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Compare the brute force recursive DFS approach and the backtracking with early pruning approach for Path Sum II. When is backtracking with pruning significantly better?

hard⚖️ Approach Comparison Q8 of Q15
Tree: Depth-First Search - Path Sum II (All Root-to-Leaf Paths)
Compare the brute force recursive DFS approach and the backtracking with early pruning approach for Path Sum II. When is backtracking with pruning significantly better?
AWhen the tree is very shallow and has few paths.
BWhen node values are all positive and pruning can cut large subtrees early.
CWhen node values are negative and pruning is ineffective.
DWhen the target sum is zero regardless of tree structure.
Step-by-Step Solution
Solution:

  1. Step 1: Understand pruning effect

    Pruning works by stopping recursion when current sum exceeds target, effective if values are positive.

  2. Step 2: Negative values break pruning

    With negative values, sums can decrease later, so pruning may skip valid paths, making brute force safer.

  3. Final Answer:

    Option B → Option B

  4. Quick Check:

    Pruning is effective only with positive node values [OK]
Quick Trick: Pruning works best with positive values [OK]
Common Mistakes:
MISTAKES
  • Assuming pruning always helps
  • Ignoring negative values impact
Trap Explanation:
PITFALL
  • Candidates often overlook that pruning assumes monotonic sum increase.
Interviewer Note:
CONTEXT
  • Tests understanding of pruning assumptions and when to avoid it.
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