[Solved] The following code attempts to solve the Equal Partition problem using a 1D DP array.... Which line contains a subtle bug that can cause incorrect results on some inputs? | Dynamic Programming: Knapsack

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

The following code attempts to solve the Equal Partition problem using a 1D DP array. Which line contains a subtle bug that can cause incorrect results on some inputs?

def canPartition(nums):
    total = sum(nums)
    target = total // 2
    dp = [False] * (target + 1)
    dp[0] = True

    for num in nums:
        for w in range(num, target + 1):
            dp[w] = dp[w] or dp[w - num]

    return dp[target]

ALine 2: Missing check if total is even before proceeding

BLine 4: Initializing dp array with false instead of true

CLine 6: Iterating forwards in dp array instead of backwards

DLine 8: Returning dp[target] without verifying dp array correctness

Step-by-Step Solution

Solution:

Step 1: Identify missing even check
Line 2 does not check if total is even, but this causes no incorrect dp updates, only wasted computation.
Step 2: Analyze dp iteration direction
Line 6 iterates forwards, which causes reuse of updated dp values in the same iteration, leading to counting elements multiple times and incorrect results.
Final Answer:
Option C -> Option C
Quick Check:
Backward iteration is required to avoid reusing updated dp values in the same iteration [OK]

Quick Trick: DP must iterate backwards to avoid reuse in 1D array [OK]

Common Mistakes:

MISTAKES

Iterating forwards in dp updates
Skipping even sum check

Trap Explanation:

PITFALL

Forwards iteration looks natural but breaks 0/1 knapsack logic by reusing updated states

Interviewer Note:

CONTEXT

Checks if candidate knows subtle DP update order bugs that cause wrong answers

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More Dynamic Programming: Knapsack Quizzes

The following code attempts to solve the Equal Partition problem using a 1D DP array. Which line contains a subtle bug that can cause incorrect results on some inputs?

Step 1: Identify missing even check

Step 2: Analyze dp iteration direction

Final Answer:

Quick Check:

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