Operating Systems - FCFS Scheduling - Convoy Effect & Waiting Time
What is the time complexity of calculating waiting times for n processes scheduled using FCFS, assuming burst times are known?
What is the time complexity of calculating waiting times for n processes scheduled using FCFS, assuming burst times are known?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand waiting time calculation
Waiting time for process i is sum of bursts of all previous processes.Step 2: Analyze complexity
Using prefix sums, waiting times for all n processes can be computed in O(n) total time.
Naive summation per process is O(n^2), but prefix sums optimize to O(n).Final Answer:
Option C -> Option CQuick Check:
Prefix sums reduce complexity to linear [OK]
Quick Trick: Prefix sums enable O(n) waiting time calculation [OK]
Common Mistakes:
MISTAKES- Assuming naive O(n^2) without prefix sums
- Thinking waiting time calculation is constant time
- Confusing logarithmic complexity with prefix sums
Trap Explanation:
PITFALL- Candidates often forget prefix sums optimize waiting time calculation from O(n^2) to O(n).
Interviewer Note:
CONTEXT- Tests understanding of algorithmic optimization in waiting time computation.
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