二叉树遍历序列还原

迷南。 2022-06-02 07:23 202阅读 0赞

给出二叉树的中序遍历序列和后序遍历序列，编程还原该二叉树。

**输入：**  
　　第1行为二叉树的中序遍历序列  
　　第2行为二叉树的后序遍历序列

**输出：**  
　　二叉树的按层遍历序列

<table style="width:1615px; margin-bottom:20px; background-color:transparent"> 
 <thead> 
  <tr> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> &nbsp;</th> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> 测试输入<span><a href="http://online.bit.edu.cn/moodle/help.php?component=programming&amp;identifier=input&amp;lang=zh_cn" title="关于“测试输入”的帮助" style="color:rgb(67,142,185)" rel="nofollow"><img src="http://online.bit.edu.cn/moodle/theme/image.php/lambda/core/1510491239/help" alt="关于“测试输入”的帮助" style="vertical-align:text-bottom; border:0px; height:16px; padding-left:3px; width:16px"></a></span></th> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> 期待的输出<span><a href="http://online.bit.edu.cn/moodle/help.php?component=programming&amp;identifier=expectedoutput&amp;lang=zh_cn" title="关于“期待的输出”的帮助" style="color:rgb(67,142,185)" rel="nofollow"><img src="http://online.bit.edu.cn/moodle/theme/image.php/lambda/core/1510491239/help" alt="关于“期待的输出”的帮助" style="vertical-align:text-bottom; border:0px; height:16px; padding-left:3px; width:16px"></a></span></th> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> 时间限制<span><a href="http://online.bit.edu.cn/moodle/help.php?component=programming&amp;identifier=timelimit&amp;lang=zh_cn" title="关于“时间限制”的帮助" style="color:rgb(67,142,185)" rel="nofollow"><img src="http://online.bit.edu.cn/moodle/theme/image.php/lambda/core/1510491239/help" alt="关于“时间限制”的帮助" style="vertical-align:text-bottom; border:0px; height:16px; padding-left:3px; width:16px"></a></span></th> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> 内存限制<span><a href="http://online.bit.edu.cn/moodle/help.php?component=programming&amp;identifier=memlimit&amp;lang=zh_cn" title="关于“内存限制”的帮助" style="color:rgb(67,142,185)" rel="nofollow"><img src="http://online.bit.edu.cn/moodle/theme/image.php/lambda/core/1510491239/help" alt="关于“内存限制”的帮助" style="vertical-align:text-bottom; border:0px; height:16px; padding-left:3px; width:16px"></a></span></th> 
   <th style="padding:4px; line-height:20px; vertical-align:bottom; border-top-width:0px"> 额外进程<span><a href="http://online.bit.edu.cn/moodle/help.php?component=programming&amp;identifier=nproc&amp;lang=zh_cn" title="关于“{$a} 个额外进程”的帮助" style="color:rgb(67,142,185)" rel="nofollow"><img src="http://online.bit.edu.cn/moodle/theme/image.php/lambda/core/1510491239/help" alt="关于“{$a} 个额外进程”的帮助" style="vertical-align:text-bottom; border:0px; height:16px; padding-left:3px; width:16px"></a></span></th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 测试用例 1</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64768&amp;test=82491&amp;type=in&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">badcfeg↵</span></li> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">bdfgeca↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64768&amp;test=82491&amp;type=out&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">abcdefg↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 1秒</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 64M</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 0</td> 
  </tr> 
  <tr> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 测试用例 2</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64768&amp;test=82492&amp;type=in&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">cbdafeg↵</span></li> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">cbdfgea↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64768&amp;test=82492&amp;type=out&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">adebfgc↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 1秒</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 64M</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 0</td> 
  </tr> 
  <tr> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 测试用例 3</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64768&amp;test=82493&amp;type=in&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">edcba↵</span></li> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">edcba↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64768&amp;test=82493&amp;type=out&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">abcde↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 1秒</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 64M</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle; background-color:rgb(249,249,249)"> 0</td> 
  </tr> 
  <tr> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 测试用例 6</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64768&amp;test=82496&amp;type=in&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">bdfgeca↵</span></li> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">gfedcba↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> <a href="http://online.bit.edu.cn/moodle/mod/programming/testcase/download_io.php?id=64768&amp;test=82496&amp;type=out&amp;download=0" style="color:rgb(67,142,185); font-size:9pt" rel="nofollow">以文本方式显示</a> 
    <div style="vertical-align:top; padding:0px 5px 0px 0px; width:10em; height:10em; overflow:auto"> 
     <ol style="padding-left:0px; margin-bottom:0px; margin-left:2.5em; overflow:visible"> 
      <li style="line-height:20px; font-family:Consolas,'Courier New',Courier,mono,serif; margin:0px; padding:0px; overflow:visible"> <span style="margin:0px; padding:0px; white-space:nowrap; background-color:rgb(211,211,211)">abcdefg↵</span></li> 
     </ol> 
    </div> </td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 1秒</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 64M</td> 
   <td style="padding:4px; line-height:20px; vertical-align:middle"> 0</td> 
  </tr> 
 </tbody> 
</table>

