Binary Tree to Binary Search Tree Conversion
Given a Binary Tree, convert it to a Binary Search Tree. The conversion must be done in such a way that keeps the original structure of Binary Tree.
Example 1 Input: 10 / \ 2 7 / \ 8 4 Output: 8 / \ 4 10 / \ 2 7 Example 2 Input: 10 / \ 30 15 / \ 20 5 Output: 15 / \ 10 20 / \ 5 30
Following is a 3 step solution for converting Binary tree to Binary Search Tree.
- Create a temp array arr that stores inorder traversal of the tree. This step takes O(n) time.
- Sort the temp array arr. Time complexity of this step depends upon the sorting algorithm. In the following implementation, Quick Sort is used which takes (n^2) time. This can be done in O(nLogn) time using Heap Sort or Merge Sort.
- Again do inorder traversal of tree and copy array elements to tree nodes one by one. This step takes O(n) time.
Following is the implementation of the above approach. The main function to convert is highlighted in the following code.
Following is the inorder traversal of the converted BST 5 10 15 20 30
- Time Complexity: O(nlogn). This is the complexity of the sorting algorithm which we are using after first in-order traversal, rest of the operations take place in linear time.
- Auxiliary Space: O(n). Use of data structure ‘array’ to store in-order traversal.
We will be covering another method for this problem which converts the tree using O(height of the tree) extra space.