Combination Sum

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Problem

Given a list of distinct positive integers and a target, return all unique combinations where the chosen numbers sum to the target. The same number may be reused an unlimited number of times.

Examples

Example 1

Input:candidates = [2,3,6,7], target = 7

Output:[[2,2,3],[7]]

Example 2

Input:candidates = [2,3,5], target = 8

Output:[[2,2,2,2],[2,3,3],[3,5]]

Constraints

1 <= candidates.length <= 30

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How to approach it: the Backtracking pattern

Explore a decision one choice at a time, undo it if it doesn't lead anywhere, and try the next option. It's a systematic way to generate every valid combination, permutation, or arrangement.

Look for this pattern when

The problem asks for "all possible" combinations, subsets, permutations, or valid arrangements.
A greedy or direct-formula approach doesn't work because you genuinely need to explore multiple branches.

Read the full Backtracking guide →

Video walkthroughs

Original problem on LeetCode ↗