Mix Order Traversal of a Binary Tree
Last Updated :
15 Jul, 2025
Given a Binary Tree consisting of N nodes, the task is to print its Mix Order Traversal.
Mix Order Traversal is a tree traversal technique, which involves any two of the existing traversal techniques like Inorder, Preorder and Postorder Traversal. Any two of them can be performed or alternate levels of given tree and a mix traversal can be obtained.
Examples:
Input: N = 6
Output: 7 4 5 1 3 6
Explanation:
Inorder-Preorder Mix Traversal is applied to the given tree in the following order:
Inorder Traversal is applied at level 0
Preorder Traversal is applied at level 1
Inorder Traversal at level 2.
Output: 4 5 7 1 6 3
Explanation:
Inorder-Postorder Mix Traversal is applied to the given tree in the following order:
Inorder Traversal is applied at level 0
Postorder Traversal is applied at level 1
Inorder Traversal at level 2.
Approach:
The possible Mix Order Traversals are as follows:
Inorder-Preorder Mix Traversal
Steps for inorder() will be:
- Perform Preorder Traversal on the left subtree.
- Print the current node.
- Perform Preorder Traversal on right subtree.
Steps for preorder() will be:
- Print the current node.
- Perform Inorder Traversal on left subtree(root->left).
- Perform Inorder Traversal on right subtree.
Below is the implementation of the above approach:
C++
// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
void inOrder(struct node* root);
void preOrder(struct node* root);
// Node structure
struct node {
char data;
struct node *left, *right;
};
// Creates and initialize a new node
struct node* newNode(char ch)
{
// Allocating memory to a new node
struct node* n = (struct node*)
malloc(sizeof(struct node));
n->data = ch;
n->left = NULL;
n->right = NULL;
return n;
}
// Perform Inorder Traversal
void inOrder(struct node* root)
{
if (root) {
preOrder(root->left);
cout << root->data << " ";
preOrder(root->right);
}
}
// Perform Preorder Traversal
void preOrder(struct node* root)
{
if (root) {
cout << root->data << " ";
inOrder(root->left);
inOrder(root->right);
}
}
// Driver Code
int main()
{
// Given tree
struct node* root = newNode('1');
root->left = newNode('7');
root->right = newNode('3');
root->left->left = newNode('4');
root->left->right = newNode('5');
root->right->left = newNode('6');
// Perform Mix order traversal
inOrder(root);
return 0;
}
// Java program to implement
// the above approach
import java.util.*;
class GFG{
// Node structure
static class node
{
char data;
node left, right;
};
// Creates and initialize a new node
static node newNode(char ch)
{
// Allocating memory to a new node
node n = new node();
n.data = ch;
n.left = null;
n.right = null;
return n;
}
// Perform Inorder Traversal
static void inOrder(node root)
{
if (root != null)
{
preOrder(root.left);
System.out.print(root.data + " ");
preOrder(root.right);
}
}
// Perform Preorder Traversal
static void preOrder(node root)
{
if (root != null)
{
System.out.print(root.data + " ");
inOrder(root.left);
inOrder(root.right);
}
}
// Driver Code
public static void main(String[] args)
{
// Given tree
node root = newNode('1');
root.left = newNode('7');
root.right = newNode('3');
root.left.left = newNode('4');
root.left.right = newNode('5');
root.right.left = newNode('6');
// Perform Mix order traversal
inOrder(root);
}
}
// This code is contributed by 29AjayKumar
# Python3 program to implement the above approach
# Node structure
class node:
def __init__(self):
self.data = 0
self.left = None
self.right = None
# Creates and initialize a new node
def newNode(ch):
# Allocating memory to a new node
n = node()
n.data = ch
n.left = None
n.right = None
return n
# Perform Inorder Traversal
def inOrder(root):
if root != None:
preOrder(root.left)
print(root.data, end = " ")
preOrder(root.right)
# Perform Preorder Traversal
def preOrder(root):
if root != None:
print(root.data, end = " ")
inOrder(root.left)
inOrder(root.right)
# Driver Code
# Given tree
root = newNode('1')
root.left = newNode('7')
root.right = newNode('3')
root.left.left = newNode('4')
root.left.right = newNode('5')
root.right.left = newNode('6')
# Perform Mix order traversal
inOrder(root)
