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Binary Tree to DLL

Given a Binary Tree (BT), convert it to a Doubly Linked List(DLL) In-Place. The left and right pointers in nodes are to be used as previous and next pointers respectively in converted DLL. The order of nodes in DLL must be same as Inorder of the given Binary Tree. The first node of Inorder traversal (left most node in BT) must be head node of the DLL.

Following two different solutions have been discussed for this problem.
Convert a given Binary Tree to Doubly Linked List | Set 1
Convert a given Binary Tree to Doubly Linked List | Set 2

In this post, a third solution is discussed which seems to be the simplest of all. The idea is to do inorder traversal of the binary tree. While doing inorder traversal, keep track of the previously visited node in a variable say prev. For every visited node, make it next of prev and previous of this node as prev.

Thanks to rahul, wishall and all other readers for their useful comments on the above two posts.

Following is C++ implementation of this solution.

 `// A C++ program for in-place conversion of Binary Tree to DLL``#include ``using` `namespace` `std;` `/* A binary tree node has data, and left and right pointers */``struct` `node``{``    ``int` `data;``    ``node* left;``    ``node* right;``};` `// A simple recursive function to convert a given Binary tree to Doubly``// Linked List``// root --> Root of Binary Tree``// head --> Pointer to head node of created doubly linked list``void` `BinaryTree2DoubleLinkedList(node *root, node **head)``{``    ``// Base case``    ``if` `(root == NULL) ``return``;` `    ``// Initialize previously visited node as NULL. This is``    ``// static so that the same value is accessible in all recursive``    ``// calls``    ``static` `node* prev = NULL;` `    ``// Recursively convert left subtree``    ``BinaryTree2DoubleLinkedList(root->left, head);` `    ``// Now convert this node``    ``if` `(prev == NULL)``        ``*head = root;``    ``else``    ``{``        ``root->left = prev;``        ``prev->right = root;``    ``}``    ``prev = root;` `    ``// Finally convert right subtree``    ``BinaryTree2DoubleLinkedList(root->right, head);``}` `/* Helper function that allocates a new node with the``   ``given data and NULL left and right pointers. */``node* newNode(``int` `data)``{``    ``node* new_node = ``new` `node;``    ``new_node->data = data;``    ``new_node->left = new_node->right = NULL;``    ``return` `(new_node);``}` `/* Function to print nodes in a given doubly linked list */``void` `printList(node *node)``{``    ``while` `(node!=NULL)``    ``{``        ``cout << node->data << ``" "``;``        ``node = node->right;``    ``}``}` `/* Driver program to test above functions*/``int` `main()``{``    ``// Let us create the tree shown in above diagram``    ``node *root        = newNode(10);``    ``root->left        = newNode(12);``    ``root->right       = newNode(15);``    ``root->left->left  = newNode(25);``    ``root->left->right = newNode(30);``    ``root->right->left = newNode(36);` `    ``// Convert to DLL``    ``node *head = NULL;``    ``BinaryTree2DoubleLinkedList(root, &head);` `    ``// Print the converted list``    ``printList(head);` `    ``return` `0;``}`

Output:

`25 12 30 10 36 15 `

Note that use of static variables like above is not a recommended practice (we have used static for simplicity). Imagine a situation where same function is called for two or more trees, the old value of prev would be used in next call for a different tree. To avoid such problems, we can use double pointer or reference to a pointer.

Time Complexity: The above program does a simple inorder traversal, so time complexity is O(n) where n is the number of nodes in given binary tree.