The Subset Sum Problem Solved in Linear Time for Dense Enough Inputs

The Subset Sum Problem (SSP) is an NP-complete problem that asks if a subset of given integers sums up to a specific target value. While brute-force solutions are exponential, a common approach uses dynamic programming, which is a pseudo-polynomial algorithm. This content introduces a new "Interval-based solution" algorithm designed to solve the SSP. This new algorithm achieves linear time complexity, O(n), provided that the input values are sufficiently close to each other, a condition referred to as being "dense enough."