# This code is contributed by divyeshrabadiya07.
// C# program to implement
// the above approach
using System;
class GFG{
// Node structure
class node
{
public char data;
public node left, right;
};
// Creates and initialize a new node
static node newNode(char ch)
{
// Allocating memory to a new node
node n = new node();
n.data = ch;
n.left = null;
n.right = null;
return n;
}
// Perform Inorder Traversal
static void inOrder(node root)
{
if (root != null)
{
preOrder(root.left);
Console.Write(root.data + " ");
preOrder(root.right);
}
}
// Perform Preorder Traversal
static void preOrder(node root)
{
if (root != null)
{
Console.Write(root.data + " ");
inOrder(root.left);
inOrder(root.right);
}
}
// Driver Code
public static void Main(String[] args)
{
// Given tree
node root = newNode('1');
root.left = newNode('7');
root.right = newNode('3');
root.left.left = newNode('4');
root.left.right = newNode('5');
root.right.left = newNode('6');
// Perform Mix order traversal
inOrder(root);
}
}
// This code is contributed by sapnasingh4991
<script>
// Javascript program to implement
// the above approach
// Node structure
class node
{
constructor()
{
this.data = 0;
this.left = null;
this.right = null;
}
};
// Creates and initialize a new node
function newNode(ch)
{
// Allocating memory to a new node
var n = new node();
n.data = ch;
n.left = null;
n.right = null;
return n;
}
// Perform Inorder Traversal
function inOrder(root)
{
if (root != null)
{
preOrder(root.left);
document.write(root.data + " ");
preOrder(root.right);
}
}
// Perform Preorder Traversal
function preOrder(root)
{
if (root != null)
{
document.write(root.data + " ");
inOrder(root.left);
inOrder(root.right);
}
}
// Driver Code
// Given tree
var root = newNode('1');
root.left = newNode('7');
root.right = newNode('3');
root.left.left = newNode('4');
root.left.right = newNode('5');
root.right.left = newNode('6');
// Perform Mix order traversal
inOrder(root);
</script>
The time complexity for both inOrder and preOrder traversals is O(n), where n is the number of nodes in the tree. This is because each node is visited once.
Auxiliary space complexity:
The auxiliary space of newNode function is O(1), because it only allocates memory for a single node.
The auxiliary space complexity of inOrder and preOrder functions is O(h), where h is the height of the tree.
Preorder-Postorder Mix Traversal
Steps for preorder() are as follows:
- Print the current node.
- Perform Postorder traversal on left subtree.
- Perform Postorder Traversal on the right subtree.
Steps for postorder() are as follows:
- Perform preorder traversal on the left subtree.
- Perform preorder traversal on right subtree.
- Print the current node.
Below is the implementation of the above approach:
C++
// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
void preOrder(struct node* root);
void postOrder(struct node* root);
// Node structure
struct node {
char data;
struct node *left, *right;
};
// Creates and initialize a new node
struct node* newNode(char ch)
{
// Allocating memory to a new node
struct node* n = (struct node*)
malloc(sizeof(struct node));
n->data = ch;
n->left = NULL;
n->right = NULL;
return n;
}
// Perform Preorder Traversal
void preOrder(struct node* root)
{
if (root) {
cout << root->data << " ";
postOrder(root->left);
postOrder(root->right);
}
}
// Perform Postorder Traversal
void postOrder(struct node* root)
{
if (root) {
preOrder(root->left);
preOrder(root->right);
cout << root->data << " ";
}
}
// Driver Code
int main()
{
// Given tree
struct node* root = newNode('A');
root->left = newNode('B');
root->right = newNode('C');
root->left->left = newNode('F');
root->left->right = newNode('D');
root->right->right = newNode('E');
// Starting Mix order traversal
preOrder(root);
return 0;
}
// Java Program to implement
// the above approach
class GFG{
// Node structure
static class node
{
char data;
node left, right;
};
// Creates and initialize a new node
static node newNode(char ch)
{
// Allocating memory to a new node
node n = new node();
n.data = ch;
n.left = null;
n.right = null;
return n;
}
// Perform Preorder Traversal
static void preOrder(node root)
{
if (root != null)
{
System.out.print(root.data + " ");
postOrder(root.left);
postOrder(root.right);
}
}
// Perform Postorder Traversal
static void postOrder(node root)
{
if (root != null)
{
preOrder(root.left);
preOrder(root.right);
System.out.print(root.data + " ");
}
}
// Driver Code
public static void main(String[] args)
{
// Given tree
node root = newNode('A');
root.left = newNode('B');
root.right = newNode('C');
root.left.left = newNode('F');
root.left.right = newNode('D');
root.right.right = newNode('E');
// Starting Mix order traversal
preOrder(root);
}
}
// This code is contributed by Rajput-Ji
# Python3 Program to implement the above approach
# Node structure
class node:
def __init__(self):
self.data = '0'
self.left = None
self.right = None
# Creates and initialize a new node
def newNode(ch):
# Allocating memory to a new node
n = node()
n.data = ch
n.left = None
n.right = None
return n
# Perform Preorder Traversal
def preOrder(root):
if root != None:
print(root.data, end = " ")
postOrder(root.left)
postOrder(root.right)
# Perform Postorder Traversal
def postOrder(root):
if root != None:
preOrder(root.left)
preOrder(root.right)
print(root.data, end = " ")
# Given tree
root = newNode('A')
root.left = newNode('B')
root.right = newNode('C')
root.left.left = newNode('F')
root.left.right = newNode('D')
root.right.right = newNode('E')
# Starting Mix order traversal
preOrder(root)
