Dynamic Programming: Knapsack - Target Sum
In the bottom-up DP solution for the Target Sum problem, which of the following modifications is necessary to correctly handle arrays containing zero values?
In the bottom-up DP solution for the Target Sum problem, which of the following modifications is necessary to correctly handle arrays containing zero values?
medium⬆️ Bottom-up DP Q7 of Q15
Step-by-Step Solution
Solution:
Step 1: Initialize DP array
Set dp[offset] = 1 to represent one way to reach sum zero before processing any numbers.Step 2: Process each number including zeros
For each number, update dp by adding ways to reach sums with +num and -num.Step 3: Handle zeros correctly
Since zero can be assigned + or -, it doubles the count of ways for the same sum, so dp values must be doubled when zero is encountered.Final Answer:
Option C -> Option CQuick Check:
Zero values double ways by doubling dp counts [OK]
Quick Trick: Zero values double ways by doubling dp counts [OK]
Common Mistakes:
MISTAKES- Ignoring zero doubling effect
- Assuming zero contributes only one way
- Incorrectly skipping zero updates
Trap Explanation:
PITFALL- Skipping zero doubling or mishandling zeros causes wrong counts.
Interviewer Note:
CONTEXT- Tests understanding of zero handling in DP.
Master "Target Sum" in Dynamic Programming: Knapsack
Want More Practice?
15+ quiz questions · All difficulty levels · Free
Free Signup - Practice All QuestionsMore Dynamic Programming: Knapsack Quizzes