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97. Construct Binary Search Tree from a given Preorder Traversal using Recursion
Objective: - Given a preorder traversal, construct BST from that.
Input: Preorder traversal
Similar Problem: This problem is similar to the - Construct Binary Search Tree from a given Preorder Traversal Using Stack (Without Recursion)
Approach:
The solution to the problem is similar to isBST Max-Min Solution.
"Your root value can have any value between -∞ to + ∞, say it is 30 here, When you validate the right child of 30, it can take any value between 30 and + ∞. When you validate the left child of 30, it can take any value between — ∞ and 30. likewise
So the idea is to Pass the minimum and maximum values between which the node’s value must lie.
- Example: int[] preOrder = { 20, 10, 5, 1, 7, 15, 30, 25, 35, 32, 40 };
- The first element in the preorder[] will be the root, which is 20 here.
- we start with the range minimum = Integer.MIN_VALUE and maximum = Interger.MAX_VALUE, so your root can take any value between this range.
- So when putting the left node of 20(root), it must lie within the range of minimum = Integer.MIN_VALUE and maximum = 20, so check the next element in the preorder[], if it lies in this range, make it the left child to the root, else it must be the right child of the root, and so on. See the figure for a better understanding. ( see the execution sequence)
- Solve it recursively.
Time Complexity: O(n)
Output:
Inorder Traversal of Constructed Tree : 1 5 7 10 15 20 25 30 32 35 40