给定一棵二叉树，任务是在边界层顺序遍历中打印这棵树的所有层。
Boundary Level order traversal: In this traversal, the first element of the level (starting boundary) is printed first, followed by last element (ending boundary). Then the process is repeated for the second and last-second element, till the complete level has been printed.
例子：
Input:
1
/ \
12 13
/ \ / \
11 6 4 11
/ / \ / \
23 7 9 2 4
Output:
1
12 13
11 11 6 4
23 4 7 2 9
Input:
7
/ \
22 19
/ \ \
3 6 13
/ \ \ / \
1 5 8 1 4
/
23
Output:
7
22 19
3 13 6
1 4 5 1 8
23
方法：
- 为了在 Boundary Level order traversal 中打印 level，我们需要先对二叉树进行 Level Order Traversal 来获取每个 level 的值。
- 这里队列数据结构用于在执行级别顺序遍历时存储树的级别。
- 然后对于每个级别，首先打印级别的第一个元素(起始边界)，然后是最后一个元素(结束边界)。然后对第二个和最后一个元素重复该过程，直到打印出完整的关卡。
下面是上述方法的实现：
C++
// C++ program for printing a
// Levels of Binary Tree in a
// start end fashion
#include
using namespace std;
// A Tree node
struct Node {
int key;
struct Node *left, *right;
};
// Utility function to create a new node
Node* newNode(int key)
{
Node* temp = new Node;
temp->key = key;
temp->left = temp->right = NULL;
return (temp);
}
// Utility function to print level in
// start end fashion
void printLevelUtil(struct Node* queue[],
int index, int size)
{
while (index < size) {
cout << queue[index++]->key << " "
<< queue[size--]->key << " ";
}
if (index == size) {
cout << queue[index]->key << " ";
}
cout << endl;
}
// Utility function to print level in start
// end fashion in a given Binary tree
void printLevel(struct Node* node,
struct Node* queue[],
int index, int size)
{
// Print root node value
// as a single value in a
// binary tree
cout << queue[index]->key << endl;
// Level order traversal of Tree
while (index < size) {
int curr_size = size;
while (index < curr_size) {
struct Node* temp = queue[index];
if (temp->left != NULL) {
queue[size++] = temp->left;
}
if (temp->right != NULL) {
queue[size++] = temp->right;
}
index++;
}
// Print level in a desire fashion
printLevelUtil(queue, index, size - 1);
}
}
// Function to find total no of nodes
int findSize(struct Node* node)
{
if (node == NULL)
return 0;
return 1
+ findSize(node->left)
+ findSize(node->right);
}
// Function to print level in start end
// fashion in a given binary tree
void printLevelInStartEndFashion(
struct Node* node)
{
int t_size = findSize(node);
struct Node* queue[t_size];
queue[0] = node;
printLevel(node, queue, 0, 1);
}
// Driver Code
int main()
{
/* 10
/ \
13 13
/ \
14 15
/ \ / \
21 22 22 21
/
8 */
// Create Binary Tree as shown
Node* root = newNode(10);
root->left = newNode(13);
root->right = newNode(13);
root->right->left = newNode(14);
root->right->right = newNode(15);
root->right->left->left = newNode(21);
root->right->left->right = newNode(22);
root->right->right->left = newNode(22);
root->right->right->right = newNode(21);
root->right->right->right->left = newNode(8);
// Print Levels In Start End Fashion
printLevelInStartEndFashion(root);
return 0;
} Java
// Java program for printing a
// Levels of Binary Tree in a
// start end fashion
class GFG{
// A Tree node
static class Node {
int key;
Node left, right;
};
// Utility function to create a new node
static Node newNode(int key)
{
Node temp = new Node();
temp.key = key;
temp.left = temp.right = null;
return (temp);
}
// Utility function to print level in
// start end fashion
static void printLevelUtil(Node queue[],
int index, int size)
{
while (index < size) {
System.out.print(queue[index++].key+ " "
+ queue[size--].key+ " ");
}
if (index == size) {
System.out.print(queue[index].key+ " ");
}
System.out.println();
}
// Utility function to print level in start
// end fashion in a given Binary tree
static void printLevel(Node node,
Node queue[],
int index, int size)
{
// Print root node value
// as a single value in a
// binary tree
System.out.print(queue[index].key +"\n");
// Level order traversal of Tree
while (index < size) {
int curr_size = size;
while (index < curr_size) {
Node temp = queue[index];
if (temp.left != null) {
queue[size++] = temp.left;
}
if (temp.right != null) {
queue[size++] = temp.right;
}
index++;
}
// Print level in a desire fashion
printLevelUtil(queue, index, size - 1);
}
}
// Function to find total no of nodes
static int findSize(Node node)
{
if (node == null)
return 0;
return 1
+ findSize(node.left)
+ findSize(node.right);
}
// Function to print level in start end
// fashion in a given binary tree
static void printLevelInStartEndFashion(
Node node)
{
int t_size = findSize(node);
Node []queue = new Node[t_size];
queue[0] = node;
printLevel(node, queue, 0, 1);
}
// Driver Code
public static void main(String[] args)
{
/* 10
/ \
13 13
/ \
14 15
/ \ / \
21 22 22 21
/
8 */
// Create Binary Tree as shown
Node root = newNode(10);
root.left = newNode(13);
