Dynamic Programming: Knapsack - Target Sum
Given the following code snippet implementing the space-optimized bottom-up DP for Target Sum, what is the output for nums = [1, 1, 1, 1, 1] and target = 3?
Given the following code snippet implementing the space-optimized bottom-up DP for Target Sum, what is the output for nums = [1, 1, 1, 1, 1] and target = 3?
easy🧾 Code Trace Q3 of Q15
Step-by-Step Solution
Solution:
Step 1: Trace dp array updates
Initial dp[offset]=1 means sum=0 has 1 way. Each 1 adds ways to sums ±1 from previous sums.Step 2: Calculate ways to reach target=3
For 5 ones, number of ways to get sum=3 is known to be 5 (combinatorial count of sign assignments).Final Answer:
Option A -> Option AQuick Check:
Classic example output for Target Sum with 5 ones and target 3 is 5 [OK]
Quick Trick: Classic example: 5 ones, target 3 -> 5 ways [OK]
Common Mistakes:
MISTAKES- Off-by-one in indexing dp
- Confusing sum with target offset
Trap Explanation:
PITFALL- Candidates often miscalculate offset or forget to check dp boundaries, leading to wrong counts.
Interviewer Note:
CONTEXT- Tests ability to mentally execute DP code and understand indexing.
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