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    [LeetCode 39] Combination Sum

    Published Jun 12, 2022 [  Backtracking  ]

    Problem

    Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order.

    The same number may be chosen from candidates an unlimited number of times. Two combinations are unique if the frequency of at least one of the chosen numbers is different.

    It is guaranteed that the number of unique combinations that sum up to target is less than 150 combinations for the given input.

    Example 1:

    Input: candidates = [2,3,6,7], target = 7
    Output: [[2,2,3],[7]]
    Explanation:
    2 and 3 are candidates, and 2 + 2 + 3 = 7. Note that 2 can be used multiple times.
    7 is a candidate, and 7 = 7.
    These are the only two combinations.
    

    Example 2:

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

    Example 3:

    Input: candidates = [2], target = 1
    Output: []
    

    Constraints:

    • 1 <= candidates.length <= 30
    • 1 <= candidates[i] <= 200
    • All elements of candidates are distinct.
    • 1 <= target <= 500

    Thoughts

    • For each number in candidates, we can either include it or not include it, this affects the total sum & how we move the pointer
    • Total sum/remain is the success condition, and pointer location at the end or invalid sum/remain value is the fail condition

    TypeScript

    function combinationSum(candidates: number[], target: number): number[][] {
        const LEN: number = candidates.length;
        const res: number[][] = []
        
        const candidate: number[] = []
        const dfs = (i: number, remain: number) => {
           
            if(remain === 0) {
                res.push([...candidate])
                return
            }
             if(i === LEN || remain < 0) return;
            
            // using current number
            candidate.push(candidates[i])
            // duplicate
            dfs(i, remain - candidates[i])
            
            // not using current number, move to next
            candidate.pop()
            dfs(i + 1, remain)
        }
        
        dfs(0, target)
        
        return res;
    };
    

    Reference