Given the following partial memo dictionary from a top-down DP solution for Target Sum: {(3, 2): 3, (4, 3): 5, (5, 1): 2} and knowing the input array length is 5, which of the following input arrays and target sums could produce this memo state?

hard🔄 Reverse Engineer Q9 of Q15

Dynamic Programming: Knapsack - Target Sum

Anums = [1, 2, 1, 1, 1], target = 3

Bnums = [1, 1, 1, 1, 1], target = 3

Cnums = [2, 2, 1, 1, 1], target = 4

Dnums = [1, 1, 2, 2, 1], target = 2

Step-by-Step Solution

Solution:

Step 1: Interpret memo keys
Memo keys (i, current_sum) represent number of ways to reach current_sum at index i.
Step 2: Match known example
The memo entries correspond to the classic example nums=[1,1,1,1,1], target=3, where dp counts match these values.
Final Answer:
Option B -> Option B
Quick Check:
Memo matches known counts for all ones and target 3 [OK]

Quick Trick: Memo keys match index and sum states for classic example [OK]

Common Mistakes:

MISTAKES

Ignoring index in memo keys
Assuming arbitrary arrays without verifying counts

Trap Explanation:

PITFALL

Candidates often overlook that memo keys include index and sum, not just sums.

Interviewer Note:

CONTEXT

Tests deep understanding of DP state representation and memoization.

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More Dynamic Programming: Knapsack Quizzes

Given the following partial memo dictionary from a top-down DP solution for Target Sum: {(3, 2): 3, (4, 3): 5, (5, 1): 2} and knowing the input array length is 5, which of the following input arrays and target sums could produce this memo state?

Step 1: Interpret memo keys

Step 2: Match known example

Final Answer:

Quick Check:

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