Construct a special tree from given preorder traversal

Given an array pre[] that represents the Preorder traversal of a special binary tree where every node has either 0 or 2 children. One more array preLN[] is given which has only two possible values ‘L’ and ‘N’. The value ‘L’ in preLN[] indicates that the corresponding node in Binary Tree is a leaf node and the value ‘N’ indicates that the corresponding node is a non-leaf node. The task is to construct the tree from the given two arrays.

Example:

Input:  pre[] = {10, 30, 20, 5, 15},  preLN[] = {'N', 'N', 'L', 'L', 'L'}
Output:

👁 Construct-a-special-tree-from-given-preorder-traversal

[Expected Approach] Using Pre-Order Traversal - O(n) Time and O(h) Space

The first element in pre[] will always be root. So we can easily figure out the root. If the left subtree is empty, the right subtree must also be empty, and the preLN[] entry for root must be ‘L’. We can simply create a node and return it. If the left and right subtrees are not empty, then recursively call for left and right subtrees and link the returned nodes to root.  

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[Alternate Approach] Using Stack - O(n) Time and O(h) Space

The idea is to use a stack to implement pre-order traversal and construct the binary tree and return the root node.

Step by step implementation:

1. As the Pre-order Traversal is given, so we first create the root node and insert it into an empty stack.
2. Traverse the given pre-order traversal.
   1. Create the node corresponding to the current value.
   2. Check the top node in the stack:
      • If left of top node is null, then set the current node as left of top node.
      • Else, right of top node is null, then set the current node as right of top node and pop the top node.
   3. If the present node is not a leaf node, push node into the stack.
3. Return the root of the constructed tree.

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Related article:

• Construct the full k-ary tree from its preorder traversal