Algorithms‎ > ‎Trees‎ > ‎BST‎ > ‎

## Sorted Linked List to Balanced BST

January 17, 2012

Given a Singly Linked List which has data members sorted in ascending order. Construct a Balanced Binary Search Tree which has same data members as the given Linked List.

Examples:

```Input:  Linked List 1->2->3
Output: A Balanced BST
2
/  \
1    3

Output: A Balanced BST
4
/   \
2     6
/  \   / \
1   3  4   7

Output: A Balanced BST
3
/  \
2    4
/
1

Output: A Balanced BST
4
/   \
2     6
/  \   /
1   3  5
```

Method 1 (Simple)
Following is a simple algorithm where we first find the middle node of list and make it root of the tree to be constructed.

```1) Get the Middle of the linked list and make it root.
2) Recursively do same for left half and right half.
a) Get the middle of left half and make it left child of the root
created in step 1.
b) Get the middle of right half and make it right child of the
root created in step 1.

```

Time complexity: O(nLogn) where n is the number of nodes in Linked List.

See this forum thread for more details.

Method 2 (Tricky)
The method 1 constructs the tree from root to leaves. In this method, we construct from leaves to root. The idea is to insert nodes in BST in the same order as the appear in Linked List, so that the tree can be constructed in O(n) time complexity. We first count the number of nodes in the given Linked List. Let the count be n. After counting nodes, we take left n/2 nodes and recursively construct the left subtree. After left subtree is constructed, we allocate memory for root and link the left subtree with root. Finally, we recursively construct the right subtree and link it with root.
While constructing the BST, we also keep moving the list head pointer to next so that we have the appropriate pointer in each recursive call.
Following is C implementation of method 2. The main code which creates Balanced BST is highlighted.

 `#include``#include` `/* Link list node */``struct` `LNode``{``    ``int` `data;``    ``struct` `LNode* next;``};` `/* A Binary Tree node */``struct` `TNode``{``    ``int` `data;``    ``struct` `TNode* left;``    ``struct` `TNode* right;``};` `struct` `TNode* newNode(``int` `data);``int` `countLNodes(``struct` `LNode *head);``struct` `TNode* sortedListToBSTRecur(``struct` `LNode **head_ref, ``int` `n);`  `/* This function counts the number of nodes in Linked List and then calls``   ``sortedListToBSTRecur() to construct BST */``struct` `TNode* sortedListToBST(``struct` `LNode *head)``{``    ``/*Count the number of nodes in Linked List */``    ``int` `n = countLNodes(head);` `    ``/* Construct BST */``    ``return` `sortedListToBSTRecur(&head, n);``}` `/* The main function that constructs balanced BST and returns root of it.``       ``head_ref -->  Pointer to pointer to head node of linked list``       ``n  --> No. of nodes in Linked List */``struct` `TNode* sortedListToBSTRecur(``struct` `LNode **head_ref, ``int` `n)``{``    ``/* Base Case */``    ``if` `(n <= 0)``        ``return` `NULL;` `    ``/* Recursively construct the left subtree */``    ``struct` `TNode *left = sortedListToBSTRecur(head_ref, n/2);` `    ``/* Allocate memory for root, and link the above constructed left ``       ``subtree with root */``    ``struct` `TNode *root = newNode((*head_ref)->data);``    ``root->left = left;` `    ``/* Change head pointer of Linked List for parent recursive calls */``    ``*head_ref = (*head_ref)->next;` `    ``/* Recursively construct the right subtree and link it with root ``      ``The number of nodes in right subtree  is total nodes - nodes in ``      ``left subtree - 1 (for root) which is n-n/2-1*/``    ``root->right = sortedListToBSTRecur(head_ref, n-n/2-1);` `    ``return` `root;``}`   `/* UTILITY FUNCTIONS */` `/* A utility function that returns count of nodes in a given Linked List */``int` `countLNodes(``struct` `LNode *head)``{``    ``int` `count = 0;``    ``struct` `LNode *temp = head;``    ``while``(temp)``    ``{``        ``temp = temp->next;``        ``count++;``    ``}``    ``return` `count;``}` `/* Function to insert a node at the beginging of the linked list */``void` `push(``struct` `LNode** head_ref, ``int` `new_data)``{``    ``/* allocate node */``    ``struct` `LNode* new_node =``        ``(``struct` `LNode*) ``malloc``(``sizeof``(``struct` `LNode));``    ``/* put in the data  */``    ``new_node->data  = new_data;` `    ``/* link the old list off the new node */``    ``new_node->next = (*head_ref);` `    ``/* move the head to point to the new node */``    ``(*head_ref)    = new_node;``}` `/* Function to print nodes in a given linked list */``void` `printList(``struct` `LNode *node)``{``    ``while``(node!=NULL)``    ``{``        ``printf``(``"%d "``, node->data);``        ``node = node->next;``    ``}``}` `/* Helper function that allocates a new node with the``   ``given data and NULL left and right pointers. */``struct` `TNode* newNode(``int` `data)``{``    ``struct` `TNode* node = (``struct` `TNode*)``                         ``malloc``(``sizeof``(``struct` `TNode));``    ``node->data = data;``    ``node->left = NULL;``    ``node->right = NULL;` `    ``return` `node;``}` `/* A utility function to print preorder traversal of BST */``void` `preOrder(``struct` `TNode* node)``{``    ``if` `(node == NULL)``        ``return``;``    ``printf``(``"%d "``, node->data);``    ``preOrder(node->left);``    ``preOrder(node->right);``}` `/* Drier program to test above functions*/``int` `main()``{``    ``/* Start with the empty list */``    ``struct` `LNode* head = NULL;` `    ``/* Let us create a sorted linked list to test the functions``     ``Created linked list will be 7->6->5->4->3->2->1 */``    ``push(&head, 7);``    ``push(&head, 6);``    ``push(&head, 5);``    ``push(&head, 4);``    ``push(&head, 3);``    ``push(&head, 2);``    ``push(&head, 1);` `    ``printf``(``"\n Given Linked List "``);``    ``printList(head);` `    ``/* Convert List to BST */``    ``struct` `TNode *root = sortedListToBST(head);``    ``printf``(``"\n PreOrder Traversal of constructed BST "``);``    ``preOrder(root);` `    ``return` `0;``}`

Time Complexity: O(n)