使用C ++以漂亮的方式打印二叉树 [英] Print binary tree in a pretty way using c++
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问题描述
尝试在c ++中打印如下的二叉树时，我是个位":
I am a "bit" lost trying to print a binary tree like below in c++:
8
/ \
/ \
/ \
5 10
/ \ / \
2 6 9 11
我知道如何获取树的高度和每个级别中的节点数，但是我无法弄清楚如何在根和第二个级别之间设置正确的空格数(下面有3行3个级别的根，但我相信并非每次都这样，我认为这可能是较大树木的3倍的高度).
I know how to get the height of the tree and the number of nodes in each level, but I couldn't figure out how to set the right number of spaces between the root and the second level (there are 3 lines under the root for 3 levels but I believe it is not this everytime,I thought it could be 3 times the height for greater trees).
我想在打印行中的这些空格以及行之间的行数方面有所帮助.谢谢.
I would like to have some help to print these spaces in the rows and the number of lines between the rows.Thank you.
我正在用C ++进行编码
I am coding in c++
Get height
int tree::getHeight(No *node) {
if (node == NULL) return 0;
return 1 + max(getHeight(node->esq), getHeight(node->dir));
}
Get number of nodes per line
void tree::getLine(const No *root, int depth, vector<int>& vals){
int placeholder = 10;
if (depth <= 0 && root != nullptr) {
vals.push_back(root->chave);
return;
}
if (root->esq != nullptr)
getLine(root->esq, depth-1, vals);
else if (depth-1 <= 0)
vals.push_back(placeholder);
if (root->dir != nullptr)
getLine(root->dir, depth-1, vals);
else if (depth-1 <= 0)
vals.push_back(placeholder);
}
推荐答案
这里是一个示例代码，用于创建基于文本的二叉树表示形式.此演示使用了最小有用的二叉树类(BinTree)，并且占用空间很小，只是为了避免使示例的大小过大.
Here is an example of code creating a text-based representation of a binary tree. This demonstration uses a minimally useful binary tree class (BinTree), with a small footprint, just to avoid bloating the example's size.
它的文本呈现成员函数更严重，使用迭代而不是递归，如在该类的其他部分中所见.
Its text-rendering member functions are more serious, using iteration rather than recursion, as found in other parts of the class.
这分三步完成，首先将一个由字符串值组成的行向量放在一起.
This does its job in three steps, first a vector of rows of string values is put together.
然后用于格式化代表树的文本字符串行.
Then this is used to format lines of text strings representing the tree.
然后将字符串清理干净并转储到cout.
Then the strings are cleaned up and dumped to cout.
作为一个额外的好处，该演示还包括随机树"功能，可以持续数小时的娱乐活动.
As an added bonus, the demo includes a "random tree" feature, for hours of nonstop entertainment.
#include <iostream>
#include <vector>
#include <string>
#include <sstream>
#include <algorithm>
#include <random>
using std::vector;
using std::string;
using std::cout;
template <typename T>
class BinTree {
struct Node {
T value;
Node *left,*right;
Node() : left(nullptr),right(nullptr) {}
Node(const T& value) :value(value),left(nullptr),right(nullptr) {}
// stack-abusing recursion everywhere, for small code
~Node() { delete left; delete right; }
int max_depth() const {
const int left_depth = left ? left->max_depth() : 0;
const int right_depth = right ? right->max_depth() : 0;
return (left_depth > right_depth ? left_depth : right_depth) + 1;
}
};
Node *root;
public:
BinTree() : root(nullptr) {}
~BinTree() { delete root; }
int get_max_depth() const { return root ? root->max_depth() : 0; }
void clear() { delete root; root = nullptr; }
void insert() {}
template <typename ...Args>
void insert(const T& value, Args...more) {
if(!root) {
root = new Node(value);
} else {
Node* p = root;
for(;;) {
if(value == p->value) return;
Node* &pchild = value < p->value ? p->left : p->right;
if(!pchild) {
pchild = new Node(value);
break;
}
p = pchild;
}
}
insert(more...);
}
struct cell_display {
string valstr;
bool present;
cell_display() : present(false) {}
cell_display(std::string valstr) : valstr(valstr), present(true) {}
};
using display_rows = vector< vector< cell_display > >;
// The text tree generation code below is all iterative, to avoid stack faults.
