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Given the following partial memoization cache after processing a binary tree for sum root-to-leaf numbers: memo = { (node_id=5, current_number=12): 34, (node_id=3, current_number=1): 46 } If the final sum returned is 80, which of the following could be the original root-to-leaf path values?

hard🔄 Reverse Engineer Q9 of Q15
Tree: Depth-First Search - Sum Root to Leaf Numbers
Given the following partial memoization cache after processing a binary tree for sum root-to-leaf numbers: memo = { (node_id=5, current_number=12): 34, (node_id=3, current_number=1): 46 } If the final sum returned is 80, which of the following could be the original root-to-leaf path values?
APaths 12->5 and 1->3 with sums 34 and 46 respectively
BPaths 3->1 and 5->12 with sums 46 and 34 respectively
CPaths 5->12 and 3->1 with sums 34 and 46 respectively
DPaths 1->3 and 12->5 with sums 46 and 34 respectively
Step-by-Step Solution
Solution:

  1. Step 1: Interpret memo keys as (node_id, current_number)

    Keys indicate the node id and the current number accumulated before processing that node.

  2. Step 2: Understand path direction

    Paths 3->1 and 5->12 correspond to keys (3,1) and (5,12) respectively.

  3. Step 3: Sum values 46 + 34 = 80 matches final sum

    Paths 3->1 and 5->12 with sums 46 and 34 respectively correctly match keys and sum to final total.

  4. Final Answer:

    Option B -> Option B

  5. Quick Check:

    Keys correspond to node then current_number, sums add to 80 [OK]
Quick Trick: Memo keys show node then current_number [OK]
Common Mistakes:
MISTAKES
  • Confusing order of nodes in keys
  • Mismatching sums to final total
Trap Explanation:
PITFALL
  • Candidates often reverse node and number order or misinterpret memo keys.
Interviewer Note:
CONTEXT
  • Tests deep understanding of memoization state and path reconstruction.
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