y1&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&))=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&c&&%maze(m,n+randperm(y2-n-1,1))=0;&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&x1&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&o&&-&/span&&span class=&n&&x1&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&n&&n&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&x2&/span&&span class=&o&&-&/span&&span class=&n&&m&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&n&&n&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&k&&case&/span& &span class=&mi&&3&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&y1&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&n&/span&&span class=&o&&-&/span&&span class=&n&&y1&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&))=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&n&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&y2&/span&&span class=&o&&-&/span&&span class=&n&&n&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&))=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&c&&%maze(x1+randperm(m-x1-1,1),n)=0;&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&x2&/span&&span class=&o&&-&/span&&span class=&n&&m&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&n&&n&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&k&&case&/span& &span class=&mi&&4&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&y1&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&n&/span&&span class=&o&&-&/span&&span class=&n&&y1&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&))=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&n&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&y2&/span&&span class=&o&&-&/span&&span class=&n&&n&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&))=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&x1&/span&&span class=&o&&+&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&o&&-&/span&&span class=&n&&x1&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&n&&n&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&c&&%maze(m+randperm(x2-m-1,1),n)=0;&/span&
&span class=&k&&end&/span&
&span class=&c&&%继续分割&/span&
&span class=&k&&if&/span&&span class=&p&&(&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&o&&-&/span&&span class=&n&&x1&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mi&&3&/span&&span class=&p&&)&/span&&span class=&o&&&&&/span&&span class=&p&&(&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&n&/span&&span class=&o&&-&/span&&span class=&n&&y1&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mi&&3&/span&&span class=&p&&)&/span&
&span class=&n&&dvd&/span&&span class=&p&&(&/span&&span class=&n&&x1&/span&&span class=&p&&,&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&y1&/span&&span class=&p&&,&/span&&span class=&n&&n&/span&&span class=&p&&);&/span&
&span class=&k&&end&/span&
&span class=&k&&if&/span&&span class=&p&&(&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&o&&-&/span&&span class=&n&&x1&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mi&&3&/span&&span class=&o&&&&&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&n&/span&&span class=&o&&-&/span&&span class=&n&&y2&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mi&&3&/span&&span class=&p&&)&/span&
&span class=&n&&dvd&/span&&span class=&p&&(&/span&&span class=&n&&x1&/span&&span class=&p&&,&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&n&/span&&span class=&p&&,&/span&&span class=&n&&y2&/span&&span class=&p&&);&/span&
