给定二叉树，任务是打印树的之字形顺序。
例子：
Input :
7
/ \
6 5
/ /
4 3
/ \
2 1
Output : 7 5 6 4 3 1 2
Input :
1
/ \
2 3
/ \
4 5
Output : 1 3 2 4 5
我们已经使用迭代方法讨论了锯齿形遍历，在这篇文章中，我们将使用递归来解决它。
递归方法：想法是以级别顺序方式但略有不同的方式遍历树。我们将使用一个变量标志，并将其值初始设置为零。当我们完成树的级别顺序遍历时，从右到左，我们将标志的值设置为一，以便下次我们可以从左到右遍历树，并且当我们完成遍历时，我们将其值设置回归零。我们将重复整个步骤，直到我们完全遍历了二叉树为止。
下面是上述方法的实现：
C++
// C++ program to print zigzag
// traversal of a binary tree
// using Recursion
#include
using namespace std;
// Binary tree node
struct node
{
struct node* left;
struct node* right;
int data;
};
// Function to create a new
// Binary Tree Node
struct node* newNode(int data)
{
struct node* temp = new node;
temp->data = data;
temp->left = NULL;
temp->right = NULL;
return temp;
}
// Recursive Function to find height
// of binary tree
int heightOfTree(struct node* root)
{
if(root == NULL)
return 0;
int lheight = heightOfTree(root->left);
int rheight = heightOfTree(root->right);
return max(lheight + 1 ,rheight + 1);
}
// Function to print nodes from right to left
void printRightToLeft(struct node* root ,int level)
{
if(root == NULL)
return;
if(level == 1)
cout << root->data << " " ;
else if(level > 1)
{
printRightToLeft(root->right ,level - 1);
printRightToLeft(root->left ,level - 1);
}
}
// Function to print nodes from left to right
void printLeftToRight(struct node* root ,int level)
{
if(root == NULL)
return;
if(level == 1)
cout << root->data << " " ;
else if(level > 1)
{
printLeftToRight(root->left ,level - 1);
printLeftToRight(root->right ,level - 1);
}
}
// Function to print Reverse ZigZag of
// a Binary tree
void printZigZag(struct node* root )
{
// Flag is used to mark the change
// in level
int flag = 0;
// Height of tree
int height = heightOfTree(root);
for(int i = 1 ; i <= height ; i++)
{
// If flag value is one print nodes
// from right to left
if(flag == 1)
{
printRightToLeft(root ,i);
// Mark flag as zero so that next time
// nodes are printed from left to right
flag = 0;
}
// If flag is zero print nodes
// from left to right
else if(flag == 0)
{
printLeftToRight(root ,i);
// Mark flag as one so that next time
// nodes are printed from right to left
flag = 1;
}
}
}
// Driver code
int main()
{
struct node* root = newNode(7);
root->left = newNode(4);
root->right = newNode(5);
root->left->left = newNode(9);
root->right->right = newNode(10);
root->left->left->left = newNode(6);
root->left->left->right = newNode(11);
printZigZag(root);
return 0;
} Java
// Java program to print zigzag
// traversal of a binary tree
// using Recursion
class GfG
{
// Binary tree node
static class node
{
node left;
node right;
int data;
}
// Function to create a new
// Binary Tree Node
static node newNode(int data)
{
node temp = new node();
temp.data = data;
temp.left = null;
temp.right = null;
return temp;
}
// Recursive Function to find height
// of binary tree
static int heightOfTree(node root)
{
if(root == null)
return 0;
int lheight = heightOfTree(root.left);
int rheight = heightOfTree(root.right);
return Math.max(lheight + 1 ,rheight + 1);
}
// Function to print nodes from right to left
static void printRightToLeft(node root ,int level)
{
if(root == null)
return;
if(level == 1)
System.out.print(root.data + " ") ;
else if(level > 1)
{
printRightToLeft(root.right ,level - 1);
printRightToLeft(root.left ,level - 1);
}
}
// Function to print nodes from left to right
static void printLeftToRight(node root ,int level)
{
if(root == null)
return;
if(level == 1)
System.out.print(root.data + " ") ;
else if(level > 1)
{
printLeftToRight(root.left ,level - 1);
printLeftToRight(root.right ,level - 1);
}
}
// Function to print Reverse ZigZag of
// a Binary tree
static void printZigZag(node root )
{
// Flag is used to mark the change
// in level
int flag = 0;
// Height of tree
int height = heightOfTree(root);
for(int i = 1 ; i <= height ; i++)
{
// If flag value is one print nodes
// from right to left
if(flag == 1)
{
printRightToLeft(root ,i);
// Mark flag as zero so that next time
// nodes are printed from left to right
flag = 0;
}
// If flag is zero print nodes
// from left to right
else if(flag == 0)
{
printLeftToRight(root ,i);
// Mark flag as one so that next time
// nodes are printed from right to left
flag = 1;
}
}
}
// Driver code
