Greedy Algorithms - Maximum Units on a Truck
What is the time complexity of the optimal greedy solution for the Maximum Units on a Truck problem, assuming n is the number of box types and truckSize is the truck capacity?
What is the time complexity of the optimal greedy solution for the Maximum Units on a Truck problem, assuming n is the number of box types and truckSize is the truck capacity?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Solution:
Step 1: Identify main operations
The algorithm sorts boxTypes by units per box descending, which takes O(n log n).Step 2: Analyze iteration cost
After sorting, it iterates over boxTypes once, O(n), picking boxes until truckSize is exhausted.Final Answer:
Option A -> Option AQuick Check:
Sorting dominates, so total complexity is O(n log n) [OK]
Quick Trick: Sorting dominates time complexity [OK]
Common Mistakes:
MISTAKES- Confusing truckSize as multiplicative factor
- Assuming O(n * truckSize) due to iteration
- Ignoring sorting cost
Trap Explanation:
PITFALL- Candidates often think iterating up to truckSize causes O(n * truckSize), but iteration is over n box types only.
Interviewer Note:
CONTEXT- Tests understanding of sorting cost and iteration bounds in greedy algorithms.
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