Dynamic Programming for the Subset Sum Problem

The subset sum problem is a basic problem in the field of theoretical computer science, especially in the complexity theory [3]. The input is a sequence of positive integers and a target positive integer. The task is to determine if there exists a subsequence of the input sequence with sum equal to the target integer. It is known that the problem is NP-hard [2] and can be solved by dynamic programming in pseudo-polynomial time [1]. In this article we formalize the recurrence relation of the dynamic programming.