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 to get the 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 to get the smallest number?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Identify operations per digit
Each digit is pushed onto the stack once and can be popped at most once when a smaller digit arrives.Step 2: Analyze total operations
Since each push and pop happens at most once per digit, total operations are proportional to n.Final Answer:
Option A -> Option AQuick Check:
Stack operations are linear in n, no nested loops [OK]
Quick Trick: Each digit pushed/popped once -> O(n) time [OK]
Common Mistakes:
MISTAKES- Assuming worst case k pops per digit -> O(n*k)
- Confusing with sorting complexity
- Thinking nested loops are needed
Trap Explanation:
PITFALL- It's tempting to think each digit causes multiple pops, but total pops ≤ n.
Interviewer Note:
CONTEXT- Checks if candidate understands amortized analysis of stack operations.
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