&span class=&k&&end&/span&
&span class=&k&&if&/span&&span class=&p&&(&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&o&&-&/span&&span class=&n&&x2&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mi&&3&/span&&span class=&o&&&&&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&n&/span&&span class=&o&&-&/span&&span class=&n&&y1&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mi&&3&/span&&span class=&p&&)&/span&
&span class=&n&&dvd&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&x2&/span&&span class=&p&&,&/span&&span class=&n&&y1&/span&&span class=&p&&,&/span&&span class=&n&&n&/span&&span class=&p&&);&/span&
&span class=&k&&end&/span&
&span class=&k&&if&/span&&span class=&p&&(&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&o&&-&/span&&span class=&n&&x2&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mi&&3&/span&&span class=&o&&&&&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&n&/span&&span class=&o&&-&/span&&span class=&n&&y2&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mi&&3&/span&&span class=&p&&)&/span&
&span class=&n&&dvd&/span&&span class=&p&&(&/span&&span class=&n&&m&/span&&span class=&p&&,&/span&&span class=&n&&x2&/span&&span class=&p&&,&/span&&span class=&n&&n&/span&&span class=&p&&,&/span&&span class=&n&&y2&/span&&span class=&p&&);&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&/code&&/pre&&/div&&br&&p&Prim算法：&/p&&figure&&img src=&https://pic1.zhimg.com/ef7f5a843b78ebcad048_b.png& data-rawwidth=&576& data-rawheight=&514& class=&origin_image zh-lightbox-thumb& width=&576& data-original=&https://pic1.zhimg.com/ef7f5a843b78ebcad048_r.jpg&&&/figure&&div class=&highlight&&&pre&&code class=&language-matlab&&&span class=&c&&%prime算法&/span&
&span class=&n&&L&/span&&span class=&p&&=&/span&&span class=&mi&&51&/span&&span class=&p&&;&/span&
&span class=&c&&%迷宫大小,奇数时小边界&/span&
&span class=&n&&maze&/span&&span class=&p&&=&/span&&span class=&nb&&ones&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&);&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&walls&/span&&span class=&p&&=[&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&3&/span&&span class=&p&&,&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&;&/span&&span class=&mi&&3&/span&&span class=&p&&,&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&0&/span&&span class=&p&&];&/span&
&span class=&k&&while&/span&&span class=&p&&(&/span&&span class=&o&&~&/span&&span class=&nb&&isempty&/span&&span class=&p&&(&/span&&span class=&n&&walls&/span&&span class=&p&&))&/span&
&span class=&p&&[&/span&&span class=&n&&a&/span&&span class=&p&&,&/span&&span class=&n&&b&/span&&span class=&p&&]=&/span&&span class=&nb&&size&/span&&span class=&p&&(&/span&&span class=&n&&walls&/span&&span class=&p&&);&/span&
&span class=&n&&wn&/span&&span class=&p&&=&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&n&&a&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&);&/span&
&span class=&n&&w&/span&&span class=&p&&=&/span&&span class=&n&&walls&/span&&span class=&p&&(&/span&&span class=&n&&wn&/span&&span class=&p&&,:);&/span&&span class=&c&&%随机选一个墙&/span&
&span class=&n&&walls&/span&&span class=&p&&(&/span&&span class=&n&&wn&/span&&span class=&p&&,:)=[];&/span&
&span class=&n&&x&/span&&span class=&p&&=&/span&&span class=&n&&w&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&n&&w&/span&&span class=&p&&(&/span&&span class=&mi&&3&/span&&span class=&p&&);&/span&
