Abstract: Given a multiset of n positive integers and a target sum S, the subset sum problem is to find a subset such that the sum of its elements is as close as possible to S without exceeding S. We ...

Bio-inspired computational methods have gained popularity recently. These methods mimic the seemingly complex behavior of organisms to tackle difficult and often overwhelming problems. For example, ...

Researchers have successfully used a quantum algorithm to solve a complex century-old mathematical problem long considered impossible for even the most powerful conventional supercomputers. The ...

Using an advanced Monte Carlo method, Caltech researchers found a way to tame the infinite complexity of Feynman diagrams and solve the long-standing polaron problem, unlocking deeper understanding of ...

When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works. Breaking space news, the latest updates on rocket launches, skywatching events and more! You are ...

John Peterson does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...

A new proof illuminates the hidden patterns that emerge when addition becomes impossible. The simplest ideas in mathematics can also be the most perplexing. Take addition. It’s a straightforward ...

The original version of this story appeared in Quanta Magazine. For computer scientists, solving problems is a bit like mountaineering. First they must choose a problem to solve—akin to identifying a ...

Take the number of elements n and the list of n integers as input, followed by the target sum x. Use combinations from the itertools library to generate all possible subsets of the list. For each ...