Welcome to the Combination Sum Calculator! This tool is designed to tackle complex number combination problems with ease. Simply enter your full set of numbers in the first text field, type your target sum in the second field, and click the “Calculate” button to see the results. It goes beyond traditional calculators and online tools, handling challenges like floating-point precision and combinations that include negative numbers with ease.
The Combination Sum Calculator is a powerful tool designed to efficiently and accurately solve complex number combination problems. Its core function is to find all possible combinations of numbers from a given set that add up to a specified target sum. Unlike traditional calculators or basic online tools, this calculator can handle large sets of numbers, floating-point values, and even negative numbers—situations that often cause precision issues in standard calculations.
Using the tool is simple: enter your full set of numbers and the target sum, then let the calculator find all valid combinations. For example:
1.With the number set [2, 3, 5, 7] and a target sum of 10, it will identify [3, 7] and [2, 3, 5] as valid combinations.
2.If the set contains floating-point numbers, like [1.5, 2.5, 3.5] with a target of 5.0, it can accurately detect [1.5, 3.5], avoiding common floating-point precision issues.
3.For sets including negative numbers, such as [5, -2, 7, 3] with a target of 5, it can find [5] and [7, -2] among the possible combinations.
By automating what would otherwise be tedious manual calculations, the Combination Sum Calculator saves time and ensures accuracy. It’s an essential tool for students, engineers, data analysts, or anyone working with numerical data and combinatorial problems.
The Combination Sum Calculator addresses a problem that is similar to the Subset Sum Problem, but with a crucial distinction: elements from the candidate set can be reused an unlimited number of times.
Given:
1.A set of distinct numeric candidates (real numbers, including negatives and decimals)
$C = \{c_1, c_2, \dots, c_n\}$
2.A target sum $T$ (which can also be any real number).
Objective: To find all unique integer vectors
$\mathbf{k} = (k_1, k_2, \dots, k_n)$
that satisfy the following equation:
$$\sum_{i=1}^{n} k_i \cdot c_i = T$$
Subject to the constraint:
$$k_i \ge 0 \quad \text{and } k_i \in \mathbb{Z}$$
Where:
1.$c_i$: The $i$-th numeric candidate in the set $C$. (This value can be any real number.)
2.$k_i$: The frequency (the number of times) the candidate $c_i$ is used in the resulting combination. ($k_i$ must be a non-negative integer).
3.$T$: The target sum (a real number).
Note on Uniqueness: Two combinations are considered unique if the frequency ($k_i$) of at least one candidate number ($c_i$) is different between them.