Dynamic Programming: Knapsack - Minimum Cost for Tickets
If the minimum cost tickets problem is extended to allow tickets covering fractional days (e.g., 1.5 days) with real-valued costs, which approach best adapts to solve this variant efficiently?
If the minimum cost tickets problem is extended to allow tickets covering fractional days (e.g., 1.5 days) with real-valued costs, which approach best adapts to solve this variant efficiently?
hard🔁 Follow-Up Q10 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand fractional day coverage
Tickets now cover fractional days, so travel days are no longer discrete integers.Step 2: Discretize timeline into small intervals
Discretize the timeline into small intervals (e.g., half-days) to approximate fractional coverage.Step 3: Apply continuous DP over discretized intervals
Apply DP over discretized intervals to compute minimum cost efficiently.Final Answer:
Option B -> Option BQuick Check:
Discretization enables DP on fractional intervals [OK]
Quick Trick: Discretize fractional days to apply DP [OK]
Common Mistakes:
MISTAKES- Ignoring fractional parts and using integer DP
- Assuming greedy works for fractional coverage
- Trying exhaustive backtracking which is inefficient
Trap Explanation:
PITFALL- Ignoring fractional days leads to incorrect or inefficient solutions
Interviewer Note:
CONTEXT- Tests ability to adapt DP to continuous or fractional problem variants
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