What is the space complexity of the backtracking solution for letter case permutation on a string of length n with k letters?

medium🪤 Complexity Trap Q6 of Q15

Subsets & Combinations - Letter Case Permutation

AO(2^k * n) only for output storage

BO(2^k * n) output storage plus O(n) recursion stack

CO(k) recursion stack only

DO(n) recursion stack plus O(2^k * n) output storage

Step-by-Step Solution

Solution:

Step 1: Recursion stack depth
Maximum recursion depth is n (string length), so O(n) stack space.
Step 2: Output storage
There are 2^k outputs, each of length n -> O(2^k * n) space.
Step 3: Total space complexity
Dominated by output storage plus recursion stack -> O(2^k * n) plus O(n) stack.
Final Answer:
Option B -> Option B
Quick Check:
Output storage dominates space, recursion stack adds O(n) [OK]

Quick Trick: Output storage dominates space complexity [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Interviewer Note:

CONTEXT

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