public static void main(String[] args)
{
node root = newNode(7);
root.left = newNode(4);
root.right = newNode(5);
root.left.left = newNode(9);
root.right.right = newNode(10);
root.left.left.left = newNode(6);
root.left.left.right = newNode(11);
printZigZag(root);
}
}
// This code is contributed by Prerna Saini.Python3
# Python3 program to print zigzag traversal
# of a binary tree using Recursion
# Binary tree node
class Node:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
# Recursive Function to find height
# of binary tree
def heightOfTree(root):
if root == None:
return 0
lheight = heightOfTree(root.left)
rheight = heightOfTree(root.right)
return max(lheight + 1, rheight + 1)
# Function to print nodes from right to left
def printRightToLeft(root, level):
if root == None:
return
if level == 1:
print(root.data, end = " ")
elif level > 1:
printRightToLeft(root.right, level - 1)
printRightToLeft(root.left, level - 1)
# Function to print nodes from left to right
def printLeftToRight(root, level):
if root == None:
return
if level == 1:
print(root.data, end = " ")
elif level > 1:
printLeftToRight(root.left, level - 1)
printLeftToRight(root.right, level - 1)
# Function to print Reverse ZigZag of
# a Binary tree
def printZigZag(root):
# Flag is used to mark the
# change in level
flag = 0
# Height of tree
height = heightOfTree(root)
for i in range(1, height + 1):
# If flag value is one print nodes
# from right to left
if flag == 1:
printRightToLeft(root, i)
# Mark flag as zero so that next time
# nodes are printed from left to right
flag = 0
# If flag is zero print nodes
# from left to right
elif flag == 0:
printLeftToRight(root, i)
# Mark flag as one so that next time
# nodes are printed from right to left
flag = 1
# Driver code
if __name__ == "__main__":
root = Node(7)
root.left = Node(4)
root.right = Node(5)
root.left.left = Node(9)
root.right.right = Node(10)
root.left.left.left = Node(6)
root.left.left.right = Node(11)
printZigZag(root)
# This code is contributed by Rituraj JainC#
// C# program to print zigzag
// traversal of a binary tree
// using Recursion
using System;
class GfG
{
// Binary tree node
public class node
{
public node left;
public node right;
public int data;
}
// Function to create a new
// Binary Tree Node
static node newNode(int data)
{
node temp = new node();
temp.data = data;
temp.left = null;
temp.right = null;
return temp;
}
// Recursive Function to find height
// of binary tree
static int heightOfTree(node root)
{
if(root == null)
return 0;
int lheight = heightOfTree(root.left);
int rheight = heightOfTree(root.right);
return Math.Max(lheight + 1 ,rheight + 1);
}
// Function to print nodes from right to left
static void printRightToLeft(node root ,int level)
{
if(root == null)
return;
if(level == 1)
Console.Write(root.data + " ") ;
else if(level > 1)
{
printRightToLeft(root.right ,level - 1);
printRightToLeft(root.left ,level - 1);
}
}
// Function to print nodes from left to right
static void printLeftToRight(node root ,int level)
{
if(root == null)
return;
if(level == 1)
Console.Write(root.data + " ") ;
else if(level > 1)
{
printLeftToRight(root.left ,level - 1);
printLeftToRight(root.right ,level - 1);
}
}
// Function to print Reverse ZigZag of
// a Binary tree
static void printZigZag(node root )
{
// Flag is used to mark the change
// in level
int flag = 0;
// Height of tree
int height = heightOfTree(root);
for(int i = 1 ; i <= height ; i++)
{
// If flag value is one print nodes
// from right to left
if(flag == 1)
{
printRightToLeft(root, i);
// Mark flag as zero so that next time
// nodes are printed from left to right
flag = 0;
}
// If flag is zero print nodes
// from left to right
else if(flag == 0)
{
printLeftToRight(root, i);
// Mark flag as one so that next time
// nodes are printed from right to left
flag = 1;
}
}
}
// Driver code
public static void Main()
{
node root = newNode(7);
root.left = newNode(4);
root.right = newNode(5);
root.left.left = newNode(9);
root.right.right = newNode(10);
root.left.left.left = newNode(6);
root.left.left.right = newNode(11);
printZigZag(root);
}
}
/* This code contributed by PrinciRaj1992 */输出：
7 5 4 9 10 11 6
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