Dsa Dp Knapsack 01

In this tutorial, you'll learn about How to Fix 0/1 Knapsack Errors. We cover key concepts, practical examples, and best practices.

Fix 0/1 knapsack errors when capacity loop goes wrong direction (unbounded instead of 0/1).

Quick Fix

Wrong

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

Correct O(nW). But 1D space optimization requires reverse W loop.

Right

def ks(weights,vals,W):
    dp=[0]*(W+1)
    for i in range(len(weights)):
        for w in range(W,weights[i]-1,-1):
            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 -> 9 (items 1+4). O(nW) time, O(W) space.

Prevention

For 0/1 knapsack, iterate capacity backwards to avoid reusing items. 1D array.

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