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/1bfadf00ae14 “STC单片机电压测量”是一个以STC系列单片机为基础的电压检测应用案例,它涵盖了硬件电路设计、软件编程以及数据处理等核心知识点。STC单片机凭借其低功耗、高性价比和丰富的I/O接口,在电子工程领域得到了广泛应用。 STC是Specialized Technology Corporation的缩写,该公司的单片机基于8051内核,具备内部振荡器、高速运算能力、ISP(在系统编程)和IAP(在应用编程)功能,非常适合用于各种嵌入式控制系统。 在源代码方面,“浅雪”风格的代码通常简洁易懂,非常适合初学者学习。其中,“main.c”文件是程序的入口,包含了电压测量的核心逻辑;“STARTUP.A51”是启动代码,负责初始化单片机的硬件环境;“电压测量_uvopt.bak”和“电压测量_uvproj.bak”可能是Keil编译器的配置文件备份,用于设置编译选项和项目配置。 对于3S锂电池电压测量,3S锂电池由三节锂离子电池串联而成,标称电压为11.1V。测量时需要考虑电池的串联特性,通过分压电路将高电压转换为单片机可接受的范围,并实时监控,防止过充或过放,以确保电池的安全和寿命。 在电压测量电路设计中,“电压测量.lnp”文件可能包含电路布局信息,而“.hex”文件是编译后的机器码,用于烧录到单片机中。电路中通常会使用ADC(模拟数字转换器)将模拟电压信号转换为数字信号供单片机处理。 在软件编程方面,“StringData.h”文件可能包含程序中使用的字符串常量和数据结构定义。处理电压数据时,可能涉及浮点数运算,需要了解STC单片机对浮点数的支持情况,以及如何高效地存储和显示电压值。 用户界面方面,“电压测量.uvgui.kidd”可能是用户界面的配置文件,用于显示测量结果。在嵌入式系统中,用
资源下载链接为: https://pan.quark.cn/s/abbae039bf2a 在 Android 开发中,Fragment 是界面的一个模块化组件,可用于在 Activity 中灵活地添加、删除或替换。将 ListView 集成到 Fragment 中,能够实现数据的动态加载与列表形式展示,对于构建复杂且交互丰富的界面非常有帮助。本文将详细介绍如何在 Fragment 中使用 ListView。 首先,需要在 Fragment 的布局文件中添加 ListView 的 XML 定义。一个基本的 ListView 元素代码如下: 接着,创建适配器来填充 ListView 的数据。通常会使用 BaseAdapter 的子类,如 ArrayAdapter 或自定义适配器。例如,创建一个简单的 MyListAdapter,继承自 ArrayAdapter,并在构造函数中传入数据集: 在 Fragment 的 onCreateView 或 onActivityCreated 方法中,实例化 ListView 和适配器,并将适配器设置到 ListView 上: 为了提升用户体验,可以为 ListView 设置点击事件监听器: 性能优化也是关键。设置 ListView 的 android:cacheColorHint 属性可提升滚动流畅度。在 getView 方法中复用 convertView,可减少视图创建,提升性能。对于复杂需求,如异步加载数据,可使用 LoaderManager 和 CursorLoader,这能更好地管理数据加载,避免内存泄漏,支持数据变更时自动刷新。 总结来说,Fragment 中的 ListView 使用涉及布局设计、适配器创建与定制、数据绑定及事件监听。掌握这些步骤,可构建功能强大的应用。实际开发中,还需优化 ListView 性能,确保应用流畅运
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