39 Combination Sum

39. Combination Sum

1. Question

Given a set of candidate numbers (C)(without duplicates)and a target number (T), find all unique combinations inCwhere the candidate numbers sums toT.

Thesamerepeated number may be chosen fromCunlimited number of times.

Note:

• All numbers (including target) will be positive integers.

• The solution set must not contain duplicate combinations.

For example, given candidate set[2, 3, 6, 7]and target7, A solution set is:

[
  [7],
  [2, 2, 3]
]

2. Implementation

(1) Backtracking

class Solution {
    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        List<List<Integer>> res = new ArrayList<>();
        List<Integer> combinations = new ArrayList<>();
        getCombinations(candidates, 0, 0, target, combinations, res);
        return res;
    }

    public void getCombinations(int[] candidates, int index, int sum, int target, List<Integer> combinations, List<List<Integer>> res) {
        if (sum > target) {
            return;
        }

        if (sum == target) {
            res.add(new ArrayList<>(combinations));
            return;
        }

        for (int i = index; i < candidates.length; i++) {
            combinations.add(candidates[i]);
            getCombinations(candidates, i, sum + candidates[i], target, combinations, res);
            combinations.remove(combinations.size() - 1);
        }
    }
}

3. Time & Space Complexity

Backtracking: 时间复杂度O(2^n), 空间复杂度O(2^n)