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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:

Step 1: Understand traversal cost
Each node is visited once, so base cost is O(N).
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.
Step 3: Combine costs
Overall complexity is O(N * 2^L) due to exploring all paths and copying them.
Final Answer:
Option A → Option A
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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