# This code is contributed by divyesh072019.
// C# Program to implement
// the above approach
using System;
class GFG{
// Node structure
class node
{
public char data;
public node left, right;
};
// Creates and initialize a new node
static node newNode(char ch)
{
// Allocating memory to a new node
node n = new node();
n.data = ch;
n.left = null;
n.right = null;
return n;
}
// Perform Preorder Traversal
static void preOrder(node root)
{
if (root != null)
{
Console.Write(root.data + " ");
postOrder(root.left);
postOrder(root.right);
}
}
// Perform Postorder Traversal
static void postOrder(node root)
{
if (root != null)
{
preOrder(root.left);
preOrder(root.right);
Console.Write(root.data + " ");
}
}
// Driver Code
public static void Main(String[] args)
{
// Given tree
node root = newNode('A');
root.left = newNode('B');
root.right = newNode('C');
root.left.left = newNode('F');
root.left.right = newNode('D');
root.right.right = newNode('E');
// Starting Mix order traversal
preOrder(root);
}
}
// This code is contributed by Rohit_ranjan
<script>
// Javascript Program to implement the above approach
// Node structure
class node
{
constructor() {
this.left;
this.right;
this.data;
}
}
// Creates and initialize a new node
function newNode(ch)
{
// Allocating memory to a new node
let n = new node();
n.data = ch;
n.left = null;
n.right = null;
return n;
}
// Perform Preorder Traversal
function preOrder(root)
{
if (root != null)
{
document.write(root.data + " ");
postOrder(root.left);
postOrder(root.right);
}
}
// Perform Postorder Traversal
function postOrder(root)
{
if (root != null)
{
preOrder(root.left);
preOrder(root.right);
document.write(root.data + " ");
}
}
// Given tree
let root = newNode('A');
root.left = newNode('B');
root.right = newNode('C');
root.left.left = newNode('F');
root.left.right = newNode('D');
root.right.right = newNode('E');
// Starting Mix order traversal
preOrder(root);
// This code is contributed by rameshtravel07.
</script>
Time Complexity: O(N) where N is the number of nodes in the tree.
Auxiliary Space: O(log(N))
Inorder-Postorder Mix Traversal
Steps for inorder() are as follows:
- Perform Postorder Traversal on the left subtree.
- Print the current node.
- Perform Postorder Traversal on the right subtree.
Steps for postorder() will be:
- Perform Inorder Traversal on left subtree.
- Perform Inorder Traversal on right subtree.
- Print the current node.
