数据结构实践——迷宫问题之图深度优先遍历解法

本文是针对[数据结构基础系列(7)：图]的实践项目。

【项目 - 迷宫问题之图深度优先遍历解法】  
　　设计一个程序，采用深度优先遍历算法的思路，解决迷宫问题。  
　　（1）建立迷宫对应的图数据结构，并建立其邻接表表示。  
　　（2）采用深度优先遍历的思路设计算法，输出从入口(1,1)点到出口(M,N)的所有迷宫路径。 

[模型建立] 
　　将迷宫中的每一格作为一个顶点，相邻格子可以到达，则对应的顶点之间存在边相连。 
　　例如，下面的迷宫 
 
在使用数组表示时，用０表示格子是空地，用１表示格子处是墙，对应的矩阵是：

<code class="hljs mathematica has-numbering" style="display: block; padding: 0px; background-color: transparent; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background-position: initial initial; background-repeat: initial initial;">    int mg[M+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>][<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">N</span>+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>]=   //迷宫数组    <span class="hljs-list" style="box-sizing: border-box;">{        {1,1,1,1,1,1}</span>,        <span class="hljs-list" style="box-sizing: border-box;">{1,0,0,0,1,1}</span>,        <span class="hljs-list" style="box-sizing: border-box;">{1,0,1,0,0,1}</span>,        <span class="hljs-list" style="box-sizing: border-box;">{1,0,0,0,1,1}</span>,        <span class="hljs-list" style="box-sizing: border-box;">{1,1,0,0,0,1}</span>,        <span class="hljs-list" style="box-sizing: border-box;">{1,1,1,1,1,1}</span>    };</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; background-color: rgb(238, 238, 238); top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right;"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li></ul>

建立的图结构为： 
 
于是，从(1,1)到(4,4)的迷宫问题，转化为寻找顶点(1,1)到顶点(4,4)的路径的问题。

[参考代码]