// get_row_display builds a vector of vectors of cell_display structs
// each vector of cell_display structs represents one row, starting at the root
display_rows get_row_display() const {
// start off by traversing the tree to
// build a vector of vectors of Node pointers
vector<Node*> traversal_stack;
vector< std::vector<Node*> > rows;
if(!root) return display_rows();
Node *p = root;
const int max_depth = root->max_depth();
rows.resize(max_depth);
int depth = 0;
for(;;) {
// Max-depth Nodes are always a leaf or null
// This special case blocks deeper traversal
if(depth == max_depth-1) {
rows[depth].push_back(p);
if(depth == 0) break;
--depth;
continue;
}
// First visit to node? Go to left child.
if(traversal_stack.size() == depth) {
rows[depth].push_back(p);
traversal_stack.push_back(p);
if(p) p = p->left;
++depth;
continue;
}
// Odd child count? Go to right child.
if(rows[depth+1].size() % 2) {
p = traversal_stack.back();
if(p) p = p->right;
++depth;
continue;
}
// Time to leave if we get here
// Exit loop if this is the root
if(depth == 0) break;
traversal_stack.pop_back();
p = traversal_stack.back();
--depth;
}
// Use rows of Node pointers to populate rows of cell_display structs.
// All possible slots in the tree get a cell_display struct,
// so if there is no actual Node at a struct's location,
// its boolean "present" field is set to false.
// The struct also contains a string representation of
// its Node's value, created using a std::stringstream object.
display_rows rows_disp;
std::stringstream ss;
for(const auto& row : rows) {
rows_disp.emplace_back();
for(Node* pn : row) {
if(pn) {
ss << pn->value;
rows_disp.back().push_back(cell_display(ss.str()));
ss = std::stringstream();
} else {
rows_disp.back().push_back(cell_display());
} } }
return rows_disp;
}
// row_formatter takes the vector of rows of cell_display structs
// generated by get_row_display and formats it into a test representation
// as a vector of strings
vector<string> row_formatter(const display_rows& rows_disp) const {
using s_t = string::size_type;
// First find the maximum value string length and put it in cell_width
s_t cell_width = 0;
for(const auto& row_disp : rows_disp) {
for(const auto& cd : row_disp) {
if(cd.present && cd.valstr.length() > cell_width) {
cell_width = cd.valstr.length();
} } }
// make sure the cell_width is an odd number
if(cell_width % 2 == 0) ++cell_width;
// formatted_rows will hold the results
vector<string> formatted_rows;
// some of these counting variables are related,
// so its should be possible to eliminate some of them.
s_t row_count = rows_disp.size();
// this row's element count, a power of two
s_t row_elem_count = 1 << (row_count-1);
// left_pad holds the number of space charactes at the beginning of the bottom row
s_t left_pad = 0;
// Work from the level of maximum depth, up to the root
// ("formatted_rows" will need to be reversed when done)
for(s_t r=0; r<row_count; ++r) {
const auto& cd_row = rows_disp[row_count-r-1]; // r reverse-indexes the row
// "space" will be the number of rows of slashes needed to get
// from this row to the next. It is also used to determine other
// text offsets.
s_t space = (s_t(1) << r) * (cell_width + 1) / 2 - 1;
// "row" holds the line of text currently being assembled
string row;
// iterate over each element in this row
for(s_t c=0; c<row_elem_count; ++c) {
// add padding, more when this is not the leftmost element
row += string(c ? left_pad*2+1 : left_pad, ' ');
if(cd_row[c].present) {
// This position corresponds to an existing Node
const string& valstr = cd_row[c].valstr;
// Try to pad the left and right sides of the value string
// with the same number of spaces. If padding requires an
// odd number of spaces, right-sided children get the longer
// padding on the right side, while left-sided children
// get it on the left side.
