# Questions tagged [subset-sum]

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### Divide a number in k powers of 2

Example N = 9 and K=3 4 + 4 + 1 = 9 . What I have tried. We can not go on dividing with 2. We can use unbounded knapsack with array elements from 2^0 to 2^32.
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### multiset variant of subset sum problem known algorithms

I have been working in the time analysis for an exact solver I designed for the subset sum problem accepting multisets as input instances, and determined its time complexity to be dependent on the ...
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### Finding the Range of Solutions for KSum Variation

Preface I asked a question before where I was looking to understand the complexity class of the following problem: Given a range of integers $\{a,a+1,...,b-1,b\}$, find a subset of size $k$ such ...
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### Find a partition of multiset of binomial coefficients with constriants

Given the multiset $S$ where the elements are defined by the binomial coefficient ${n \choose k}$ where $n \in \mathbb{N}$ and $0\leq k \leq n$ find the partition $P$ of $S$ such that the sum of ...
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### Reducing subset sum to even subset sum

I'm trying to learn reduction. I have this problem called "even subset sum" that's very similar to subset sum. It's the same problem as as subset sum except that the only numbers allowed are even ...
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### Subset sum problem with an extra condition [closed]

A sub-set sum problem is described that giving a set of integers $S$ and a constant $C$, find a subset $s$ of $S$ so that the sum of integers in $s$ is maximum but not greater than $C$. maximize\...
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### Proof of NP Completeness of set-partition problem

I have reduced subset sum problem to set partition problem but do not know whether it is correct and so I need your help. MY METHOD In subset sum problem we have to find a subset $S_1$ of set $S$ so ...
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### Subset sum problem, given that a valid subset exists

I have a problem at work. I need to find a subset of a set of positive integers that sums to a certain value. I know there is a subset but I need to find it. Is this new problem the same as the ...
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### Subset sum exponential solution - how does the sorting work?

The wiki for the subset sum problem found here it states that you take the list of N elements and split it into two lists of N/2 elements. You then generate all the subsets for each list (each having ...
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### How to find sets of polynomially bounded numbers whose subset sums are different?

Let $n$ be any positibe integer and set $N=\{1,\dots,n\}$. Now select two arbitrary but different subsets of $N$, say $S$ and $S'$. We are interested in finding a function $\pi(A)=\sum_{i\in A}a_i$ ...
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### Is this an $NP$-complete problem: Product-2-Partition

I want to prove the NP-hardness of my problem P in scheduling. I was trying with Partition, 3-Partition and Subset product, But neither was successful. Now, I can reduce a problem, say PRODUCT-2-...
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### Maximum Equal Sum K Subsequences

Given an array we need to find maximum equal sum $K$ subsequences, i.e. we want the sum to be maximized such that there are exactly $K$ non-overlapping subsequences each having the same sum. Example: ...
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### Find the lexicographically smallest order of N numbers such that the total of N numbers <= Threshold value

GIven a number N, Threshold T and an array A. Find the lexicographically smallest order of N numbers from A such that the total of these N numbers is <= T. This question is a simplification of ...
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### Understanding algorithm for maximum sum of non-consecutive elements

There is a well-known problem in CS of finding the maximum sum of non-consecutive integers in a list. There is even an SO post about how to solve it: https://stackoverflow.com/questions/4487438/...
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### Finding the maximum possible size of S, where S is a set of pairwise-disjoint subsets of the list, and every element of S sums to k

Say I had a list of numbers in the range of 1-20 for example: [5, 16, 17, 3, 2, 14, 4, 9, 11, 19], and an integer k (let's say k = 40) How would I find the maximum possible size of S, where S is a ...
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### Can the subset sum problem work with an undefined set?

To give a brief outline of my actual problem, I'm attempting to identify possible impurities in proteins. I have a theoretical mass and an experimental mass, and the difference between the two would ...
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### Is integer factorization reducible to subset sum?

Is it possible to solve the FACT (integer factorization) problem in polynomial time if we know the polynomial Subset Sum algorithm? We assume that we know the algorithm solving the problem of Subset ...
I need some help with the following question: Recall the subset sum problem, which is known to be NP-complete: "Given a finite set of natural numbers and a number $n$, decide whether a subset ...
I was wondering if anybody knows if there is an algorithm for Subset-sum, preferably exact, having a $O(n)$ Time Complexity or near-linear ($n$ = number of elements in the input set) I remember that ...