[Solved] Consider the following Python code for the Equal Partition problem.... What is the value of dp[target] after processing the input [1, 5, 11, 5]? | Dynamic Programming: Knapsack

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

Consider the following Python code for the Equal Partition problem. What is the value of dp[target] after processing the input [1, 5, 11, 5]?

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

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

    return dp[target]

print(canPartition([1,5,11,5]))

Atrue

Bfalse

Cnull (error occurs)

DDepends on order of iteration

Step-by-Step Solution

Solution:

Step 1: Calculate total and target
The total sum is 1 + 5 + 11 + 5 = 22, which is even, so target = 11.
Step 2: Trace dp array updates for each num
After processing all nums, dp[11] becomes True because subset {11} or {5,5,1} sums to 11.
Final Answer:
Option A -> Option A
Quick Check:
Input is classic example where partition exists; dp[target] is True [OK]

Quick Trick: Sum is even and dp[target] tracks subset sums [OK]

Common Mistakes:

MISTAKES

Confusing dp[target] with dp[target-1]
Forgetting to iterate backwards in dp update

Trap Explanation:

PITFALL

Some think dp[target] remains false due to off-by-one or forward iteration errors

Interviewer Note:

CONTEXT

Checks candidate's ability to mentally execute DP code and understand dp array meaning

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More Dynamic Programming: Knapsack Quizzes

Consider the following Python code for the Equal Partition problem. What is the value of dp[target] after processing the input [1, 5, 11, 5]?

Step 1: Calculate total and target

Step 2: Trace dp array updates for each num

Final Answer:

Quick Check:

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