Dsa Dp Knapsack Unbounded

In this tutorial, you'll learn about How to Fix Unbounded Knapsack Errors. We cover key concepts, practical examples, and best practices.

Fix unbounded knapsack errors when forward vs backward capacity loop confusion with 0/1.

Quick Fix

Wrong

def uk(weights,vals,W):
    dp=[0]*(W+1)
    for i in range(len(weights)):
        for w in range(W,weights[i]-1,-1):  # 0/1 backward, wrong for unbounded!
            dp[w]=max(dp[w], vals[i]+dp[w-weights[i]])
    return dp[W]

Backward loop treats items as 0/1. Don't allow multiple uses.

Right

def uk(weights,vals,W):
    dp=[0]*(W+1)
    for w in range(1,W+1):
        for i in range(len(weights)):
            if weights[i]<=w:
                dp[w]=max(dp[w], vals[i]+dp[w-weights[i]])
    return dp[W]

weights=[1,3,4,5], vals=[1,4,5,7], W=7 -> 13 (four 1+one 3 items).

Prevention

For unbounded, iterate capacity forwards. Each item can be used multiple times.

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