[Solved] You are given an array of positive integers and a number k. The task is to determine if the array can be partitioned... Which algorithmic approach guarantees an optimal solution for this problem? | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Partition to K Equal Sum Subsets

You are given an array of positive integers and a number k. The task is to determine if the array can be partitioned into k subsets such that the sum of elements in each subset is equal. Which algorithmic approach guarantees an optimal solution for this problem?

AGreedy algorithm that repeatedly picks the largest element and tries to fit it into subsets

BDynamic programming with bitmask tabulation that tracks subset sums for all combinations

CSimple backtracking without memoization that tries all possible assignments

DSorting the array and using a two-pointer technique to pair elements

Step-by-Step Solution

Step 1: Understand problem constraints
The problem requires partitioning into equal sum subsets, which is a classic NP-complete problem requiring exploration of subsets.
Step 2: Identify algorithmic pattern
Dynamic programming with bitmask tabulation efficiently explores all subsets and tracks partial sums modulo target, guaranteeing optimality.
Final Answer:
Option B -> Option B
Quick Check:
Bitmask DP covers all subsets systematically [OK]

Quick Trick: Bitmask DP tracks all subset sums efficiently [OK]

Common Mistakes:

MISTAKES

Assuming greedy always works for equal sum partition
Using backtracking without memoization leads to timeouts

Trap Explanation:

PITFALL

Greedy and simple backtracking seem intuitive but fail on complex distributions; bitmask DP is less obvious but correct.

Interviewer Note:

CONTEXT

Tests if candidate can recognize the correct pattern beyond naive or greedy approaches.

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Which algorithmic approach guarantees an optimal solution for this problem?

Step 1: Understand problem constraints

Step 2: Identify algorithmic pattern

Final Answer:

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