<code class="hljs cpp has-numbering" style="display: block; padding: 0px; background-color: transparent; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background-position: initial initial; background-repeat: initial initial;"><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include <stdio.h></span><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include <malloc.h></span><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#define MaxSize 100</span><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#define M 4</span><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#define N 4</span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//以下定义邻接表类型</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">typedef</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">struct</span> ANode            <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//边的结点结构类型</span>{    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i,j;                    <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//该边的终点位置(i,j)</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">struct</span> ANode *nextarc;      <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//指向下一条边的指针</span>} ArcNode;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">typedef</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">struct</span> Vnode            <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//邻接表头结点的类型</span>{    ArcNode *firstarc;          <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//指向第一条边</span>} VNode;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">typedef</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">struct</span>{    VNode adjlist[M+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>][N+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>];    <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//邻接表头节点数组</span>} ALGraph;                      <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//图的邻接表类型</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">typedef</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">struct</span>{    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i;                      <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//当前方块的行号</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> j;                      <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//当前方块的列号</span>} Box;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">typedef</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">struct</span>{    Box data[MaxSize];    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> length;                 <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//路径长度</span>} PathType;                     <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//定义路径类型</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> visited[M+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>][N+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>]= {<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>};<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> count=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> CreateList(ALGraph *&G,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> mg[][N+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>])<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//建立迷宫数组对应的邻接表G</span>{    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i,j,i1,j1,di;    ArcNode *p;    G=(ALGraph *)<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">malloc</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(ALGraph));    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (i=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; i<M+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>; i++)                   <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//给邻接表中所有头节点的指针域置初值</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (j=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; j<N+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>; j++)            G->adjlist[i][j].firstarc=NULL;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (i=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i<=M; i++)                    <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//检查mg中每个元素</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (j=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; j<=N; j++)            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (mg[i][j]==<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>)            {                di=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;                <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span> (di<<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">4</span>)                {                    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">switch</span>(di)                    {                    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">case</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>:                        i1=i-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;                        j1=j;                        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">break</span>;                    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">case</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>:                        i1=i;                        j1=j+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;                        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">break</span>;                    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">case</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>:                        i1=i+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;                        j1=j;                        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">break</span>;                    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">case</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">3</span>:                        i1=i, j1=j-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;                        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">break</span>;                    }                    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (mg[i1][j1]==<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>)                          <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//(i1,j1)为可走方块</span>                    {                        p=(ArcNode *)<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">malloc</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(ArcNode));   <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//创建一个节点*p</span>                        p->i=i1;                        p->j=j1;                        p->nextarc=G->adjlist[i][j].firstarc;   <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//将*p节点链到链表后</span>                        G->adjlist[i][j].firstarc=p;                    }                    di++;                }            }}<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//输出邻接表G</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> DispAdj(ALGraph *G){    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i,j;    ArcNode *p;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (i=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; i<M+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>; i++)        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (j=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; j<N+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>; j++)        {            <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"  [%d,%d]: "</span>,i,j);            p=G->adjlist[i][j].firstarc;            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span> (p!=NULL)            {                <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"(%d,%d)  "</span>,p->i,p->j);                p=p->nextarc;            }            <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\n"</span>);        }}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> FindPath(ALGraph *G,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> xi,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> yi,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> xe,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> ye,PathType path){    ArcNode *p;    visited[xi][yi]=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;                   <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//置已访问标记</span>    path.data[path.length].i=xi;    path.data[path.length].j=yi;    path.length++;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (xi==xe && yi==ye)    {        <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"  迷宫路径%d: "</span>,++count);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> k=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; k<path.length; k++)            <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"(%d,%d) "</span>,path.data[k].i,path.data[k].j);        <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"\n"</span>);    }    p=G->adjlist[xi][yi].firstarc;  <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//p指向顶点v的第一条边顶点</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span> (p!=NULL)    {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (visited[p->i][p->j]==<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//若(p->i,p->j)方块未访问,递归访问它</span>            FindPath(G,p->i,p->j,xe,ye,path);        p=p->nextarc;               <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//p指向顶点v的下一条边顶点</span>    }    visited[xi][yi]=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> main(){    ALGraph *G;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> mg[M+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>][N+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>]=                           <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//迷宫数组</span>    {        {<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>},        {<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>},        {<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>},        {<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>},        {<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>},        {<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>}    };    CreateList(G,mg);    <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"迷宫对应的邻接表:\n"</span>);    DispAdj(G); <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//输出邻接表</span>    PathType path;    path.length=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;    <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"所有的迷宫路径:\n"</span>);    FindPath(G,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,M,N,path);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; background-color: rgb(238, 238, 238); top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right;"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li><li style="box-sizing: border-box; padding: 0px 5px;">119</li><li style="box-sizing: border-box; padding: 0px 5px;">120</li><li style="box-sizing: border-box; padding: 0px 5px;">121</li><li style="box-sizing: border-box; padding: 0px 5px;">122</li><li style="box-sizing: border-box; padding: 0px 5px;">123</li><li style="box-sizing: border-box; padding: 0px 5px;">124</li><li style="box-sizing: border-box; padding: 0px 5px;">125</li><li style="box-sizing: border-box; padding: 0px 5px;">126</li><li style="box-sizing: border-box; padding: 0px 5px;">127</li><li style="box-sizing: border-box; padding: 0px 5px;">128</li><li style="box-sizing: border-box; padding: 0px 5px;">129</li><li style="box-sizing: border-box; padding: 0px 5px;">130</li><li style="box-sizing: border-box; padding: 0px 5px;">131</li><li style="box-sizing: border-box; padding: 0px 5px;">132</li><li style="box-sizing: border-box; padding: 0px 5px;">133</li><li style="box-sizing: border-box; padding: 0px 5px;">134</li><li style="box-sizing: border-box; padding: 0px 5px;">135</li><li style="box-sizing: border-box; padding: 0px 5px;">136</li><li style="box-sizing: border-box; padding: 0px 5px;">137</li><li style="box-sizing: border-box; padding: 0px 5px;">138</li><li style="box-sizing: border-box; padding: 0px 5px;">139</li><li style="box-sizing: border-box; padding: 0px 5px;">140</li><li style="box-sizing: border-box; padding: 0px 5px;">141</li><li style="box-sizing: border-box; padding: 0px 5px;">142</li><li style="box-sizing: border-box; padding: 0px 5px;">143</li><li style="box-sizing: border-box; padding: 0px 5px;">144</li><li style="box-sizing: border-box; padding: 0px 5px;">145</li></ul>

测试时，换作下面的迷宫试一试：