Dynamic Programming: Knapsack - Perfect Squares
Given the following bottom-up DP code for the Perfect Squares problem, what is the output of
numSquares(12)?Given the following bottom-up DP code for the Perfect Squares problem, what is the output of numSquares(12)?
easy🧾 Code Trace Q3 of Q15
Step-by-Step Solution
Solution:
Step 1: Trace dp array for i=12
Check squares ≤12: 1,4,9. dp[12] = min(dp[12], 1+dp[11], 1+dp[8], 1+dp[3])Step 2: Use known dp values
dp[3]=3 (1+1+1), dp[8]=2 (4+4), dp[11]=3 (9+1+1). So dp[12] = min(inf,4,3,4) = 3.Final Answer:
Option B -> Option BQuick Check:
Optimal count for 12 is 3 (4+4+4) [OK]
Quick Trick: Check dp for 12 using squares 1,4,9 -> minimal count 3 [OK]
Common Mistakes:
MISTAKES- Miscounting dp values for subproblems
- Assuming greedy picks 9 then 3 ones = 4
- Off-by-one errors in loops
Trap Explanation:
PITFALL- Candidates often pick 4 due to greedy thinking largest square first.
Interviewer Note:
CONTEXT- Tests ability to mentally execute DP code and understand minimal count calculation
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