Financial Analyst & Algorithm Specialist
Find all unique combinations of numbers that sum up to a specific target value. This combination sum calculator is an essential tool for budgeting, inventory planning, and solving complex mathematical subset problems.
Combination Sum Calculator
Combination Sum Calculator Formula
The calculation uses a recursive backtracking algorithm to solve for $X$:
$$Target = \sum_{i=1}^{n} (C_i \times k_i)$$
Where $C_i$ is the candidate number and $k_i$ is the frequency of that number in the combination.
Variables:
- Target Sum (T): The total value you want the subset of numbers to add up to.
- Candidates (C): The pool of numbers available to be chosen for the combination.
- Repetition: Whether a single number from the pool can be used multiple times to reach the target.
Related Calculators
What is Combination Sum Calculator?
A combination sum calculator is a specialized mathematical tool designed to find sets of numbers from a given list that, when added together, equal a specific target sum. This problem is a variation of the “Knapsack Problem” and the “Subset Sum Problem,” which are foundational in computer science and financial optimization.
Professionals use this logic for various tasks, such as matching invoices to total payments, optimizing manufacturing cut lengths, or determining which product bundles fit within a client’s budget constraints.
How to Calculate Combination Sum (Example)
- Identify Target: Let’s say your target sum is 8.
- List Candidates: Your available numbers are 2, 3, and 5.
- Iterate Combinations:
- Try 2: [2, 2, 2, 2] = 8 (Valid)
- Try 2 & 3: [2, 3, 3] = 8 (Valid)
- Try 3 & 5: [3, 5] = 8 (Valid)
- Verify: Ensure no other unique combinations exist within the constraints.
Frequently Asked Questions (FAQ)
What is the difference between combination sum and subset sum? Combination sum usually allows for the repetition of elements from the candidate list, whereas subset sum typically treats each element in the input list as a unique instance.
Can the calculator handle decimal numbers? Yes, this calculator supports both integers and decimal values for the target and candidate numbers.
Why are no results showing? If the target sum is smaller than all candidate numbers (and negative values aren’t provided), no combination can mathematically reach the target.
Is there a limit to the number of combinations? For performance reasons, this calculator limits the output to the first 100 unique combinations found.