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Suppose the knapsack problem is extended to select items with two constraints: weight and volume, both limited. Which approach best handles this variant?

hard🎤 Interviewer Follow-up Q10 of Q15

Dynamic Programming: Knapsack - 0/1 Knapsack Problem

Suppose the knapsack problem is extended to select items with two constraints: weight and volume, both limited. Which approach best handles this variant?

AGreedy algorithm sorting by value-to-weight ratio

BStandard 0/1 Knapsack DP ignoring volume

CDivide and conquer splitting items by weight only

DMulti-dimensional dynamic programming with states dp[i][w][v]

Step-by-Step Solution

Solution:

Step 1: Understand problem extension
Two constraints require tracking both weight and volume simultaneously.
Step 2: Identify suitable approach
Multi-dimensional DP with dp[i][w][v] handles both constraints but is expensive.
Step 3: Consider divide and conquer
Divide and conquer splitting by weight only ignores volume constraint, so not sufficient.
Final Answer:
Option D -> Option D
Quick Check:
Multi-constraint knapsack requires multi-dimensional DP to track all constraints [OK]

Quick Trick: Two constraints -> multi-dimensional DP

Common Mistakes:

MISTAKES

Using standard 0/1 knapsack ignoring extra constraint
Assuming greedy works with multiple constraints

Trap Explanation:

PITFALL

Candidates underestimate complexity of multi-constraint knapsack.

Interviewer Note:

CONTEXT

Tests knowledge of advanced knapsack variants and solution adaptations

Master "0/1 Knapsack Problem" in Dynamic Programming: Knapsack

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