Given a list of binary strings and two integers m and n representing the maximum allowed zeros and ones respectively, which approach is most suitable to find the maximum number of strings that can be selected without exceeding these limits?

easy💻 Programming Q1 of Q15

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

Given a list of binary strings and two integers m and n representing the maximum allowed zeros and ones respectively, which approach is most suitable to find the maximum number of strings that can be selected without exceeding these limits?

AGreedy algorithm sorting strings by length

BDynamic programming using a 2D knapsack approach

CDepth-first search with backtracking only

DSorting strings by number of zeros and picking the first <code>m</code>

Step-by-Step Solution

Solution:

Step 1: Identify problem constraints
The problem limits the total zeros and ones used, which are two separate constraints.
Step 2: Recognize problem type
This is a variation of the 2D knapsack problem where each item (string) has two weights (zeros and ones).
Step 3: Choose algorithmic pattern
Dynamic programming with a 2D DP table indexed by zeros and ones counts is the optimal approach.
Final Answer:
Option B -> Option B
Quick Check:
Two constraints imply 2D knapsack DP [OK]

Quick Trick: Two constraints require 2D knapsack DP [OK]

Common Mistakes:

MISTAKES

Assuming greedy approach works for multiple constraints
Ignoring the two-dimensional nature of the problem
Using DFS without memoization leading to inefficiency

Trap Explanation:

PITFALL

Greedy or single constraint knapsack approaches ignore the dual constraints and fail.

Interviewer Note:

CONTEXT

Tests understanding of problem classification and appropriate algorithmic pattern.

Master "Ones and Zeroes (2D Knapsack)" in Dynamic Programming: Knapsack

3 interactive learning modes - each teaches the same concept differently

Try It Solution Trace

Want More Practice?

15+ quiz questions · All difficulty levels · Free

Free Signup - Practice All Questions

More Dynamic Programming: Knapsack Quizzes

Given a list of binary strings and two integers m and n representing the maximum allowed zeros and ones respectively, which approach is most suitable to find the maximum number of strings that can be selected without exceeding these limits?

Step 1: Identify problem constraints

Step 2: Recognize problem type

Step 3: Choose algorithmic pattern

Final Answer:

Quick Check:

Want More Practice?