想要打印出"pretty"树

Want to print out a "pretty" btree

本文关键字:pretty 打印      更新时间:2023-10-16

截至目前,该程序按级别顺序遍历,但只是打印出数字。我想知道如何打印它,以便它看起来像下面的图片,或者只是一种显示树的不同级别及其数字的奇特方式。

       num1
      /    
num2,num3  num4,num5

我不明白的是,如何判断哪些数字应该进入相应的级别。这是代码:

// C++ program for B-Tree insertion
#include<iostream>
#include <queue>
using namespace std;
int ComparisonCount = 0;
// A BTree node
class BTreeNode
{
    int *keys;  // An array of keys
    int t;      // Minimum degree (defines the range for number of keys)
    BTreeNode **C; // An array of child pointers
    int n;     // Current number of keys
    bool leaf; // Is true when node is leaf. Otherwise false
public:
    BTreeNode(int _t, bool _leaf);   // Constructor
                                     // A utility function to insert a new key in the subtree rooted with
                                     // this node. The assumption is, the node must be non-full when this
                                     // function is called
    void insertNonFull(int k);
    // A utility function to split the child y of this node. i is index of y in
    // child array C[].  The Child y must be full when this function is called
    void splitChild(int i, BTreeNode *y);
    // A function to traverse all nodes in a subtree rooted with this node
    void traverse();
    // A function to search a key in subtree rooted with this node.
    BTreeNode *search(int k);   // returns NULL if k is not present.
                                // Make BTree friend of this so that we can access private members of this
                                // class in BTree functions
    friend class BTree;
};
// A BTree
class BTree
{
    BTreeNode *root; // Pointer to root node
    int t;  // Minimum degree
public:
    // Constructor (Initializes tree as empty)
    BTree(int _t)
    {
        root = NULL;  t = _t;
    }
    // function to traverse the tree
    void traverse()
    {
        if (root != NULL) root->traverse();
    }
    // function to search a key in this tree
    BTreeNode* search(int k)
    {
        return (root == NULL) ? NULL : root->search(k);
    }
    // The main function that inserts a new key in this B-Tree
    void insert(int k);
};
// Constructor for BTreeNode class
BTreeNode::BTreeNode(int t1, bool leaf1)
{
    // Copy the given minimum degree and leaf property
    t = t1;
    leaf = leaf1;
    // Allocate memory for maximum number of possible keys
    // and child pointers
    keys = new int[2 * t - 1];
    C = new BTreeNode *[2 * t];
    // Initialize the number of keys as 0
    n = 0;
}
// Function to traverse all nodes in a subtree rooted with this node
/*void BTreeNode::traverse()
{
// There are n keys and n+1 children, travers through n keys
// and first n children
int i;
for (i = 0; i < n; i++)
{
// If this is not leaf, then before printing key[i],
// traverse the subtree rooted with child C[i].
if (leaf == false)
{
ComparisonCount++;
C[i]->traverse();
}
cout << " " << keys[i];
}
// Print the subtree rooted with last child
if (leaf == false)
{
ComparisonCount++;
C[i]->traverse();
}
}*/
// Function to search key k in subtree rooted with this node
BTreeNode *BTreeNode::search(int k)
{
    // Find the first key greater than or equal to k
    int i = 0;
    while (i < n && k > keys[i])
        i++;
    // If the found key is equal to k, return this node
    if (keys[i] == k)
    {
        ComparisonCount++;
        return this;
    }
    // If key is not found here and this is a leaf node
    if (leaf == true)
    {
        ComparisonCount++;
        return NULL;
    }
    // Go to the appropriate child
    return C[i]->search(k);
}
// The main function that inserts a new key in this B-Tree
void BTree::insert(int k)
{
    // If tree is empty
    if (root == NULL)
    {
        ComparisonCount++;
        // Allocate memory for root
        root = new BTreeNode(t, true);
        root->keys[0] = k;  // Insert key
        root->n = 1;  // Update number of keys in root
    }
    else // If tree is not empty
    {
        // If root is full, then tree grows in height
        if (root->n == 2 * t - 1)
        {
            ComparisonCount++;
            // Allocate memory for new root
            BTreeNode *s = new BTreeNode(t, false);
            // Make old root as child of new root
