Combinations

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

经典 dfs + 回溯法

Complexity

时间复杂度 O(n!)，空间复杂度 O(n)

Code

public class Solution {
     public List<List<Integer>> combine(int n, int k) {
        List<List<Integer>> res = new ArrayList<List<Integer>>();
        ArrayList<Integer> path = new ArrayList<Integer>();
        combineRe(n, k, 1, path, res);
        return res;
    }
    
    void combineRe(int n, int k, int start, ArrayList<Integer> path, List<List<Integer>> res){
        int m = path.size();
        if (m == k) {
            ArrayList<Integer> p = new ArrayList<Integer>(path);
            res.add(p);
            return;
        }
        for (int i = start; i <= n-(k-m)+1; ++i) {
            path.add(i);
            combineRe(n,k,i+1, path, res);
            path.remove(path.size() - 1);
        }
    }
}