The Subset Sum Calculator is used to solve the classic Subset Sum Problem. It efficiently helps users find all combinations of elements (i.e., subsets) from a given set of numbers, such that the sum of all numbers within that subset precisely equals a pre-set target value.
The Subset Sum Calculator addresses a decision problem or an optimization problem. It does not have a single “mathematical formula” like an algebraic equation.Instead, it is defined and solved based on mathematical definitions and algorithmic logic.
The goal of the Subset Sum problem is: given a set $S$ , and a target value $T$, determine whether there exists a subset S'⊆Ssuch that the sum of all elements in S'equals $T$
Given:
a set (or list) of numbers S = \{x_1, x_2, \dots, x_n\}
a target value $T$
The goal is to find all subsets S\' \subseteq Sthat satisfy the following condition:
$$\sum_{x_i \in S\'} x_i = T$$
子集求和计算器（Subset Sum Calculator）解决的是一个决策问题 (Decision Problem) 或优化问题 (Optimization Problem)，它本身没有一个像代数方程那样的单一“数学公式”。相反，它是基于数学定义和算法逻辑来描述的。
子集求和问题的数学定义:
子集和问题的目标是：给定一个集合$S$， 和一个目标值$T$， 确定是否存在一个子集$S'⊆S$， 使得S'中所有元素的和等于$T$
给定:
1.一个候选数字集合 S = \{x_1, x_2, \dots, x_n\}
2.一个目标值 $T$
目的是找出所有子集 $S\' \subseteq S$ 满足下面的条件:
$$\sum_{x_i \in S\'} x_i = T$$