Dynamic Programming: Knapsack - Target Sum
Consider the same space-optimized bottom-up DP code for Target Sum. What is the output when nums = [0] and target = 0?
Consider the same space-optimized bottom-up DP code for Target Sum. What is the output when nums = [0] and target = 0?
medium🧾 Code Trace Q4 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze zero handling in dp
With nums=[0], sum=0, offset=0, dp size=1. Initially dp[0]=1.Step 2: Update dp for num=0
Adding or subtracting zero does not change sum, but both '+' and '-' count as separate ways, doubling dp[0] from 1 to 2.Final Answer:
Option A -> Option AQuick Check:
Zero doubles ways because +0 and -0 are distinct assignments [OK]
Quick Trick: Zero doubles ways since +0 and -0 differ [OK]
Common Mistakes:
MISTAKES- Ignoring zero doubling effect
- Assuming zero contributes only one way
Trap Explanation:
PITFALL- Many candidates undercount ways when zero is present, missing that sign assignments both count.
Interviewer Note:
CONTEXT- Tests edge case handling and zero value impact on DP.
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