Greedy Algorithms - Gas Station (Circular)
What is the time complexity of the optimal greedy solution using prefix sums and two pointers for the Gas Station (Circular) problem, given n stations?
What is the time complexity of the optimal greedy solution using prefix sums and two pointers for the Gas Station (Circular) problem, given n stations?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze prefix sums computation
Computing prefix sums takes O(2n) = O(n) time.Step 2: Analyze the single pass check
The loop checking prefix[i+n] - prefix[i] runs n times, each in O(1), total O(n).Final Answer:
Option C -> Option CQuick Check:
Single pass with prefix sums yields linear time [OK]
Quick Trick: Prefix sums enable O(1) range queries, total O(n) time [OK]
Common Mistakes:
MISTAKES- Assuming nested loops cause O(n²)
- Thinking sorting is needed
- Confusing space with time complexity
Trap Explanation:
PITFALL- The presence of prefix sums and a single loop misleads candidates to think it's O(n²) or O(n log n).
Interviewer Note:
CONTEXT- Checks if candidate understands how prefix sums optimize range queries and overall complexity.
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