If the Minimum Domino Rotations problem is extended so that dominoes can be rotated multiple times (reused) and values can be outside the 1-6 range, which approach best adapts to solve this variant efficiently?

hard🔁 Follow-up Q10 of Q15

Greedy Algorithms - Minimum Domino Rotations

AFixed candidate checking limited to values 1 through 6

BHash map frequency counting combined with iterative candidate validation

CSorting both arrays and using two-pointer technique

DDynamic programming over all possible rotations

Step-by-Step Solution

Solution:

Step 1: Generalize candidates
Since values can be arbitrary, use a hash map to count frequencies of all values appearing in top or bottom.
Step 2: Validate candidates
Iterate over candidates from the hash map and check if uniformity is possible by counting rotations.
Step 3: Adapt to multiple rotations and arbitrary values
This approach adapts to arbitrary values and multiple rotations efficiently.
Final Answer:
Option B -> Option B
Quick Check:
Frequency counting handles unknown ranges well. [OK]

Quick Trick: Use frequency maps for arbitrary values [OK]

Common Mistakes:

MISTAKES

Restricting candidates to 1-6 when values can be outside
Trying brute force over all rotations without pruning
Assuming original greedy approach applies unchanged

Trap Explanation:

PITFALL

Original approach fails if values are outside 1-6 or rotations can be reused.

Interviewer Note:

CONTEXT

Tests ability to generalize and adapt solutions to problem variants.

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If the Minimum Domino Rotations problem is extended so that dominoes can be rotated multiple times (reused) and values can be outside the 1-6 range, which approach best adapts to solve this variant efficiently?

Step 1: Generalize candidates

Step 2: Validate candidates

Step 3: Adapt to multiple rotations and arbitrary values

Final Answer:

Quick Check:

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