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If the postorder traversal array may contain duplicate values, which modification is essential to correctly reconstruct the binary tree from inorder and postorder traversals?

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Tree: Depth-First Search - Construct Tree from Inorder and Postorder
If the postorder traversal array may contain duplicate values, which modification is essential to correctly reconstruct the binary tree from inorder and postorder traversals?
AUse a data structure that maps values to a list of indices in inorder traversal to handle duplicates
BIgnore duplicates since they do not affect tree reconstruction
CSort the postorder array before reconstruction to group duplicates
DReplace postorder traversal with preorder traversal to avoid duplicates
Step-by-Step Solution
Solution:

  1. Step 1: Understand the problem with duplicates

    Duplicates cause ambiguity in locating root indices in inorder traversal.

  2. Step 2: Use a mapping from value to all indices

    Store all indices of each value in inorder traversal to correctly identify the root position during recursion.

  3. Step 3: Modify recursion to pick correct index instance

    Track which occurrence of the duplicate value is being used to avoid ambiguity.

  4. Final Answer:

    Option A -> Option A

  5. Quick Check:

    Duplicates require multiple index tracking [OK]
Quick Trick: Map values to all inorder indices to handle duplicates [OK]
Common Mistakes:
MISTAKES
  • Assuming duplicates can be ignored
  • Sorting traversal arrays which breaks tree structure
  • Switching traversal types unnecessarily
Trap Explanation:
PITFALL
  • Ignoring duplicates causes incorrect root index lookup and wrong tree
Interviewer Note:
CONTEXT
  • Tests understanding of handling duplicates in tree reconstruction algorithms
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