Combination (nCr) Calculator
🎯 Combination Sum Calculator – Instantly Find All Valid Combinations That Add Up to a Target
The Combination Sum Calculator is a powerful tool that finds all unique combinations of numbers from a given set that sum to a specific target value. It’s widely used in combinatorics, number theory, coding interviews, and algorithmic problem-solving.
📘 What Is a Combination Sum?
A combination sum problem involves finding combinations (not permutations) of numbers from a list that add up to a target. Repetition of numbers may or may not be allowed, based on rules.
Example Problem:
Given candidates: [2, 3, 6, 7], Target = 7
Valid combinations:
[2, 2, 3][7]
🔢 How the Calculator Works
🔹 Inputs:
- List of numbers (e.g.,
[1, 2, 3, 4, 5]) - Target sum (e.g.,
7) - Options (if available):
- Allow repetition or not
- Return sorted or all unique combinations
🔹 Output:
- All possible combinations (in list format)
- Total number of valid combinations
- Step-by-step logic (optional)
- Runtime complexity (optional for coders)
✅ Example Use Case
Candidates: [1, 2, 3]Target: 4
With repetition allowed
→ Possible combinations:
- [1, 1, 1, 1]
- [1, 1, 2]
- [1, 3]
- [2, 2]
🧠 Behind the Scenes: How It Works (Brief Algorithm)
Most calculators use backtracking or dynamic programming to explore:
- Include a number
- Exclude a number
- Repeat it (if allowed)
- Move to next index
🧰 Use Cases
- Competitive coding (Leetcode, HackerRank)
- Probability and statistics
- Mathematical modeling
- Inventory packing problems
- Budget planning in operations research
❓ FAQs – Combination Sum Calculator
🔹 Is this different from permutations?
Yes — order doesn’t matter in combinations. [2, 3] and [3, 2] are the same.
🔹 What if no combination is possible?
The calculator will return “No valid combination found.”
🔹 Can negative numbers be used?
Some calculators support it, but most assume positive integers.
🔹 How many combinations are there?
Depends on:
- Number of elements
- Repetition rules
- Target value
🔹 What’s the time complexity?
For most backtracking-based approaches: O(2n) in worst-case, optimized by pruningO(2^n) \text{ in worst-case}, \text{ optimized by pruning}O(2n) in worst-case, optimized by pruning