Below is the implementation of the above approach:
C++
// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
void inOrder(struct node* root);
void postOrder(struct node* root);
// Node structure
struct node {
char data;
struct node *left, *right;
};
// Creates and initialize a new node
struct node* newNode(char ch)
{
// Allocating memory to a new node
struct node* n = (struct node*)
malloc(sizeof(struct node));
n->data = ch;
n->left = NULL;
n->right = NULL;
return n;
}
// Perform Inorder Traversal
void inOrder(struct node* root)
{
if (root) {
postOrder(root->left);
cout << root->data << " ";
postOrder(root->right);
}
}
// Perform Postorder Traversal
void postOrder(struct node* root)
{
if (root) {
inOrder(root->left);
inOrder(root->right);
cout << root->data << " ";
}
}
// Driver Code
int main()
{
// Given tree
struct node* root = newNode('A');
root->left = newNode('B');
root->right = newNode('C');
root->left->left = newNode('F');
root->left->right = newNode('D');
root->right->right = newNode('E');
// Starting Mix order traversal
inOrder(root);
return 0;
}
// Java Program to implement
// the above approach
import java.util.*;
class GFG{
// Node structure
static class node
{
char data;
node left, right;
};
// Creates and initialize a new node
static node newNode(char ch)
{
// Allocating memory to a new node
node n = new node();
n.data = ch;
n.left = null;
n.right = null;
return n;
}
// Perform Inorder Traversal
static void inOrder(node root)
{
if (root != null)
{
postOrder(root.left);
System.out.print(root.data + " ");
postOrder(root.right);
}
}
// Perform Postorder Traversal
static void postOrder(node root)
{
if (root != null)
{
inOrder(root.left);
inOrder(root.right);
System.out.print(root.data + " ");
}
}
// Driver Code
public static void main(String[] args)
{
// Given tree
node root = newNode('A');
root.left = newNode('B');
root.right = newNode('C');
root.left.left = newNode('F');
root.left.right = newNode('D');
root.right.right = newNode('E');
// Starting Mix order traversal
inOrder(root);
}
}
// This code is contributed by sapnasingh4991
# Python3 Program to implement the above approach
# Node structure
class node:
def __init__(self):
self.data = '0'
self.left = None
self.right = None
# Creates and initialize a new node
def newNode(ch):
# Allocating memory to a new node
n = node()
n.data = ch
n.left = None
n.right = None
return n
# Perform Inorder Traversal
def inOrder(root):
if root != None:
postOrder(root.left)
print(root.data, end = " ")
postOrder(root.right)
# Perform Postorder Traversal
def postOrder(root):
if root != None:
inOrder(root.left)
inOrder(root.right)
print(root.data, end = " ")
# Given tree
root = newNode('A')
root.left = newNode('B')
root.right = newNode('C')
root.left.left = newNode('F')
root.left.right = newNode('D')
root.right.right = newNode('E')
# Starting Mix order traversal
inOrder(root)
# This code is contributed by decode2207.
// C# Program to implement
// the above approach
using System;
class GFG{
// Node structure
class node
{
public char data;
public node left, right;
};
// Creates and initialize a new node
static node newNode(char ch)
{
// Allocating memory to a new node
node n = new node();
n.data = ch;
n.left = null;
n.right = null;
return n;
}
// Perform Inorder Traversal
static void inOrder(node root)
{
if (root != null)
{
postOrder(root.left);
Console.Write(root.data + " ");
postOrder(root.right);
}
}
// Perform Postorder Traversal
static void postOrder(node root)
{
if (root != null)
{
inOrder(root.left);
inOrder(root.right);
Console.Write(root.data + " ");
}
}
// Driver Code
public static void Main(String[] args)
{
// Given tree
node root = newNode('A');
root.left = newNode('B');
root.right = newNode('C');
root.left.left = newNode('F');
root.left.right = newNode('D');
root.right.right = newNode('E');
// Starting Mix order traversal
inOrder(root);
}
}
// This code is contributed by sapnasingh4991
<script>
// Javascript Program to implement the above approach
// Node structure
class node
{
constructor() {
this.left;
this.right;
this.data;
}
}
// Creates and initialize a new node
function newNode(ch)
{
// Allocating memory to a new node
let n = new node();
n.data = ch;
n.left = null;
n.right = null;
return n;
}
// Perform Inorder Traversal
function inOrder(root)
{
if (root != null)
{
postOrder(root.left);
document.write(root.data + " ");
postOrder(root.right);
}
}
// Perform Postorder Traversal
function postOrder(root)
{
if (root != null)
{
inOrder(root.left);
inOrder(root.right);
document.write(root.data + " ");
}
}
// Given tree
let root = newNode('A');
root.left = newNode('B');
root.right = newNode('C');
root.left.left = newNode('F');
root.left.right = newNode('D');
root.right.right = newNode('E');
// Starting Mix order traversal
inOrder(root);
// This code is contributed by mukesh07.
</script>
Time Complexity: O(N)
Auxiliary Space: O(N)
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem