[Solved] Examine the following Python code snippet for a space-optimized 0/1 Knapsack implementation. Identify the bug that causes incorrect results:def knapsack_bug(weights, values, W):... | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - 0/1 Knapsack Problem

Examine the following Python code snippet for a space-optimized 0/1 Knapsack implementation. Identify the bug that causes incorrect results:

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

AThe dp array should be initialized with -1 instead of 0

BThe inner loop should iterate backwards from W down to weights[i]

CThe outer loop should iterate over weights instead of items

DThe function should return dp[0] instead of dp[W]

Step-by-Step Solution

Solution:

Step 1: Understand DP update dependency
In space-optimized 0/1 Knapsack, dp[w] depends on dp[w - weights[i]] from previous iteration.
Step 2: Identify loop direction
Iterating forwards overwrites dp values needed for future computations, causing incorrect results.
Step 3: Correct loop direction
Iterate backwards from W down to weights[i] to preserve previous state during updates.
Final Answer:
Option B -> Option B
Quick Check:
Forward iteration corrupts dp state [OK]

Quick Trick: Iterate backwards in dp array to avoid overwriting [OK]

Common Mistakes:

MISTAKES

Iterating forwards in dp array causing state corruption
Incorrect dp initialization values
Returning wrong dp index

Trap Explanation:

PITFALL

Forward iteration overwrites dp states needed for correct calculation.

Interviewer Note:

CONTEXT

Tests understanding of correct iteration order in space-optimized 0/1 Knapsack.

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More Dynamic Programming: Knapsack Quizzes

Examine the following Python code snippet for a space-optimized 0/1 Knapsack implementation. Identify the bug that causes incorrect results:

Step 1: Understand DP update dependency

Step 2: Identify loop direction

Step 3: Correct loop direction

Final Answer:

Quick Check:

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