Dynamic Programming: Knapsack - Integer Break
Given the dp array after computing integer break for n=5 as dp = [0,1,1,2,4,6], which of the following splits of 5 corresponds to the maximum product dp[5] = 6?
Given the dp array after computing integer break for n=5 as dp = [0,1,1,2,4,6], which of the following splits of 5 corresponds to the maximum product dp[5] = 6?
hard🔄 Reverse Engineer Q9 of Q15
Step-by-Step Solution
Solution:
Step 1: Check dp values for parts
dp[2]=1, dp[3]=2, dp[4]=4, dp[1]=1Step 2: Verify splits for dp[5]=6
Split 2+3: max(2,dp[2]) * max(3,dp[3])=2*3=6 (matches dp[5]); Split 1+4: 1*4=4; Split 3+3 invalid as sum > 5; Split 2+2+1 not direct split in dp.Final Answer:
Option B -> Option BQuick Check:
dp[5]=6 corresponds to split 2+3 product 6 [OK]
Quick Trick: dp[i] = max product from splits using dp values [OK]
Common Mistakes:
MISTAKES- Assuming 3+3 split for 5
- Ignoring max(j, dp[j]) usage
Trap Explanation:
PITFALL- Candidates confuse splits exceeding n or ignore dp max usage.
Interviewer Note:
CONTEXT- Tests ability to reason backwards from dp table to input splits
Master "Integer Break" in Dynamic Programming: Knapsack
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