&span class=&n&&y&/span&&span class=&p&&=&/span&&span class=&n&&w&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&n&&w&/span&&span class=&p&&(&/span&&span class=&mi&&4&/span&&span class=&p&&);&/span&
&span class=&k&&if&/span& &span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&p&&,&/span&&span class=&n&&y&/span&&span class=&p&&)&/span&&span class=&o&&~=&/span&&span class=&mi&&0&/span&&span class=&o&&&&&/span&&span class=&n&&x&/span&&span class=&o&&&&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&o&&&&&/span&&span class=&n&&x&/span&&span class=&o&&&&/span&&span class=&mi&&1&/span&&span class=&o&&&&&/span&&span class=&n&&y&/span&&span class=&o&&&&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&o&&&&&/span&&span class=&n&&y&/span&&span class=&o&&&&/span&&span class=&mi&&1&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&w&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&n&&w&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&))=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&p&&,&/span&&span class=&n&&y&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&k&&for&/span& &span class=&nb&&i&/span&&span class=&p&&=&/span&&span class=&n&&x&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&:&/span&&span class=&n&&x&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&
&span class=&c&&%加入新墙&/span&
&span class=&k&&for&/span& &span class=&nb&&j&/span&&span class=&p&&=&/span&&span class=&n&&y&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&:&/span&&span class=&n&&y&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&
&span class=&k&&if&/span& &span class=&nb&&i&/span&&span class=&o&&&&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&o&&&&&/span&&span class=&nb&&i&/span&&span class=&o&&&&/span&&span class=&mi&&1&/span&&span class=&o&&&&&/span&&span class=&nb&&j&/span&&span class=&o&&&&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&o&&&&&/span&&span class=&nb&&j&/span&&span class=&o&&&&/span&&span class=&mi&&1&/span&&span class=&o&&&&&/span&&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&nb&&i&/span&&span class=&p&&,&/span&&span class=&nb&&j&/span&&span class=&p&&)&/span&&span class=&o&&~=&/span&&span class=&mi&&0&/span&&span class=&o&&&&&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&o&&-&/span&&span class=&nb&&i&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&nb&&abs&/span&&span class=&p&&(&/span&&span class=&n&&y&/span&&span class=&o&&-&/span&&span class=&nb&&j&/span&&span class=&p&&)&/span&&span class=&o&&==&/span&&span class=&mi&&1&/span&
&span class=&n&&walls&/span&&span class=&p&&=[&/span&&span class=&n&&walls&/span&&span class=&p&&;&/span&&span class=&nb&&i&/span&&span class=&p&&,&/span&&span class=&nb&&j&/span&&span class=&p&&,&/span&&span class=&nb&&i&/span&&span class=&o&&-&/span&&span class=&n&&x&/span&&span class=&p&&,&/span&&span class=&nb&&j&/span&&span class=&o&&-&/span&&span class=&n&&y&/span&&span class=&p&&];&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&n&&image&/span&&span class=&p&&(&/span&&span class=&mi&&50&/span&&span class=&o&&*&/span&&span class=&n&&maze&/span&&span class=&p&&)&/span&
&/code&&/pre&&/div&&br&&p&Kruskal算法:(添加)&/p&&figure&&img src=&https://pic2.zhimg.com/v2-e491ee3cbe637aa9ced5_b.png& data-rawwidth=&576& data-rawheight=&514& class=&origin_image zh-lightbox-thumb& width=&576& data-original=&https://pic2.zhimg.com/v2-e491ee3cbe637aa9ced5_r.jpg&&&/figure&&div class=&highlight&&&pre&&code class=&language-matlab&&&span class=&n&&L&/span&&span class=&p&&=&/span&&span class=&mi&&101&/span&&span class=&p&&;&/span&&span class=&c&&%迷宫大小，奇数&/span&
