77 Combinations

77. Combinations

1. Question

Given two integersnandk, return all possible combinations ofknumbers out of 1 ...n.

For example, Ifn= 4 and k= 2, a solution is:

[
  [2,4],
  [3,4],
  [2,3],
  [1,2],
  [1,3],
  [1,4],
]

2. Implementation

(1) Backtracking

class Solution {
    public List<List<Integer>> combine(int n, int k) {
        List<List<Integer>> res = new ArrayList<>();
        List<Integer> combination = new ArrayList<>();
        getCombinations(1, n, k, combination, res);
        return res;
    }

    public void getCombinations(int start, int n, int k, List<Integer> combination, List<List<Integer>> res) {
        if (k == 0) {
            res.add(new ArrayList<>(combination));
            return;
        }

        for (int i = start; i <= n; i++) {
            combination.add(i);
            getCombinations(i + 1, n, k - 1, combination, res);
            combination.remove(combination.size() - 1);
        }
    }
}

3. Time & Space Complexity

Backtracking: 时间复杂度O(C(n,k)), 空间复杂度O(C(n, k))