Greedy Algorithms - Minimum Platforms (Train Stations)
What is the auxiliary space complexity of the min-heap based algorithm for minimum platforms, considering the heap and input storage?
What is the auxiliary space complexity of the min-heap based algorithm for minimum platforms, considering the heap and input storage?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze heap space usage
The heap can hold up to n departure times in worst case, so O(n) space.Step 2: Consider input storage and sorting
Sorting creates a list of n tuples (arrival, departure), also O(n) space. However, if implemented recursively (not here), recursion stack could add more space.Step 3: Recognize that total auxiliary space is O(n)
Heap + sorted list = O(n) space, not O(n^2).Final Answer:
Option C -> Option CQuick Check:
Heap and sorted list both O(n) space [OK]
Quick Trick: Heap stores up to n elements -> O(n) space [OK]
Common Mistakes:
MISTAKES- Forgetting heap space
- Assuming constant space
- Confusing time and space complexity
Trap Explanation:
PITFALL- Candidates often underestimate auxiliary space by ignoring heap or sorted array storage.
Interviewer Note:
CONTEXT- Tests understanding of auxiliary space in heap-based algorithms.
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