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If the problem is modified so that the postorder traversal may contain duplicate values, which of the following changes is necessary to correctly reconstruct the tree?

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Tree: Depth-First Search - Construct Tree from Inorder and Postorder
If the problem is modified so that the postorder traversal may contain duplicate values, which of the following changes is necessary to correctly reconstruct the tree?
AModify the algorithm to store indices of all occurrences of each value in inorder and track usage to avoid ambiguity.
BUse a hash map from value to index in inorder traversal as before, ignoring duplicates.
CSwitch to preorder and inorder traversals which do not have duplicates.
DUse a greedy approach attaching nodes as left children to handle duplicates.
Step-by-Step Solution

  1. Step 1: Understand the impact of duplicates

    Duplicates break the uniqueness of value-to-index mapping in inorder traversal, so a simple hash map is insufficient.

  2. Step 2: Required modification

    Store all indices of each value in inorder and track which occurrence is used to correctly split subtrees and avoid ambiguity.

  3. Step 3: Why other options fail

    Ignoring duplicates or switching traversals does not solve ambiguity; greedy approach fails to reconstruct correct structure.

  4. Final Answer:

    Option A -> Option A

  5. Quick Check:

    Tracking multiple indices per value is necessary for duplicates [OK]
Quick Trick: Duplicates require tracking all indices, not just one [OK]
Common Mistakes:
MISTAKES
  • Ignoring duplicates in hash map
  • Assuming unique values always
  • Switching traversal types incorrectly
Trap Explanation:
PITFALL
  • Candidates often assume unique values; duplicates require more complex bookkeeping.
Interviewer Note:
CONTEXT
  • Tests depth of understanding and ability to adapt algorithm to relaxed constraints.
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