Combination Sum Calculator

Combination Sum:

Finds all unique combinations of numbers that sum to the target value

Found Combinations:

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1. What is Combination Sum?

The Combination Sum problem finds all unique combinations of numbers that add up to a given target value. Each number may be used multiple times in the combination.

2. How Does the Calculator Work?

The calculator uses a backtracking algorithm to explore all possible combinations:

Sort the input numbers
Recursively try adding each number to the current combination
If the sum equals the target, save the combination
If the sum exceeds the target, backtrack and try a different path

3. Importance of Combination Sum

Details: This algorithm has applications in number theory, cryptography, and resource allocation problems where you need to find all possible ways to reach a target value.

4. Using the Calculator

Tips: Enter numbers separated by commas and the target integer value. The calculator will find all unique combinations where the sum equals the target.

5. Frequently Asked Questions (FAQ)

Q1: Can numbers be used more than once?
A: Yes, each number in the input can be used multiple times in the combinations.

Q2: What if no combinations are found?
A: The calculator will display a message indicating no valid combinations were found for the given target.

Q3: Is there a limit to the number of input values?
A: While there's no hard limit, very large input sets may take longer to process.

Q4: How are duplicate combinations handled?
A: The calculator ensures each combination is unique, even if the input contains duplicate numbers.

Q5: What's the time complexity of this algorithm?
A: The time complexity is O(N^T) where N is the number of candidates and T is the target value.