Dynamic Programming: Knapsack - Minimum Cost for Tickets
Consider the following code snippet implementing the minimum cost for tickets problem. What is the value of dp[0] after the loop completes for the input days = [1,4,6] and costs = [2,7,15]?
Consider the following code snippet implementing the minimum cost for tickets problem. What is the value of dp[0] after the loop completes for the input days = [1,4,6] and costs = [2,7,15]?
easy🧾 Code Trace Q12 of Q15
Step-by-Step Solution
Step 1: Trace dp from the end
dp[3] = 0 (base case). For i=2 (day=6): - 1-day ticket: cost=2 + dp[3]=2 - 7-day ticket: cost=7 + dp[3]=7 - 30-day ticket: cost=15 + dp[3]=15 Minimum = 2 -> dp[2]=2Step 2: Calculate dp[1] and dp[0]
i=1 (day=4): - 1-day: cost=2 + dp[2]=4 - 7-day: cost=7 + dp[3]=7 - 30-day: cost=15 + dp[3]=15 Minimum=4 -> dp[1]=4 i=0 (day=1): - 1-day: cost=2 + dp[1]=6 - 7-day: cost=7 + dp[3]=7 - 30-day: cost=15 + dp[3]=15 Minimum=6 -> dp[0]=6Final Answer:
Option A -> Option AQuick Check:
dp[0] correctly computed as 6 [OK]
Quick Trick: Trace dp from end to start carefully [OK]
Common Mistakes:
MISTAKES- Off-by-one in dp indexing
- Miscomputing next_i with bisect
- Confusing costs and dp sums
Trap Explanation:
PITFALL- Candidates often miscalculate dp[i] by mixing indices or forgetting dp base case.
Interviewer Note:
CONTEXT- Tests ability to mentally execute bottom-up DP with binary search indexing.
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