Given a Binary Search Tree, convert it into a Min-Heap containing the same elements in O(n) time. Do this in-place.
Input: Binary Search Tree 8 / \ 4 12 / \ / \ 2 6 10 14 Output - Min Heap 2 / \ 4 6 / \ / \ 8 10 12 14 [Or any other tree that follows Min Heap properties and has same keys]
If we are allowed to use extra space, we can perform inorder traversal of the tree and store the keys in an auxiliary array. As we’re doing inorder traversal on a BST, array will be sorted. Finally, we construct a complete binary tree from the sorted array. We construct the binary tree level by level and from left to right by taking next minimum element from sorted array. The constructed binary tree will be a min-Heap. This solution works in O(n) time, but is not in-place.
How to do it in-place?
The idea is to convert the binary search tree into a sorted linked list first. We can do this by traversing the BST in inorder fashion. We add nodes at the beginning of current linked list and update head of the list using pointer to head pointer. Since we insert at the beginning, to maintain sorted order, we first traverse the right subtree before the left subtree. i.e. do a reverse inorder traversal.
Finally we convert the sorted linked list into a min-Heap by setting the left and right pointers appropriately. We can do this by doing a Level order traversal of the partially built Min-Heap Tree using queue and traversing the linked list at the same time. At every step, we take the parent node from queue, make next two nodes of linked list as children of the parent node, and enqueue the next two nodes to queue. As the linked list is sorted, the min-heap property is maintained.
Below is the implementation of above idea –
2 4 6 8 10 12 14
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- Convert a BST to a Binary Tree such that sum of all greater keys is added to every key
- Convert a normal BST to Balanced BST
- Convert BST to Min Heap
- Convert BST to Max Heap
- Red-Black Trees | Top-Down Insertion
- Implementing a BST where every node stores the maximum number of nodes in the path till any leaf
- Pre-Order Successor of all nodes in Binary Search Tree
- Lexicographically Smallest Topological Ordering
- Print Binary Search Tree in Min Max Fashion
- Implementing Backward Iterator in BST
- Implementing Forward Iterator in BST
- Number of pairs with a given sum in a Binary Search Tree
- Find the minimum absolute difference in two different BST's
- Nodes from given two BSTs with sum equal to X
Improved By : SHUBHAMSINGH10