Lecture 117:-  Combination Sum

The "Combination Sum" problem is a classic problem in computer science that involves finding all possible combinations of elements in an array that add up to a given target sum. Each element in the array can be used multiple times to form combinations, and the order of elements in a combination does not matter.

Here's how you can approach the Combination Sum problem using a recursive backtracking approach in Python:

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def combination_sum(candidates, target): def backtrack(start, target, path): if target == 0: result.append(path[:]) return for i in range(start, len(candidates)): if candidates[i] <= target: path.append(candidates[i]) backtrack(i, target - candidates[i], path) path.pop() result = [] backtrack(0, target, []) return result # Example usage candidates = [2, 3, 6, 7] target = 7 combinations = combination_sum(candidates, target) print(combinations)

In this example, the combination_sum function takes a list of candidates (positive integers) and a target sum as input. It uses a helper function backtrack to explore all possible combinations that add up to the target sum. The function maintains a path list to keep track of the current combination being formed.

The backtrack function iterates through the candidates starting from a specified index (start). It adds candidates to the current path and recursively explores combinations that include the current candidate. If the target sum is reached, the current path is added to the result list.

The time complexity of this solution depends on the input size and the nature of the candidates. It can vary, but in the worst case, it can be exponential due to the branching factor of the recursion. However, pruning techniques and optimizations can be applied to reduce the search space and improve performance.

Note that this is a basic example of solving the Combination Sum problem using backtracking. There are other approaches, such as dynamic programming, that can be used to solve this problem as well.