[Solved] The following code attempts to implement the space-optimized 0/1 Knapsack solution.... Identify the line that contains a subtle bug that can cause incorrect results. | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - 0/1 Knapsack Problem

The following code attempts to implement the space-optimized 0/1 Knapsack solution. Identify the line that contains a subtle bug that can cause incorrect results.

def knapsack_space_optimized(weights, values, W):
    n = len(weights)
    dp = [0] * (W + 1)
    for i in range(n):
        for w in range(weights[i], W + 1):  # Note: iterating forwards
            dp[w] = max(dp[w], dp[w - weights[i]] + values[i])
    return dp[W]

ALine 5: Inner loop iterating forwards over weights.

BLine 4: Outer loop iterating over items.

CLine 2: Initializing dp array with zeros.

DLine 6: Updating dp[w] with max of current and new value.

Step-by-Step Solution

Solution:

Step 1: Analyze iteration order in inner loop
The inner loop iterates forwards from weights[i] to W, which causes the current item to be counted multiple times in the same iteration, violating 0/1 knapsack constraints.
Step 2: Correct iteration direction
Iterating backwards (from W down to weights[i]) ensures each item is only counted once per capacity, preserving correctness.
Final Answer:
Option A -> Option A
Quick Check:
Forward iteration causes overcounting items [OK]

Quick Trick: Inner loop must iterate backwards to avoid overcounting [OK]

Common Mistakes:

MISTAKES

Iterating forwards in dp array updates for 0/1 knapsack.

Trap Explanation:

PITFALL

Forward iteration looks natural but breaks the 0/1 constraint by reusing updated dp values in the same iteration.

Interviewer Note:

CONTEXT

Tests if candidate knows subtle iteration order requirement in space-optimized DP.

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More Dynamic Programming: Knapsack Quizzes

The following code attempts to implement the space-optimized 0/1 Knapsack solution. Identify the line that contains a subtle bug that can cause incorrect results.

Step 1: Analyze iteration order in inner loop

Step 2: Correct iteration direction

Final Answer:

Quick Check:

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