Greedy Algorithms - Task Scheduler (CPU Cooling)
What is the space complexity of the optimal Task Scheduler algorithm using a max-heap and frequency map for
m unique tasks?What is the space complexity of the optimal Task Scheduler algorithm using a max-heap and frequency map for m unique tasks?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Identify data structures
Frequency map stores counts for m unique tasks -> O(m) space.Step 2: Analyze heap space
Heap stores up to m elements, so O(m) space; recursion stack is not used.Step 3: Consider auxiliary space
Heap operations use O(log m) auxiliary space for internal heapify operations, but total space is dominated by O(m).Final Answer:
Option A -> Option AQuick Check:
Main data structures require O(m) space [OK]
Quick Trick: Total space dominated by frequency map and heap, O(m) [OK]
Common Mistakes:
MISTAKES- Forgetting auxiliary heap space
- Confusing total space with auxiliary space
Trap Explanation:
PITFALL- Candidates often report auxiliary space only, ignoring total space complexity.
Interviewer Note:
CONTEXT- Tests nuanced understanding of space usage in heap-based algorithms
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