Which modification to the algorithm is necessary to handle this constraint correctly?
hard🎤 Interviewer Follow-up Q15 of Q15
Dynamic Programming: Knapsack - Minimum Cost for Tickets
Suppose the problem is modified so that each ticket can be used multiple times but only on distinct travel days (no overlapping coverage). Which modification to the algorithm is necessary to handle this constraint correctly?
AUse a top-down DP with memoization and add a visited set to track used tickets
BChange binary search to linear scan to find next uncovered day to avoid reuse overlap
CModify DP state to include the last day covered and ensure no overlapping ticket durations
DNo change needed; the existing bottom-up DP with binary search works as is
Step-by-Step Solution
Step 1: Understand new constraint
Tickets can be reused but cannot overlap coverage on travel days. This requires tracking coverage intervals explicitly.
Step 2: Modify DP state
DP must include last covered day or interval to ensure no overlapping coverage. Without this, DP may double count days or reuse tickets incorrectly.
Step 3: Evaluate other options
Adding visited sets or linear scans is inefficient or insufficient. Existing DP assumes unlimited overlapping coverage, so no change is incorrect.
Final Answer:
Option C -> Option C
Quick Check:
DP state must track coverage to prevent overlap [OK]
Quick Trick:Track coverage intervals in DP state for reuse constraints [OK]
Common Mistakes:
MISTAKES
Assuming no change needed
Using visited sets without DP state change
Replacing binary search with linear scan
Trap Explanation:
PITFALL
Naive reuse breaks DP correctness; state must track coverage to avoid overlap.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt DP state for complex constraints and coverage tracking.
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