Grokking the Coding Interview: Patterns for Coding Questions
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Solution: Minimum Subset Sum Difference

Problem Statement

Given a set of positive numbers, partition the set into two subsets with minimum difference between their subset sums.

Example 1:

Input: {1, 2, 3, 9}
Output: 3
Explanation: We can partition the given set into two subsets where minimum absolute difference 
between the sum of numbers is '3'. Following are the two subsets: {1, 2, 3} & {9}.

Example 2:

Input: {1, 2, 7, 1, 5}
Output: 0
Explanation: We can partition the given set into two subsets where minimum absolute difference 
between the sum of number is '0'

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Naresh Ch

· 4 years ago

would some version of knapsack solution still apply if the set contained negative numbers?

Would be really helpful if negative numbers solution was also discussed here.

Thanks!

Show 1 reply
J

J

· 4 years ago

Bottom-up DP solution fails test case [53,54,3,61,67] for LC 1049. Last Stone Weight II https://leetcode.com/problems/last-stone-weight-ii/description/

Zac Bolton

Zac Bolton

· a year ago

The initialization for the first row in the bottom up DP approach is:

    # with only one number, we can form a subset only when the required sum is equal to 

    # that number

    for j in range(0, int(s/2)+1):

      dp[0][j] = num[0] == j

However this is wrong and could cause compounding wrong answers resulting in an incorrect output.

The issue is that it overwrites the dp[0][0] cell to False, when it should be true. The fix is to start the for loop at 1, instead of 0.

    for j in range(1, int(s/2)+1):

      dp[0][j] = num[0] == j