[Solved] Suppose the problem is modified so that digits can be removed multiple times (i.e.... Which of the following algorithmic changes correctly adapts the solution? | Greedy Algorithms

Greedy Algorithms - Remove K Digits (Smallest Number)

Suppose the problem is modified so that digits can be removed multiple times (i.e., digits can be reused after removal) to form the smallest number after k removals. Which of the following algorithmic changes correctly adapts the solution?

AUse dynamic programming to consider all sequences with repeated digits allowed

BSort digits and pick the smallest k digits to remove, ignoring order

CUse the same greedy stack approach but allow re-inserting popped digits later

DUse a priority queue to always remove the largest digit available at each step

Step-by-Step Solution

Step 1: Understand reuse of digits breaks greedy assumptions
Allowing reuse means the problem is no longer about removing fixed digits but about sequences with repetition, invalidating the greedy stack approach.
Step 2: Why dynamic programming is needed
DP can explore all subsequences with repeated digits and track minimal results, handling reuse correctly.
Final Answer:
Option A -> Option A
Quick Check:
Greedy fails with reuse; DP handles repeated digit choices [OK]

Quick Trick: Reuse breaks greedy; DP needed for repeated choices [OK]

Common Mistakes:

MISTAKES

Trying to reuse greedy stack with re-insertion
Sorting digits ignores order and reuse constraints
Using priority queue removes largest digit but ignores reuse

Trap Explanation:

PITFALL

Greedy looks tempting but fails because reuse breaks monotonicity assumptions.

Interviewer Note:

CONTEXT

Tests candidate's ability to adapt algorithms to problem variants and recognize when greedy fails.

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More Greedy Algorithms Quizzes

Which of the following algorithmic changes correctly adapts the solution?

Step 1: Understand reuse of digits breaks greedy assumptions

Step 2: Why dynamic programming is needed

Final Answer:

Quick Check:

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