Combinations

Problem

Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.

For example,

If n = 4 and k = 2, a solution is:

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

Solution

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

    private void helper(List<List<Integer>> res, List<Integer> list, int start, int n, int k) {
        if(list.size() == k) {
            res.add(new ArrayList<>(list));
            return;
        }
        for(int i = start; i <= n; i++) {
            list.add(i);
            helper(res, list, i + 1, n, k);
            list.remove(list.size() - 1);
        }
    }
}

Analysis

Typical backtracking solution above there. This one is similar to 46_permutations, however, there are some distinguishes. First of all, we need an int start to record the starting index in each execution of helper() function. We also start the for loop from i = start and we don't need to check if the list already contains the number, because the number is always increased before calling the helper() function. The given nums are from 1 to n, not a list or array with random numbers.