            s->C[0] = root;
            // Split the old root and move 1 key to the new root
            s->splitChild(0, root);
            // New root has two children now.  Decide which of the
            // two children is going to have new key
            int i = 0;
            if (s->keys[0] < k)
            {
                ComparisonCount++;
                i++;
            }s->C[i]->insertNonFull(k);
            // Change root
            root = s;
        }
        else  // If root is not full, call insertNonFull for root
            root->insertNonFull(k);
    }
}
// A utility function to insert a new key in this node
// The assumption is, the node must be non-full when this
// function is called
void BTreeNode::insertNonFull(int k)
{
    // Initialize index as index of rightmost element
    int i = n - 1;
    // If this is a leaf node
    if (leaf == true)
    {
        ComparisonCount++;
        // The following loop does two things
        // a) Finds the location of new key to be inserted
        // b) Moves all greater keys to one place ahead
        while (i >= 0 && keys[i] > k)
        {
            keys[i + 1] = keys[i];
            i--;
        }
        // Insert the new key at found location
        keys[i + 1] = k;
        n = n + 1;
    }
    else // If this node is not leaf
    {
        // Find the child which is going to have the new key
        while (i >= 0 && keys[i] > k)
            i--;
        // See if the found child is full
        if (C[i + 1]->n == 2 * t - 1)
        {
            ComparisonCount++;
            // If the child is full, then split it
            splitChild(i + 1, C[i + 1]);
            // After split, the middle key of C[i] goes up and
            // C[i] is splitted into two.  See which of the two
            // is going to have the new key
            if (keys[i + 1] < k)
                i++;
        }
        C[i + 1]->insertNonFull(k);
    }
}
// A utility function to split the child y of this node
// Note that y must be full when this function is called
void BTreeNode::splitChild(int i, BTreeNode *y)
{
    // Create a new node which is going to store (t-1) keys
    // of y
    BTreeNode *z = new BTreeNode(y->t, y->leaf);
    z->n = t - 1;
    // Copy the last (t-1) keys of y to z
    for (int j = 0; j < t - 1; j++)
        z->keys[j] = y->keys[j + t];
    // Copy the last t children of y to z
    if (y->leaf == false)
    {
        ComparisonCount++;
        for (int j = 0; j < t; j++)
            z->C[j] = y->C[j + t];
    }
    // Reduce the number of keys in y
    y->n = t - 1;
    // Since this node is going to have a new child,
    // create space of new child
    for (int j = n; j >= i + 1; j--)
        C[j + 1] = C[j];
    // Link the new child to this node
    C[i + 1] = z;
    // A key of y will move to this node. Find location of
    // new key and move all greater keys one space ahead
    for (int j = n - 1; j >= i; j--)
        keys[j + 1] = keys[j];
    // Copy the middle key of y to this node
    keys[i] = y->keys[t - 1];
    // Increment count of keys in this node
    n = n + 1;
}
void BTreeNode::traverse()
{
    std::queue<BTreeNode*> queue;
    queue.push(this);
    while (!queue.empty())
    {
        BTreeNode* current = queue.front();
        queue.pop();
        int i;
        for (i = 0; i < current->n; i++)  //*
        {
            if (current->leaf == false)  //*
            {
                ComparisonCount++;
                queue.push(current->C[i]);
            }cout << " " << current->keys[i] << endl;
        }
        if (current->leaf == false)  //*
        {
            ComparisonCount++;
            queue.push(current->C[i]);
        }
    }
}
// Driver program to test above functions
int main()
{
    BTree t(4); // A B-Tree with minium degree 4
    srand(29324);
    for (int i = 0; i<10; i++)
    {
        int p = rand() % 10000;
        t.insert(p);
    }
    cout << "Traversal of the constucted tree is "<<endl;
    t.traverse();
    int k = 6;
    (t.search(k) != NULL) ? cout << "nPresent" : cout << "nNot Present" << endl;
    k = 28;
    (t.search(k) != NULL) ? cout << "nPresent" : cout << "nNot Present" << endl;
    cout << "There are " << ComparisonCount << " comparisons." << endl;
    system("pause");
    return 0;
}

