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What is the worst-case time complexity of a recursive backtracking solution that finds all root-to-leaf paths summing to a target in a binary tree with N nodes and maximum path length L?

medium📊 Complexity Q5 of Q15
Tree: Depth-First Search - Path Sum II (All Root-to-Leaf Paths)
What is the worst-case time complexity of a recursive backtracking solution that finds all root-to-leaf paths summing to a target in a binary tree with N nodes and maximum path length L?
AO(N * 2^L)
BO(N^2)
CO(N * L)
DO(L^N)
Step-by-Step Solution
Solution:

  1. Step 1: Understand traversal cost

    Each node is visited once, so base cost is O(N).

  2. Step 2: Consider path enumeration

    In worst case, number of root-to-leaf paths can be exponential in path length L, up to 2^L.

  3. Step 3: Combine costs

    Overall complexity is O(N * 2^L) due to exploring all paths and copying them.

  4. Final Answer:

    Option A → Option A

  5. Quick Check:

    Exponential paths cause exponential time [OK]
Quick Trick: Exponential paths cause O(N * 2^L) time [OK]
Common Mistakes:
MISTAKES
  • Assuming linear time ignoring path enumeration
  • Confusing path length L with number of nodes N
  • Mistaking polynomial for exponential complexity
Trap Explanation:
PITFALL
  • Ignoring exponential number of paths leads to underestimating complexity
Interviewer Note:
CONTEXT
  • Tests understanding of complexity in recursive path enumeration
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