Dynamic Programming: Knapsack - Perfect Squares
Given the following partial dp array for the Perfect Squares problem: dp = [0,1,2,3,1,2,3,4,2,3,4,5,3], what is the original input
n for which this dp was computed?Given the following partial dp array for the Perfect Squares problem: dp = [0,1,2,3,1,2,3,4,2,3,4,5,3], what is the original input n for which this dp was computed?
hard🔄 Reverse Engineer Q9 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand dp array meaning
dp[i] stores minimal number of perfect squares summing to i.Step 2: Identify dp length
dp length is 13, so last index is 12, meaning dp computed up to n=12.Step 3: Confirm dp[12] value
dp[12] = 3 matches known minimal count for 12 (4+4+4).Final Answer:
Option C -> Option CQuick Check:
dp array length - 1 = n -> 12 [OK]
Quick Trick: dp array length minus one equals n [OK]
Common Mistakes:
MISTAKES- Misreading dp length
- Confusing dp indices with values
- Assuming dp stores sums not counts
Trap Explanation:
PITFALL- Candidates often confuse dp array length with n or misinterpret dp meaning.
Interviewer Note:
CONTEXT- Tests ability to reverse engineer input from DP state
Master "Perfect Squares" in Dynamic Programming: Knapsack
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