[Solved] You are given a list of days when you will travel and three types of tickets with different durations and costs.... Which algorithmic approach guarantees an optimal solution for this problem? | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Minimum Cost for Tickets

You are given a list of days when you will travel and three types of tickets with different durations and costs. You want to minimize the total cost to cover all travel days. Which algorithmic approach guarantees an optimal solution for this problem?

ADynamic programming using bottom-up tabulation with binary search to find the next uncovered day

BGreedy algorithm that always buys the cheapest ticket for the current day

CPure recursion without memoization, exploring all ticket combinations

DSorting days and using a sliding window to pick tickets covering maximum days

Step-by-Step Solution

Step 1: Understand problem constraints
The problem requires covering all travel days with minimum cost, where tickets have different durations and costs.
Step 2: Identify suitable algorithm
Greedy fails because cheapest ticket today may not cover future days optimally. Pure recursion is exponential and inefficient. Sliding window doesn't handle overlapping durations well. Bottom-up DP with binary search efficiently finds next uncovered day and computes minimal cost.
Final Answer:
Option A -> Option A
Quick Check:
DP with binary search ensures optimal substructure and efficient lookup [OK]

Quick Trick: Optimal solution requires DP with binary search [OK]

Common Mistakes:

MISTAKES

Assuming greedy always works
Ignoring overlapping ticket durations
Using recursion without memoization

Trap Explanation:

PITFALL

Greedy looks plausible because it picks cheapest ticket immediately, but fails on overlapping coverage.

Interviewer Note:

CONTEXT

Tests if candidate can recognize the unbounded knapsack pattern with interval coverage and binary search optimization.

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More Dynamic Programming: Knapsack Quizzes

Which algorithmic approach guarantees an optimal solution for this problem?

Step 1: Understand problem constraints

Step 2: Identify suitable algorithm

Final Answer:

Quick Check:

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