[Solved] You are given a list of binary strings and two integers representing the maximum number of zeros and ones you can... Which algorithmic approach guarantees finding the optimal solution efficiently? | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Ones and Zeroes (2D Knapsack)

You are given a list of binary strings and two integers representing the maximum number of zeros and ones you can use. You want to find the largest subset of these strings such that the total zeros and ones in the subset do not exceed the given limits. Which algorithmic approach guarantees finding the optimal solution efficiently?

AA greedy algorithm that picks strings with the smallest length first

BA graph traversal algorithm that finds the shortest path covering all strings

CA simple recursion that tries all subsets without memoization

DA dynamic programming approach that uses a 2D state representing zeros and ones capacity

Step-by-Step Solution

Solution:

Step 1: Understand problem constraints
The problem requires selecting a subset of strings constrained by two resources: zeros and ones counts.
Step 2: Identify suitable algorithm
Dynamic programming with a 2D state (zeros and ones) efficiently explores all feasible subsets and ensures optimality.
Final Answer:
Option D -> Option D
Quick Check:
DP with 2D state matches problem constraints [OK]

Quick Trick: Two resource constraints -> 2D DP knapsack [OK]

Common Mistakes:

MISTAKES

Assuming greedy works for multi-constraint knapsack
Ignoring one resource dimension in DP

Trap Explanation:

PITFALL

Greedy looks simpler but fails because it doesn't consider both zero and one constraints simultaneously.

Interviewer Note:

CONTEXT

Tests if candidate can recognize multi-dimensional knapsack pattern from problem description.

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More Dynamic Programming: Knapsack Quizzes

Which algorithmic approach guarantees finding the optimal solution efficiently?

Step 1: Understand problem constraints

Step 2: Identify suitable algorithm

Final Answer:

Quick Check:

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