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If you need to find the top K root-to-leaf paths with the largest sums in a binary tree, which method efficiently supports this requirement?

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Tree: Depth-First Search - Path Sum II (All Root-to-Leaf Paths)
If you need to find the top K root-to-leaf paths with the largest sums in a binary tree, which method efficiently supports this requirement?
AUse DFS with a min-heap of size K to track top sums during traversal
BPerform BFS and store all paths, then sort to find top K
CApply dynamic programming to memoize maximum sums per node
DUse binary search on sum values to guess top K paths
Step-by-Step Solution
Solution:

  1. Step 1: Traverse all paths

    DFS explores all root-to-leaf paths.

  2. Step 2: Maintain top K sums

    Use a min-heap of size K to keep track of the largest sums found so far.

  3. Step 3: Efficient pruning

    Discard paths with sums smaller than the smallest in the heap to optimize.

  4. Final Answer:

    Option A → Option A

  5. Quick Check:

    Min-heap efficiently tracks top K sums [OK]
Quick Trick: Min-heap keeps top K sums efficiently during DFS [OK]
Common Mistakes:
MISTAKES
  • Storing all paths then sorting wastes memory and time
  • Dynamic programming doesn't directly find top K paths
  • Binary search on sums is not practical without path enumeration
Trap Explanation:
PITFALL
  • Sorting all paths is inefficient; min-heap optimizes top K tracking
Interviewer Note:
CONTEXT
  • Tests ability to adapt path sum problem to top K variant with efficient data structures
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