If the Ones and Zeroes problem is changed so that each binary string can be selected unlimited times, which modification to the bottom-up dynamic programming solution is required to correctly solve this variant?

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

AUpdate the DP table in increasing order of zeros and ones to allow multiple counts

BUse a top-down memoization approach instead of bottom-up

CSort strings by length before processing

DInitialize the DP table with negative infinity values

Step-by-Step Solution

Solution:

Step 1: Understand the change
Allowing unlimited usage of each string converts the problem to an unbounded knapsack variant.
Step 2: Identify DP update order
For unbounded knapsack, the DP table must be updated in increasing order of resource constraints to reuse items multiple times.
Step 3: Apply correct DP iteration
Iterate zeros from 0 to m and ones from 0 to n, updating dp[i][j] by considering current string multiple times.
Final Answer:
Option A -> Option A
Quick Check:
Unbounded knapsack requires forward DP iteration [OK]

Quick Trick: Unbounded knapsack needs forward DP iteration [OK]

Common Mistakes:

MISTAKES

Using backward iteration which suits 0/1 knapsack only
Switching to top-down unnecessarily
Incorrect DP initialization causing wrong results

Trap Explanation:

PITFALL

Backward iteration is correct for 0/1 knapsack but fails for unbounded usage.

Interviewer Note:

CONTEXT

Tests knowledge of adapting DP solutions for unbounded knapsack variants.

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More Dynamic Programming: Knapsack Quizzes

If the Ones and Zeroes problem is changed so that each binary string can be selected unlimited times, which modification to the bottom-up dynamic programming solution is required to correctly solve this variant?

Step 1: Understand the change

Step 2: Identify DP update order

Step 3: Apply correct DP iteration

Final Answer:

Quick Check:

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