Given the final dp table row for m=3 zeros and n=3 ones as follows (dp[3][0..3]): [0, 1, 1, 2], which of the following sets of strings could have produced this dp state?

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

Given the final dp table row for m=3 zeros and n=3 ones as follows (dp[3][0..3]): [0, 1, 1, 2], which of the following sets of strings could have produced this dp state? Strings: 1) "10" 2) "000" 3) "11" 4) "0"

A["000", "11"]

B["10", "000"]

C["10", "0"]

D["11", "0"]

Step-by-Step Solution

Solution:

Step 1: Analyze dp[3][j] values
dp[3][1]=1 and dp[3][3]=2 means with 3 zeros and 3 ones, max 2 strings chosen.
Step 2: Check which strings fit constraints and count
"10" (1 zero,1 one) and "0" (1 zero,0 ones) fit within 3 zeros and 3 ones and total 2 strings.
Final Answer:
Option C -> Option C
Quick Check:
Strings "10" and "0" produce dp values matching given row [OK]

Quick Trick: Match dp values with string zero/one counts [OK]

Common Mistakes:

MISTAKES

Ignoring zeros and ones counts
Assuming strings with more zeros fit

Trap Explanation:

PITFALL

Candidates often pick strings exceeding zero/one limits or misinterpret dp values.

Interviewer Note:

CONTEXT

Tests deep understanding of dp state and input relation.

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More Dynamic Programming: Knapsack Quizzes

Given the final dp table row for m=3 zeros and n=3 ones as follows (dp[3][0..3]): [0, 1, 1, 2], which of the following sets of strings could have produced this dp state?

Step 1: Analyze dp[3][j] values

Step 2: Check which strings fit constraints and count

Final Answer:

Quick Check:

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