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What is the space complexity of the optimal greedy solution for Two City Scheduling that sorts and assigns in-place?

medium🪤 Complexity Trap Q6 of Q15
Greedy Algorithms - Two City Scheduling
What is the space complexity of the optimal greedy solution for Two City Scheduling that sorts and assigns in-place?
AO(n^2) due to memoization table
BO(n) for storing sorted costs and auxiliary variables
CO(log n) due to recursion stack in sorting
DO(1) constant space if sorting is in-place
Step-by-Step Solution
Solution:
  1. Step 1: Consider sorting space

    In-place sorting algorithms like Timsort use O(1) or O(log n) auxiliary space.
  2. Step 2: Consider assignment space

    Assignment uses constant extra variables, no additional data structures.
  3. Final Answer:

    Option D -> Option D
  4. Quick Check:

    In-place sorting and simple assignment yield O(1) space [OK]
Quick Trick: In-place sorting + simple assignment -> O(1) space [OK]
Common Mistakes:
MISTAKES
  • Assuming DP memoization space
  • Forgetting recursion stack in sorting
  • Counting input storage as extra space
Trap Explanation:
PITFALL
  • Candidates confuse DP space with greedy or forget sorting auxiliary space.
Interviewer Note:
CONTEXT
  • Tests understanding of space complexity in greedy approach
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