此题有一定的借鉴成分。

这题多写了几个与本体无关的函数。BuildTree这个函数是有用的俄，而PostMidCreateTree这个函数是从网上看到的，但没成功。

InOrderTravers这个函数是因为当时没看懂题就写了个中序遍历，其实应该是Leveltravers这个函数

#include <string>   
    #include <iostream>   
    #include<queue> 
    using namespace std; 
     
    //二叉链表表示二叉树   
    typedef struct BiNode 
    { 
        char data;//节点数据   
     struct BiNode * lchild;//左孩子   
     struct BiNode * rchild;//右孩子   
    }BiNode, *BiTree; 
     
    void BuildTree(BiTree &t,string Inorder,string Postorder) 
    { 
      if (Inorder.length()==0) 
       { 
          //t = NULL; 
            return; 
        } 
      int length_Post = Postorder.length(); 
      char Rootnode = Postorder[length_Post- 1]; 
     int index = Inorder.find(Rootnode); 
        string lchild_inorder = Inorder.substr(0, index);//左孩子的中序序列 
        string rchild_inorder = Inorder.substr(index + 1);//右孩子的中序序列 
       int lchild_length = lchild_inorder.length();//左孩子长度 
        int rchild_length = rchild_inorder.length();//右孩子长度 
        string rchild_postorder = Postorder.substr(lchild_length, length_Post - 1 - lchild_length);//右孩子的后序序列 
      string lchild_postorder = Postorder.substr(0,lchild_length);//左孩子的后序序列 
     
        t = (BiTree)malloc(sizeof(BiNode)); 
        if (t) 
     { 
          t->data = Rootnode; t->lchild = t->rchild = NULL; 
         BuildTree(t->lchild,lchild_inorder,lchild_postorder);//创建左孩子 
            BuildTree(t->rchild, rchild_inorder, rchild_postorder);//创建右孩子 
      } 
    } 
     
    char post[50]; 
    char mid[50]; 
    int Position(char c) 
     { 
         return strchr(mid, c) - mid; 
     
    } 
    void PostMidCreateTree(BiTree &pn, int i, int j, int len) 
    { 
         if (len <= 0) 
             return; 
     
      pn = new BiNode; pn->lchild = pn->rchild = NULL; 
         pn->data = post[i]; 
         int m = Position(post[i]); 
         PostMidCreateTree(pn->lchild, i - 1 - (len - 1 - (m - j)), j, m - j);//注意参数:m-j左子树的长度,len-1-(m-j)右子树的长度 
         PostMidCreateTree(pn->rchild, i - 1, m + 1, len - 1 - (m - j)); 
     } 
     
    void InOrderTraverse(BiTree & t) 
    { 
     if (t != NULL) 
     { 
     
         InOrderTraverse(t->lchild); 
         cout << t->data; 
          InOrderTraverse(t->rchild); 
     } 
    } 
     
    void leveltravers(BiTree t) 
    { 
     queue<BiTree> Q; 
     BiTree cur = t; 
        Q.push(cur); 
       while (!Q.empty()) 
     { 
          cur = Q.front(); 
           Q.pop(); 
           printf("%c", cur->data); 
     
           if (cur->lchild) 
            { 
              Q.push(cur->lchild); 
            } 
          if (cur->rchild) 
                Q.push(cur->rchild); 
        } 
    } 
    int main() 
    { 
        BiTree t; 
      string Inorder; 
        string Postorder; 
      getline(cin, Inorder); 
     getline(cin, Postorder); 
       BuildTree(t, Inorder, Postorder); 
      leveltravers(t); 
       printf("\n"); 
      return 0; 
    }