首先,Janus Troelsen在主题中的回答 有没有办法在Graphviz上绘制B树? 展示了一种创建专业B树绘图的优雅方式,就像维基百科中使用的那些一样,可以通过在线粘贴内容到他链接的Web界面中,或者使用GraphViz的本地副本。所需文本文件的格式非常简单,并且很容易通过B树的标准遍历生成。Patrick Kreutzer将所有内容收集在一起,标题为"如何使用点绘制B树"。

但是,对于调试和研究正在开发的 B 树实现,使用一种将 B 树呈现为文本的简单方法可能会非常有帮助。在下文中,我将给出一个简单的C++类,它可以像这样绘制以子节点为中心的节点:

## inserting 42...
         [56 64 86]
[37 42] [62] [68 72] [95 98]
## inserting 96...
              [64]
    [56]            [86]
[37 42] [62]  [68 72] [95 96 98]

这是取自上一个主题中 B 树代码的实际输出,在将 rand() 调用中的模数更改为 100 以获得更小的数字(比充满较长数字的节点更容易一目了然)并构建具有 t = 2 的 B 树。

这里的根本问题是,使节点居中所需的信息 - 最左边的孙子的起始位置和最右边的孙子的结束位置 - 仅在遍历子树期间可用。因此,我选择了对树进行完整遍历并存储打印所需的一切的方法:节点文本和最小/最大位置信息。

这是类的声明,内联了一些无趣的东西以使其不碍事:

class BTreePrinter
{
   struct NodeInfo
   {
      std::string text;
      unsigned text_pos, text_end;  // half-open range
   };
   typedef std::vector<NodeInfo> LevelInfo;
   std::vector<LevelInfo> levels;
   std::string node_text (int const keys[], unsigned key_count);
   void before_traversal ()
   {
      levels.resize(0);
      levels.reserve(10);   // far beyond anything that could usefully be printed
   }
   void visit (BTreeNode const *node, unsigned level = 0, unsigned child_index = 0);
   void after_traversal ();
public:
   void print (BTree const &tree)
   {
      before_traversal();
      visit(tree.root);
      after_traversal();
   }
};

此类需要是BTreeNodeBTree的朋友,才能获得所需的特权访问权限。为了使本次展览的紧凑和简单,省略了许多生产质量的噪音,首先是删除了我的手指在编写课程时自动插入的所有assert()调用......

这是第一个有趣的位,通过树的完整遍历收集所有节点文本和定位信息:

void BTreePrinter::visit (BTreeNode const *node, unsigned level, unsigned child_index)
{
   if (level >= levels.size())
      levels.resize(level + 1);
   LevelInfo &level_info = levels[level];
   NodeInfo info;
   info.text_pos = 0;
   if (!level_info.empty())  // one blank between nodes, one extra blank if left-most child
      info.text_pos = level_info.back().text_end + (child_index == 0 ? 2 : 1);
   info.text = node_text(node->keys, unsigned(node->n));
   if (node->leaf)
   {
      info.text_end = info.text_pos + unsigned(info.text.length());
   }
   else // non-leaf -> do all children so that .text_end for the right-most child becomes known
   {
      for (unsigned i = 0, e = unsigned(node->n); i <= e; ++i)  // one more pointer than there are keys
         visit(node->C[i], level + 1, i);
      info.text_end = levels[level + 1].back().text_end;
   }
   levels[level].push_back(info);
}

关于布局逻辑最相关的事实是,给定节点"拥有"(覆盖)其自身及其所有后代覆盖的所有水平空间;节点范围的开始是其左邻居的范围的结束加上一个或两个空白,具体取决于左邻居是兄弟姐妹还是仅仅是表亲。节点的范围结束只有在遍历整个子树之后才会知道,此时可以通过查看最右边子树的末端来查找它。

节点转储为文本的代码通常会在BTreeNode类的轨道中找到;在这篇文章中,我已将其添加到打印机类中:

std::string BTreePrinter::node_text (int const keys[], unsigned key_count)
{
   std::ostringstream os;
   char const *sep = "";
   os << "[";
   for (unsigned i = 0; i < key_count; ++i, sep = " ")
      os << sep << keys[i];
   os << "]";
   return os.str();
}

这里有一个小帮手需要塞在某个地方:

void print_blanks (unsigned n)
{
   while (n--)
      std::cout << ' ';
}

下面是打印在树的完整遍历期间收集的所有信息的逻辑:

void BTreePrinter::after_traversal ()
{
   for (std::size_t l = 0, level_count = levels.size(); ; )
   {    
      auto const &level = levels[l];
      unsigned prev_end = 0;
      for (auto const &node: level)
      {         
         unsigned total = node.text_end - node.text_pos;
         unsigned slack = total - unsigned(node.text.length());
         unsigned blanks_before = node.text_pos - prev_end;
         print_blanks(blanks_before + slack / 2);
         std::cout << node.text;
         if (&node == &level.back())
            break;
         print_blanks(slack - slack / 2);
         prev_end += blanks_before + total;
      }
      if (++l == level_count)
         break;
      std::cout << "nn";
   }
   std::cout << "n";
}

最后,使用此类的原始 B 树代码的一个版本:

BTreePrinter printer;
BTree t(2);
srand(29324);
for (unsigned i = 0; i < 15; ++i)
{
    int p = rand() % 100;
    std::cout << "n## inserting " << p << "...nn";
    t.insert(p);
    printer.print(t);
}