Ex 10.4-3 of introduction to algorithms

本文介绍了一种使用栈实现的二叉树中序遍历非递归算法,该算法时间复杂度为O(n),适用于高度较大的二叉树场景。

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Question:
Write an O(n)-time nonrecursive procedure that, given an n-node binary tree, prints out the key of each node in the tree. Use a stack as an auxiliary data structure.

Answer:
This isn't a difficult question. But the skill of turning a recursive algorithm to non-recursive algorithm is so important, it worths a blog post.

The data structure for tree node used in this post is defined as:
  class TreeNode
  {
  public:
      int value;
      TreeNode* left; // left child node
      TreeNode* right; // right child node
  }


The simplest and cleanest algorithm for binary tree traversal is the recursion. As shown below:
  void inOrderTraversalRecursive(TreeNode* node)
  {
      if(Null == node)
          return;
      inOrderTraversalRecursive(node->left); // visit left sub-tree first
      visit(node); // visit current node
      inOrderTraversalRecursive(node->right); // visit right sub-tree
  }


In this algorithm, each time we goes down a level to the calling stack, a new stack frame will be created for the new function call. Then the context changes to the new stack frame. And the node is kept on the previous stack frame. In current stack frame, node is the left or right child of last stack frame's node. With the help of stack, after a function call is finished, the context changes back to the previous stack frame and consequently gets back to the parent node. Because this stack is managed automatically be the compiler, this algorithm becomes so simple. But this stack isn't unlimited, if the tree's height is large enough, the stack may exhaust. In order to get over this limit, we can use a heap (whose limit is far larger.) based stack data structure and manage it ourselves.

This is done in a loop. Each iteration of the loop is regarded as a function call in recursive version. At proper point of the iteration, we must push/pop node from/to stack so that the context of the iteration can be maintained.
In recursive version, if node is not null, we need to save current node in stack (push) and change node to node->left. Otherwise, the function call returns right away, which means the node is restored (pop) to the value in last call stack frame. After the left sub-tree has been visited, we visit current node.
Then we save (push) current node again and change node to node->right to visit right sub-tree. After it's done, we need to restore (pop) node. But as we can see in the recursive version, the node isn't used at all after the right sub-tree has been visited. That's to say, it's not necessary to save context before we visit right sub-tree any more. This procedure can be omitted in this case.
The last thing to determine is the termination condition. In what situation can we terminate the loop? First, it's clear that the stack should be empty when the loop terminates. But this isn't enough, the node should be null as well to terminate the loop.

  void inOrderTraversalStack(TreeNode* root)
  {
      typedef std::stack TreeStack;
      TreeStack stack;
      TreeNode *node = root;
      while(NULL != node || !stack.empty())
      {
          if(NULL != node)
          {
              stack.push(node);
              node = node->left;
          }
          else
          {
              node = stack.top();
              stack.pop();
              visit(node);
              node = node->right;
          }
      }
  }
资源下载链接为: https://pan.quark.cn/s/22ca96b7bd39 在 IT 领域,文档格式转换是常见需求,尤其在处理多种文件类型时。本文将聚焦于利用 Java 技术栈,尤其是 Apache POI 和 iTextPDF 库,实现 doc、xls(涵盖 Excel 2003Excel 2007+)以及 txt、图片等格式文件向 PDF 的转换,并实现在线浏览功能。 先从 Apache POI 说起,它是一个强大的 Java 库,专注于处理 Microsoft Office 格式文件,比如 doc 和 xls。Apache POI 提供了 HSSF 和 XSSF 两个 API,其中 HSSF 用于读写老版本的 BIFF8 格式(Excel 97-2003),XSSF 则针对新的 XML 格式(Excel 2007+)。这两个 API 均具备读取和写入工作表、单元格、公式、样式等功能。读取 Excel 文件时,可通过创建 HSSFWorkbook 或 XSSFWorkbook 对象来打开相应格式的文件,进而遍历工作簿中的每个 Sheet,获取行和列数据。写入 Excel 文件时,创建新的 Workbook 对象,添加 Sheet、Row 和 Cell,即可构建新 Excel 文件。 再看 iTextPDF,它是一个用于生成和修改 PDF 文档的 Java 库,拥有丰富的 API。创建 PDF 文档时,借助 Document 对象,可定义页面尺寸、边距等属性来定制 PDF 外观。添加内容方面,可使用 Paragraph、List、Table 等元素将文本、列表和表格加入 PDF,图片可通过 Image 类加载插入。iTextPDF 支持多种字体和样式,可设置文本颜色、大小、样式等。此外,iTextPDF 的 TextRenderer 类能将 HTML、
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