s_t long_padding = cell_width - valstr.length();
s_t short_padding = long_padding / 2;
long_padding -= short_padding;
row += string(c%2 ? short_padding : long_padding, ' ');
row += valstr;
row += string(c%2 ? long_padding : short_padding, ' ');
} else {
// This position is empty, Nodeless...
row += string(cell_width, ' ');
}
}
// A row of spaced-apart value strings is ready, add it to the result vector
formatted_rows.push_back(row);
// The root has been added, so this loop is finsished
if(row_elem_count == 1) break;
// Add rows of forward- and back- slash characters, spaced apart
// to "connect" two rows' Node value strings.
// The "space" variable counts the number of rows needed here.
s_t left_space = space + 1;
s_t right_space = space - 1;
for(s_t sr=0; sr<space; ++sr) {
string row;
for(s_t c=0; c<row_elem_count; ++c) {
if(c % 2 == 0) {
row += string(c ? left_space*2 + 1 : left_space, ' ');
row += cd_row[c].present ? '/' : ' ';
row += string(right_space + 1, ' ');
} else {
row += string(right_space, ' ');
row += cd_row[c].present ? '\\' : ' ';
}
}
formatted_rows.push_back(row);
++left_space;
--right_space;
}
left_pad += space + 1;
row_elem_count /= 2;
}
// Reverse the result, placing the root node at the beginning (top)
std::reverse(formatted_rows.begin(), formatted_rows.end());
return formatted_rows;
}
// Trims an equal number of space characters from
// the beginning of each string in the vector.
// At least one string in the vector will end up beginning
// with no space characters.
static void trim_rows_left(vector<string>& rows) {
if(!rows.size()) return;
auto min_space = rows.front().length();
for(const auto& row : rows) {
auto i = row.find_first_not_of(' ');
if(i==string::npos) i = row.length();
if(i == 0) return;
if(i < min_space) min_space = i;
}
for(auto& row : rows) {
row.erase(0, min_space);
} }
// Dumps a representation of the tree to cout
void Dump() const {
const int d = get_max_depth();
// If this tree is empty, tell someone
if(d == 0) {
cout << " <empty tree>\n";
return;
}
// This tree is not empty, so get a list of node values...
const auto rows_disp = get_row_display();
// then format these into a text representation...
auto formatted_rows = row_formatter(rows_disp);
// then trim excess space characters from the left sides of the text...
trim_rows_left(formatted_rows);
// then dump the text to cout.
for(const auto& row : formatted_rows) {
std::cout << ' ' << row << '\n';
}
}
};
int main() {
BinTree<int> bt;
// Build OP's tree
bt.insert(8,5,2,6,10,9,11);
cout << "Tree from OP:\n\n";
bt.Dump();
cout << "\n\n";
bt.clear();
// Build a random tree
// This toy tree can't balance, so random
// trees often look more like linked lists.
// Just keep trying until a nice one shows up.
std::random_device rd;
std::mt19937 rng(rd());
int MaxCount=20;
int MaxDepth=5;
const int Min=0, Max=1000;
std::uniform_int_distribution<int> dist(Min,Max);
while(MaxCount--) {
bt.insert(dist(rng));
if(bt.get_max_depth() >= MaxDepth) break;
}
cout << "Randomly generated tree:\n\n";
bt.Dump();
}
输出示例:
Tree from OP:
8
/ \
/ \
/ \
5 10
/ \ / \
2 6 9 11
Randomly generated tree:
703
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
137 965
/ \ /
/ \ /
/ \ /
/ \ /
/ \ /
/ \ /
/ \ /
41 387 786
\ / \ / \
\ / \ / \
\ / \ / \
95 382 630 726 813
\
841
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