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Consider the following code snippet implementing the optimal solution for the problem. Given the input strs = ["10", "0", "1"], m = 1, and n = 1, what is the final returned value?

easy🧾 Code Trace Q12 of Q15

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

Consider the following code snippet implementing the optimal solution for the problem. Given the input strs = ["10", "0", "1"], m = 1, and n = 1, what is the final returned value?

A2

B3

C1

D0

Step-by-Step Solution

Solution:

Step 1: Trace dp updates for "10" (zeros=1, ones=1)
dp[1][1] = max(dp[1][1], 1 + dp[0][0]) = 1
Step 2: Trace dp updates for "0" (zeros=1, ones=0) and "1" (zeros=0, ones=1)
After "0": dp[1][1] = max(1, 1 + dp[0][1]) = 1; After "1": dp[1][1] = max(1, 1 + dp[1][0]) = 1; Combining subsets "0" and "1" fits within limits, so dp[1][1] = 2
Final Answer:
Option A -> Option A
Quick Check:
Maximum subset size fitting m=1,n=1 is 2 [OK]

Quick Trick: Trace dp from largest capacity down to zero [OK]

Common Mistakes:

MISTAKES

Counting subsets incorrectly
Forgetting to iterate dp backwards

Trap Explanation:

PITFALL

Forward iteration would double count strings, leading to wrong dp values.

Interviewer Note:

CONTEXT

Tests candidate's ability to mentally execute nested loops and dp updates.

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