[Solved] If the Equal Partition problem is modified so that each element can be chosen multiple times to form subsets, which dynamic programming approach correctly solves this variant? | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Equal Partition (Partition Equal Subset Sum)

If the Equal Partition problem is modified so that each element can be chosen multiple times to form subsets, which dynamic programming approach correctly solves this variant?

AUse a 1D DP array with forward iteration over sums

BUse a 1D DP array with backward iteration over sums

CUse a 2D DP array with memoization and no iteration order change

DUse a greedy approach with sorting

Step-by-Step Solution

Solution:

Step 1: Understand the variant
Allowing unlimited use of elements changes the subset sum to an unbounded knapsack variant.
Step 2: Identify DP iteration order
For unlimited usage, iterate sums forward to allow multiple counts of the same element.
Step 3: Contrast with original problem
Original problem uses backward iteration to avoid reuse; here forward iteration is needed.
Final Answer:
Option A -> Option A
Quick Check:
Unbounded knapsack uses forward iteration [OK]

Quick Trick: Forward iteration allows multiple uses; backward prevents reuse [OK]

Common Mistakes:

MISTAKES

Using backward iteration which disallows multiple uses
Trying greedy which fails for subset sums
Confusing bounded and unbounded knapsack DP

Trap Explanation:

PITFALL

Backward iteration looks similar but prevents multiple element usage.

Interviewer Note:

CONTEXT

Tests understanding of DP iteration order for bounded vs unbounded subset sum.

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More Dynamic Programming: Knapsack Quizzes

If the Equal Partition problem is modified so that each element can be chosen multiple times to form subsets, which dynamic programming approach correctly solves this variant?

Step 1: Understand the variant

Step 2: Identify DP iteration order

Step 3: Contrast with original problem

Final Answer:

Quick Check:

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