Greedy Algorithms - Largest Number (Arrange to Form Biggest)
What is the time complexity of sorting n numbers (converted to strings) using a custom comparator that compares concatenated pairs of length up to k?
What is the time complexity of sorting n numbers (converted to strings) using a custom comparator that compares concatenated pairs of length up to k?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Sorting complexity
Sorting n elements typically takes O(n log n) comparisons in comparison-based sorts.Step 2: Comparator cost
Each comparison involves comparing concatenations of strings of length up to k, which takes O(k) time.Step 3: Number of comparisons
In worst case, sorting can require O(n^2) comparisons if the sorting algorithm is not comparison-based or if the comparator is expensive.Step 4: Total complexity
Because each comparison costs O(k), and there can be up to O(n^2) comparisons in worst case, total complexity is O(n^2 * k).Final Answer:
Option B -> Option BQuick Check:
Custom comparator can cause quadratic comparisons in worst case [OK]
Quick Trick: Worst-case sorting with expensive comparator can be O(n^2 * k) [OK]
Common Mistakes:
MISTAKES- Assuming always O(n log n)
- Ignoring comparator cost
- Confusing k with n in complexity
Trap Explanation:
PITFALL- Overlooking the cost of string concatenation in comparator leads to underestimating complexity.
Interviewer Note:
CONTEXT- Tests understanding of time complexity with custom comparators.
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