Dsa Dp Subset Sum

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

Fix subset sum errors when initialization as 0 when first element weight not set correctly.

Quick Fix

Wrong

def ss(nums,target):
    dp=[[False]*(target+1) for _ in range(len(nums)+1)]
    for i in range(len(nums)+1): dp[i][0]=True
    for i in range(1,len(nums)+1):
        for j in range(1,target+1):
            if nums[i-1]<=j: dp[i][j]=dp[i-1][j] or dp[i-1][j-nums[i-1]]
            else: dp[i][j]=dp[i-1][j]
    return dp[len(nums)][target]

Correct O(n*target). 1D optimization: reverse loop.

Right

def ss(nums,target):
    dp=[False]*(target+1); dp[0]=True
    for n in nums:
        for j in range(target,n-1,-1):
            if dp[j-n]: dp[j]=True
    return dp[target]

nums=[1,5,11,5], target=11 -> True (subsets [1,5,5] and [11] both sum to 11 if only one needed). Actually nums=[1,5,5,11], target=11 -> True. O(n*target).

Prevention

1D DP reverse loop for each number. dp[j] = dp[j] or dp[j-n] where dp[j-n] is from previous row.

DodaTech Tools

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FAQ