Combination Sum III

Key Ideas
The key idea to solve the Combination Sum III problem is to use backtracking to generate all possible combinations of size k from the numbers 1 to 9, ensuring that the sum of the combination is equal to the given target.
Problem Number
Problem Summary
Combination Sum III is a problem where you need to find all possible combinations of k numbers that add up to a given sum. The key pitfall is to ensure that the combinations are unique and that the numbers used are from 1 to 9 without repetition. Additionally, you need to handle cases where there are no valid combinations or when k is greater than the remaining numbers available.
Solution Summary
The best solution to solve the Combination Sum III problem is to use backtracking. We can start with an empty combination and iterate through all possible numbers from 1 to 9. For each number, we can add it to the combination and recursively find the remaining numbers that sum up to the target. If the sum of the combination equals the target and the combination length is 3, we add the combination to the result. By backtracking and removing the last added number, we can explore all possible combinations. This solution has a time complexity of O(9^k), where k is the target sum, and a space complexity of O(k) for the recursion stack.