Greedy Algorithms - Remove K Digits (Smallest Number)
What is the time complexity of the optimal greedy algorithm using a stack to remove k digits from a number string of length n?
What is the time complexity of the optimal greedy algorithm using a stack to remove k digits from a number string of length n?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze loop iterations
Each digit is pushed and popped at most once, so total operations are proportional to n.Step 2: Confirm no nested loops dependent on k
While loops remove digits but total removals ≤ k ≤ n, so overall linear.Final Answer:
Option A -> Option AQuick Check:
Stack-based greedy runs in O(n) time [OK]
Quick Trick: Each digit pushed/popped once -> O(n) time [OK]
Common Mistakes:
MISTAKES- Assuming nested loops cause O(n*k)
- Confusing with sorting complexity
Trap Explanation:
PITFALL- Candidates often think inner while loop causes O(n*k), but total pops ≤ k limit complexity to O(n).
Interviewer Note:
CONTEXT- Tests understanding of amortized analysis in greedy stack algorithms.
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