root.right = newNode(13);
root.right.left = newNode(14);
root.right.right = newNode(15);
root.right.left.left = newNode(21);
root.right.left.right = newNode(22);
root.right.right.left = newNode(22);
root.right.right.right = newNode(21);
root.right.right.right.left = newNode(8);
// Print Levels In Start End Fashion
printLevelInStartEndFashion(root);
}
}
// This code is contributed by Princi SinghPython3
# Python3 program for printing a
# Levels of Binary Tree in a
# start end fashion
# A Tree node
class Node:
def __init__(self, key):
self.key = key
self.left = None
self.right = None
# function to create a
# new node
def newNode(key):
temp = Node(key);
return temp;
# Utility function to print
# level in start end fashion
def printLevelUtil(queue,
index, size):
while (index < size):
print(str(queue[index].key) + ' ' +
str(queue[size].key), end = ' ')
size -= 1
index += 1
if (index == size):
print(queue[index].key,
end = ' ')
print()
# Utility function to print
# level in start end fashion
# in a given Binary tree
def printLevel(node, queue,
index, size):
# Print root node value
# as a single value in a
# binary tree
print(queue[index].key)
# Level order traversal
# of Tree
while (index < size):
curr_size = size;
while (index < curr_size):
temp = queue[index];
if (temp.left != None):
queue[size] = temp.left;
size += 1
if (temp.right != None):
queue[size] = temp.right;
size += 1
index += 1
# Print level in a desire
# fashion
printLevelUtil(queue, index,
size - 1);
# Function to find total
# no of nodes
def findSize(node):
if (node == None):
return 0;
return (1 + findSize(node.left) +
findSize(node.right));
# Function to print level in start
# end fashion in a given binary tree
def printLevelInStartEndFashion(node):
t_size = findSize(node);
queue=[0 for i in range(t_size)];
queue[0] = node;
printLevel(node, queue, 0, 1);
# Driver code
if __name__=="__main__":
''' 10
/ \
13 13
/ \
14 15
/ \ / \
21 22 22 21
/
8 '''
# Create Binary Tree as shown
root = newNode(10);
root.left = newNode(13);
root.right = newNode(13);
root.right.left = newNode(14);
root.right.right = newNode(15);
root.right.left.left = newNode(21);
root.right.left.right = newNode(22);
root.right.right.left = newNode(22);
root.right.right.right = newNode(21);
root.right.right.right.left = newNode(8);
# Print Levels In Start End Fashion
printLevelInStartEndFashion(root);
# This code is contributed by Rutvik_56C#
// C# program for printing a
// Levels of Binary Tree in a
// start end fashion
using System;
class GFG{
// A Tree node
class Node {
public int key;
public Node left, right;
};
// Utility function to create a new node
static Node newNode(int key)
{
Node temp = new Node();
temp.key = key;
temp.left = temp.right = null;
return (temp);
}
// Utility function to print level in
// start end fashion
static void printLevelUtil(Node []queue,
int index, int size)
{
while (index < size) {
Console.Write(queue[index++].key+ " "
+ queue[size--].key+ " ");
}
if (index == size) {
Console.Write(queue[index].key+ " ");
}
Console.WriteLine();
}
// Utility function to print level in start
// end fashion in a given Binary tree
static void printLevel(Node node,
Node []queue,
int index, int size)
{
// Print root node value
// as a single value in a
// binary tree
Console.Write(queue[index].key +"\n");
// Level order traversal of Tree
while (index < size) {
int curr_size = size;
while (index < curr_size) {
Node temp = queue[index];
if (temp.left != null) {
queue[size++] = temp.left;
}
if (temp.right != null) {
queue[size++] = temp.right;
}
index++;
}
// Print level in a desire fashion
printLevelUtil(queue, index, size - 1);
}
}
// Function to find total no of nodes
static int findSize(Node node)
{
if (node == null)
return 0;
return 1
+ findSize(node.left)
+ findSize(node.right);
}
// Function to print level in start end
// fashion in a given binary tree
static void printLevelInStartEndFashion(
Node node)
{
int t_size = findSize(node);
Node []queue = new Node[t_size];
queue[0] = node;
printLevel(node, queue, 0, 1);
}
// Driver Code
public static void Main(String[] args)
{
/* 10
/ \
13 13
/ \
14 15
/ \ / \
21 22 22 21
/
8 */
// Create Binary Tree as shown
Node root = newNode(10);
root.left = newNode(13);
root.right = newNode(13);
root.right.left = newNode(14);
root.right.right = newNode(15);
root.right.left.left = newNode(21);
root.right.left.right = newNode(22);
root.right.right.left = newNode(22);
root.right.right.right = newNode(21);
root.right.right.right.left = newNode(8);
// Print Levels In Start End Fashion
printLevelInStartEndFashion(root);
}
}
// This code is contributed by PrinciRaj1992输出：
10
13 13
14 15
21 21 22 22
8
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