&span class=&n&&maze&/span&&span class=&p&&=&/span&&span class=&nb&&ones&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&);&/span&
&span class=&n&&tail&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&:(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&:(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&root&/span&&span class=&p&&=&/span&&span class=&nb&&zeros&/span&&span class=&p&&((&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&4&/span&&span class=&p&&,(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&4&/span&&span class=&p&&);&/span&
&span class=&n&&gray&/span&&span class=&p&&=&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&L&/span&&span class=&o&&*&/span&&span class=&n&&L&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&;&/span&
&span class=&c&&%白点加入&/span&
&span class=&k&&for&/span& &span class=&nb&&i&/span&&span class=&p&&=&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&
&span class=&k&&for&/span& &span class=&nb&&j&/span&&span class=&p&&=&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&mi&&2&/span&&span class=&p&&:&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&nb&&i&/span&&span class=&p&&,&/span&&span class=&nb&&j&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&c&&%所有白点的tail&/span&
&span class=&k&&for&/span& &span class=&nb&&i&/span&&span class=&p&&=&/span&&span class=&mi&&1&/span&&span class=&p&&:(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&
&span class=&k&&for&/span& &span class=&nb&&j&/span&&span class=&p&&=&/span&&span class=&mi&&1&/span&&span class=&p&&:(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&
&span class=&n&&tail&/span&&span class=&p&&(&/span&&span class=&nb&&i&/span&&span class=&p&&,&/span&&span class=&nb&&j&/span&&span class=&p&&)=(&/span&&span class=&nb&&i&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&o&&+&/span&&span class=&nb&&j&/span&&span class=&p&&;&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&c&&%所有root只有自己&/span&
&span class=&k&&for&/span& &span class=&nb&&i&/span&&span class=&p&&=&/span&&span class=&mi&&1&/span&&span class=&p&&:(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&4&/span&
&span class=&n&&root&/span&&span class=&p&&(&/span&&span class=&nb&&i&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&)=&/span&&span class=&nb&&i&/span&&span class=&p&&;&/span&
&span class=&k&&end&/span&
&span class=&k&&while&/span&&span class=&p&&(&/span&&span class=&o&&~&/span&&span class=&nb&&isempty&/span&&span class=&p&&(&/span&&span class=&n&&gray&/span&&span class=&p&&))&/span&
&span class=&c&&%
tail&/span&
&span class=&c&&%
image(50*maze);&/span&
&span class=&n&&tmp&/span&&span class=&p&&=&/span&&span class=&n&&gray&/span&&span class=&p&&(&/span&&span class=&n&&randperm&/span&&span class=&p&&(&/span&&span class=&nb&&length&/span&&span class=&p&&(&/span&&span class=&n&&gray&/span&&span class=&p&&),&/span&&span class=&mi&&1&/span&&span class=&p&&));&/span&
&span class=&n&&link&/span&&span class=&p&&=[&/span&&span class=&nb&&fix&/span&&span class=&p&&((&/span&&span class=&n&&tmp&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&n&&L&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&nb&&mod&/span&&span class=&p&&(&/span&&span class=&n&&tmp&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&n&&L&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&];&/span&
