# Mix Order Traversal of a Binary Tree

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 ` `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 initilize 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

 `// Java program to implement` `// the above approach` `import` `java.util.*;`   `class` `GFG{`   `// Node structure` `static` `class` `node` `{` `    ``char` `data;` `    ``node left, right;` `};`   `// Creates and initilize 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`

## C#

 `// C# program to implement` `// the above approach` `using` `System;` `class` `GFG{`   `// Node structure` `class` `node` `{` `    ``public` `char` `data;` `    ``public` `node left, right;` `};`   `// Creates and initilize 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`

Output:

```7 4 5 1 3 6

```

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 ` `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 initilize 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

 `// Java Program to implement` `// the above approach` `class` `GFG{`   `// Node structure` `static` `class` `node` `{` `    ``char` `data;` `    ``node left, right;` `};`   `// Creates and initilize 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`

## C#

 `// C# Program to implement` `// the above approach` `using` `System;` `class` `GFG{`   `// Node structure` `class` `node` `{` `    ``public` `char` `data;` `    ``public` `node left, right;` `};`   `// Creates and initilize 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`

Output:

```A F D B E C

```

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 ` `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 initilize 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

 `// Java Program to implement` `// the above approach` `import` `java.util.*;` `class` `GFG{`   `// Node structure` `static` `class` `node ` `{` `    ``char` `data;` `    ``node left, right;` `};`   `// Creates and initilize 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`

## C#

 `// C# Program to implement` `// the above approach` `using` `System;` `class` `GFG{`   `// Node structure` `class` `node ` `{` `    ``public` `char` `data;` `    ``public` `node left, right;` `};`   `// Creates and initilize 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`

Output:

```F D B A E C

```

Time Complexity: O(N)
Auxiliary Space: O(N)

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