&span class=&c&&%找到灰墙连接的两个白点tail坐标&/span&
&span class=&k&&if&/span&&span class=&p&&(&/span&&span class=&nb&&mod&/span&&span class=&p&&(&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&==&/span&&span class=&mi&&0&/span&&span class=&p&&)&/span&
&span class=&n&&node1&/span&&span class=&p&&=[&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&,(&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&];&/span&
&span class=&n&&node2&/span&&span class=&p&&=[(&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&,(&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&];&/span&
&span class=&k&&else&/span&
&span class=&n&&node1&/span&&span class=&p&&=[(&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&,&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&];&/span&
&span class=&n&&node2&/span&&span class=&p&&=[(&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&,(&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&];&/span&
&span class=&k&&end&/span&
&span class=&c&&%开墙条件两个白点有不同tail&/span&
&span class=&n&&tn1&/span&&span class=&p&&=&/span&&span class=&n&&tail&/span&&span class=&p&&(&/span&&span class=&n&&node1&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&n&&node1&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&));&/span&
&span class=&n&&tn2&/span&&span class=&p&&=&/span&&span class=&n&&tail&/span&&span class=&p&&(&/span&&span class=&n&&node2&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&),&/span&&span class=&n&&node2&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&));&/span&
&span class=&k&&if&/span&&span class=&p&&(&/span&&span class=&n&&tn1&/span&&span class=&o&&~=&/span&&span class=&n&&tn2&/span&&span class=&p&&)&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&n&&gray&/span&&span class=&p&&=&/span&&span class=&n&&setdiff&/span&&span class=&p&&(&/span&&span class=&n&&gray&/span&&span class=&p&&,&/span&&span class=&n&&tmp&/span&&span class=&p&&);&/span&
&span class=&c&&%变成同一个tail&/span&
&span class=&k&&for&/span& &span class=&n&&k&/span&&span class=&p&&=&/span&&span class=&mi&&1&/span&&span class=&p&&:(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&4&/span&
&span class=&k&&if&/span& &span class=&n&&root&/span&&span class=&p&&(&/span&&span class=&n&&tn2&/span&&span class=&p&&,&/span&&span class=&n&&k&/span&&span class=&p&&)&/span&&span class=&o&&==&/span&&span class=&mi&&0&/span&
&span class=&k&&break&/span&&span class=&p&&;&/span&
&span class=&k&&else&/span&
&span class=&n&&tail&/span&&span class=&p&&(&/span&&span class=&nb&&fix&/span&&span class=&p&&((&/span&&span class=&n&&root&/span&&span class=&p&&(&/span&&span class=&n&&tn2&/span&&span class=&p&&,&/span&&span class=&n&&k&/span&&span class=&p&&)&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&p&&((&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&))&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&nb&&mod&/span&&span class=&p&&(&/span&&span class=&n&&root&/span&&span class=&p&&(&/span&&span class=&n&&tn2&/span&&span class=&p&&,&/span&&span class=&n&&k&/span&&span class=&p&&)&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&,(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)=&/span&&span class=&n&&tn1&/span&&span class=&p&&;&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&c&&%改变root&/span&
&span class=&n&&n&/span&&span class=&p&&=&/span&&span class=&mi&&1&/span&&span class=&p&&;&/span&
&span class=&k&&for&/span& &span class=&n&&k&/span&&span class=&p&&=&/span&&span class=&mi&&1&/span&&span class=&p&&:(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&n&&L&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&mi&&4&/span&
&span class=&k&&if&/span& &span class=&n&&root&/span&&span class=&p&&(&/span&&span class=&n&&tn1&/span&&span class=&p&&,&/span&&span class=&n&&k&/span&&span class=&p&&)&/span&&span class=&o&&==&/span&&span class=&mi&&0&/span&
&span class=&k&&if&/span& &span class=&n&&root&/span&&span class=&p&&(&/span&&span class=&n&&tn2&/span&&span class=&p&&,&/span&&span class=&n&&n&/span&&span class=&p&&)&/span&&span class=&o&&==&/span&&span class=&mi&&0&/span&
&span class=&k&&break&/span&&span class=&p&&;&/span&
&span class=&k&&else&/span&
&span class=&n&&root&/span&&span class=&p&&(&/span&&span class=&n&&tn1&/span&&span class=&p&&,&/span&&span class=&n&&k&/span&&span class=&p&&)=&/span&&span class=&n&&root&/span&&span class=&p&&(&/span&&span class=&n&&tn2&/span&&span class=&p&&,&/span&&span class=&n&&n&/span&&span class=&p&&);&/span&
&span class=&n&&n&/span&&span class=&p&&=&/span&&span class=&n&&n&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&;&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&n&&root&/span&&span class=&p&&(&/span&&span class=&n&&tn2&/span&&span class=&p&&,:)=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&k&&else&/span&
&span class=&n&&maze&/span&&span class=&p&&(&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&n&&link&/span&&span class=&p&&(&/span&&span class=&mi&&2&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&)=&/span&&span class=&mi&&1&/span&&span class=&p&&;&/span&
&span class=&n&&gray&/span&&span class=&p&&=&/span&&span class=&n&&setdiff&/span&&span class=&p&&(&/span&&span class=&n&&gray&/span&&span class=&p&&,&/span&&span class=&n&&tmp&/span&&span class=&p&&);&/span&
&span class=&k&&end&/span&
&span class=&k&&end&/span&
&span class=&n&&image&/span&&span class=&p&&(&/span&&span class=&mi&&50&/span&&span class=&o&&*&/span&&span class=&n&&maze&/span&&span class=&p&&);&/span&
&/code&&/pre&&/div&&br&&br&&p&为了增加娱乐性，还用GUI画了个很low的游戏界面：&/p&&p&不过MATLAB毕竟不是用来开发游戏的。。。
GUI链接：&a href=&//link.zhihu.com/?target=http%3A//www.ilovematlab.cn/thread--1.html& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&MATLAB基于guide的迷宫游戏&/a&&/p&&p&这三种算法比较起来的话，深度优先生成的迷宫是最难看的，其实就是一条长蛇；递归分割产生的迷宫是很多个房间，相对来说比较好看；Prim算法生成的迷宫则是一颗向四面八方生长的树，也是这里面最难走的一种。
至于kruskal算法，最后的效果跟prim差不多，但实现起来要复杂很多。。
用这些思想设计三维迷宫我觉得也是可以的。但也有局限，比如说没有环路。
其实都是从这里面搬来的：&a href=&//link.zhihu.com/?target=https%3A//en.wikipedia.org/wiki/Maze_generation_algorithm& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&Maze generation algorithm&/a&&/p&&p&有时迷宫吸引人的并不光它的复杂，还是一些精美的画面，让我沉迷于其中的世界无法自拔。所以迷宫不单是一堆套路，还是一门艺术。&/p&&p&大爱的纪念碑谷~~~&/p&
% 补充了kruskal算法 高赞答主们大可分为两类，一类是搞程序的，一类是画画的。在我看来用计算机生成随机迷宫的核心就是“遍历”，在没有环路的前提下把所有能走的地方都走一遍，得到的就是迷宫图案，再定个起点和终点就能玩了。而那些高手们自己…
首次答题。详细画迷宫步骤的&b&多图&/b&答案。&br&这里只介绍我常画的一种手绘迷宫，&b&算是我原创的迷宫风格吧&/b&，因为我没在其它地方见过类似我这样的迷宫。如有相似的，望告知，谢谢。&br&大家说的都是二维迷宫，其他的回答里有评论说想知道三维迷宫怎么画，我这里就告诉大家怎么画&b&三维迷宫。&/b&其实也不算三维迷宫，只是在二维的纸面上画，脑补出三维的场景。&br&&br&------------&br&先看一幅我以前画的迷宫，尝试走走：（迷宫答案在最后）&br&&figure&&img src=&https://pic2.zhimg.com/4bcd387d921f4ae7607e31_b.jpg& data-rawwidth=&863& data-rawheight=&1200& class=&origin_image zh-lightbox-thumb& width=&863& data-original=&https://pic2.zhimg.com/4bcd387d921f4ae7607e31_r.jpg&&&/figure&&br&&br&这种迷宫的优势在于：&br&1.无法用“左手定则”或“右手定则”（在二维迷宫中，只要沿着左墙壁或右墙壁一直走，就能走到出口）。这种迷宫若用此方法，在入口进入会回到入口。&br&2.没有断头路（在二维迷宫中，许多路是不通的，走到没路了就返回分岔口走另一条路）。这种迷宫，每一条路都相通。&br&3.走着走着就会回到入口，&b&以此捉弄玩家来取乐～&/b&&br&4.因为每一条路都是相通的，理论上有无数种走法都是正确答案。&br&5.相对来说没有普通迷宫那样会造成强烈的密集恐惧。&br&------------&br&下面向大家介绍怎么画。&br&首先要的美术功底：很简单，只需能画出类似公路俯视图的直线和曲便可，如下图这种。&br&&figure&&img src=&https://pic2.zhimg.com/4bba894c95dba6f2d1d22d82c9caf9fd_b.jpg& data-rawwidth=&800& data-rawheight=&598& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic2.zhimg.com/4bba894c95dba6f2d1d22d82c9caf9fd_r.jpg&&&/figure&&br&（图1）&br&若画得不光滑或粗细不一，多练便可。&br&&b&第一步&/b&：画入口和出口，在纸面的任意位置的行。&br&&figure&&img src=&https://pic3.zhimg.com/a376a065bd9398adfcf0c2c_b.jpg& data-rawwidth=&800& data-rawheight=&367& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic3.zhimg.com/a376a065bd9398adfcf0c2c_r.jpg&&&/figure&（图2）&br&（由于大部分迷宫在设计的时候，都是从入口开始画，最后画到出口。部分玩家喜欢逆过来玩迷宫，从出口进入，从入口出去，他们会觉得这样刚简单，其实也是有道理的，所以我在画迷宫的时候，习惯从入口开始画一半，从出口开始再画另一半，最后在中间把它们接起来。这样做，无论是玩家从入口开始玩还是从出口开始玩，难度都差不多。）&br&&b&第二步&/b&：在入口处随意画一些分岔路，可以随机发挥，不必太用心设计道路。&br&&figure&&img src=&https://pic3.zhimg.com/3ece4e9dbef_b.jpg& data-rawwidth=&800& data-rawheight=&529& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic3.zhimg.com/3ece4e9dbef_r.jpg&&&/figure&（图3）&br&继续随意画，可以不用思考到底哪一条路才是想要的正确道路。岔路太多的话，可以把部分岔路首尾相接起来。&br&&figure&&img src=&https://pic1.zhimg.com/1c8ae8dc30f96af62c34_b.jpg& data-rawwidth=&800& data-rawheight=&572& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic1.zhimg.com/1c8ae8dc30f96af62c34_r.jpg&&&/figure&（图4）&br&&b&第三步&/b&：增加迷宫的个性元素。例如同样用这种道路的画风画出“知乎”二字，它们将成为迷宫道路的一部分。&br&&figure&&img src=&https://pic3.zhimg.com/fb7aa00532_b.jpg& data-rawwidth=&800& data-rawheight=&922& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic3.zhimg.com/fb7aa00532_r.jpg&&&/figure&（图5）&br&把“知乎”与之前画的道路相连接。&br&&figure&&img src=&https://pic3.zhimg.com/358cb6da6b9e65bf679a6426cbf07066_b.jpg& data-rawwidth=&800& data-rawheight=&969& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic3.zhimg.com/358cb6da6b9e65bf679a6426cbf07066_r.jpg&&&/figure&（图6）&br&&b&第四步&/b&：开始设计迷宫的正确道路。&br&这个例子是能进入“知乎”的左边“矢”字的道路为“正确道路”。其余分岔的道路为“错误道路”，让它们首尾相接，这样就把那些“错误道路”都解决掉了。注意画那些“错误道路”的时候，别接到“矢”字上了。&br&&figure&&img src=&https://pic3.zhimg.com/2b93eb7e1c694b5d8592_b.jpg& data-rawwidth=&800& data-rawheight=&969& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic3.zhimg.com/2b93eb7e1c694b5d8592_r.jpg&&&/figure&（图7）&br&&figure&&img src=&https://pic4.zhimg.com/2cdc3b290ae46d74493eaf056addfb83_b.jpg& data-rawwidth=&800& data-rawheight=&963& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic4.zhimg.com/2cdc3b290ae46d74493eaf056addfb83_r.jpg&&&/figure&（图8）&br&此时，错误道路都首尾相连了，剩下“矢”字发出来的道路。&br&“矢”字发出来的道路，选择一条“正确道路”，其余为“错误道路”，延伸它们并让他们首尾相接，又解决掉“错误道路”了。（选择“正确道路”的时候，选那种你觉得玩家主观上不会走的道路）&br&&figure&&img src=&https://pic4.zhimg.com/8bc994ed62c98f576c2b6d8d71c412f3_b.jpg& data-rawwidth=&800& data-rawheight=&1036& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic4.zhimg.com/8bc994ed62c98f576c2b6d8d71c412f3_r.jpg&&&/figure&（图9）&br&&b&第五步&/b&：从出口开始画，按照同样的方法画迷宫。&br&&figure&&img src=&https://pic1.zhimg.com/d8bdf77d77a88b1946a8caf_b.jpg& data-rawwidth=&800& data-rawheight=&1044& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic1.zhimg.com/d8bdf77d77a88b1946a8caf_r.jpg&&&/figure&（图10）&br&继续随意画。刚才的画“乎”字的道路还没用完，可以将“乎”字的部分与出口延伸出来的道路相连。&br&&figure&&img src=&https://pic3.zhimg.com/8c036b7f6bede6d94ad16e41c6da8b7e_b.jpg& data-rawwidth=&800& data-rawheight=&1025& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic3.zhimg.com/8c036b7f6bede6d94ad16e41c6da8b7e_r.jpg&&&/figure&（图11）&br&选择“乎”字的“丶”为正确道路，其他的首尾相接。&br&&figure&&img src=&https://pic3.zhimg.com/4dfb73cd6c5715ecedc12efe_b.jpg& data-rawwidth=&800& data-rawheight=&1001& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic3.zhimg.com/4dfb73cd6c5715ecedc12efe_r.jpg&&&/figure&（图12）&br&现在发现右上角多出一条分岔路，怎么办？&br&它是“错误道路”，让它分岔成两条，然后首尾相连。为了混淆玩家视线，可以绕地图一小圈之后再回来相连。&br&&figure&&img src=&https://pic2.zhimg.com/e8b34c3b8d73f524bf9fcb91_b.jpg& data-rawwidth=&800& data-rawheight=&1063& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic2.zhimg.com/e8b34c3b8d73f524bf9fcb91_r.jpg&&&/figure&（图13）&figure&&img src=&https://pic3.zhimg.com/edc20e3cc08e6_b.jpg& data-rawwidth=&800& data-rawheight=&1068& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic3.zhimg.com/edc20e3cc08e6_r.jpg&&&/figure&（图14）&br&&b&第六步&/b&：把从入口延伸出来的“正确道路”与从出口延伸出来的“正确道路”相接。&br&&figure&&img src=&https://pic3.zhimg.com/edb1176caa0e8d2ebf870aee_b.jpg& data-rawwidth=&800& data-rawheight=&1001& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic3.zhimg.com/edb1176caa0e8d2ebf870aee_r.jpg&&&/figure&（图15）&br&&b&完成&/b&：&br&&figure&&img src=&https://pic4.zhimg.com/11ed940a4fbb46abfccb8083_b.jpg& data-rawwidth=&800& data-rawheight=&1020& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic4.zhimg.com/11ed940a4fbb46abfccb8083_r.jpg&&&/figure&（图16）&br&参考答案：（答案不唯一）&br&&figure&&img src=&https://pic1.zhimg.com/98d44c3f5e813aa6e298e_b.jpg& data-rawwidth=&800& data-rawheight=&1020& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic1.zhimg.com/98d44c3f5e813aa6e298e_r.jpg&&&/figure&（图17）&br&这幅迷宫，是我边答题边画的，画得不是很好，道路设计也比较简单。这是用签字笔快速画成的，曲线不是那么漂亮。有时间的话，可以用铅笔慢慢画，画错了可以擦掉，最后再用签字笔勾边。掌握这张方法后，就可以发挥画出有趣的或者更复杂的迷宫。&br&以上。&br&------------&br&最后，附上开始第一幅迷宫的参考答案：&br&&figure&&img src=&https://pic4.zhimg.com/46581eeabd45d16c5405623_b.jpg& data-rawwidth=&863& data-rawheight=&1200& class=&origin_image zh-lightbox-thumb& width=&863& data-original=&https://pic4.zhimg.com/46581eeabd45d16c5405623_r.jpg&&&/figure&----------&br&再附一幅我在2010年底画的迷宫，难度相对大一些：&br&（上面写有2011 HAPPY NEW YEAR，忽略小字部分的错误拼写和错别字，以及那个丑到不想说的Logo......毕竟是多年前画的了......）&br&（小字部分，Drink是我的英文名，和另一位朋友一样，这个英文名上不了台面，但我一直都没想好正式的英文名）&br&&figure&&img src=&https://pic1.zhimg.com/d6e87e2e4024acad60cdfd6_b.jpg& data-rawwidth=&1003& data-rawheight=&1440& class=&origin_image zh-lightbox-thumb& width=&1003& data-original=&https://pic1.zhimg.com/d6e87e2e4024acad60cdfd6_r.jpg&&&/figure&至于这一幅迷宫，有兴趣的可以尝试挑战一下。以后再放出答案。&br&首次答题，希望大家支持！
首次答题。详细画迷宫步骤的多图答案。 这里只介绍我常画的一种手绘迷宫，算是我原创的迷宫风格吧，因为我没在其它地方见过类似我这样的迷宫。如有相似的，望告知，谢谢。 大家说的都是二维迷宫，其他的回答里有评论说想知道三维迷宫怎么画，我这里就告诉大…
&figure&&img src=&https://pic1.zhimg.com/v2-20dd22b77d42a29835cdf2719685bcfe_b.jpg& data-rawwidth=&800& data-rawheight=&605& class=&origin_image zh-lightbox-thumb& width=&800& data-original=&https://pic1.zhimg.com/v2-20dd22b77d42a29835cdf2719685bcfe_r.jpg&&&/figure&&p&本篇将尝使用canvas + wasm画一个迷宫，生成算法主要用到连通集算法，使用wasm主要是为了提升运行效率。然后再用一个最短路径算法找到迷宫的出路，最后的效果如下：&/p&&p&&br&&/p&&figure&&img src=&https://pic3.zhimg.com/v2-aeedde3252c2_b.png& data-rawwidth=&1614& data-rawheight=&1220& class=&origin_image zh-lightbox-thumb& width=&1614& data-original=&https://pic3.zhimg.com/v2-aeedde3252c2_r.jpg&&&/figure&&p&&br&&/p&&p&&br&&/p&&h2&1. 用连通集算法生成迷宫&/h2&&p&生成迷宫的算法其实很简单，假设迷宫的大小是10 * 10，即这个迷宫有100个格子，通过不断地随机拆掉这100个格子中间的墙，直到可以从第一个格子走到最后一个格子，也就是说第一个格子和最后一个格子处于同一个连通集。具体如下操作：&/p&&p&（1）生成100个格子，每个格子都不相通&/p&&p&（2）随机选取相邻的两个格子，可以是左右相邻或者是上下相邻，判断这两个格子是不是处于同一个连通集，即能否从其中一个格子走到另外一个格子，如果不能，就拆掉它们中间的墙，让它们相连，处于同一个连通集。&/p&&p&（3）重复第二步，直到第一个格子和最后一个格子相连。&/p&&p&那这个连通集应该怎么表示呢？我们用一个一维数组来表示不同的已连通的集合，初始化的时候每个格子的值都为-1，如