77

77. Combinations (Medium)

Given two integers n and k, return all possible combinations of k numbers chosen from the range [1, n].

You may return the answer in any order.

 

Example 1:

Input: n = 4, k = 2
Output: [[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]
Explanation: There are 4 choose 2 = 6 total combinations.
Note that combinations are unordered, i.e., [1,2] and [2,1] are considered to be the same combination.

Example 2:

Input: n = 1, k = 1
Output: [[1]]
Explanation: There is 1 choose 1 = 1 total combination.

 

Constraints:

• 1 <= n <= 20
• 1 <= k <= n

Related Topics:
Backtracking

Similar Questions:

• Combination Sum (Medium)
• Permutations (Medium)

Solution 1. DFS

// OJ: https://leetcode.com/problems/combinations/
// Author: github.com/lzl124631x
// Time: O(K!)
// Space: O(K)
class Solution {
public:
    vector<vector<int>> combine(int n, int k) {
        vector<vector<int>> ans;
        vector<int> tmp;
        function<void(int)> dfs = [&](int start) {
            if (tmp.size() == k) {
                ans.push_back(tmp);
                return;
            }
            for (int i = start; i <= n - k + tmp.size() + 1; ++i) {
                tmp.push_back(i);
                dfs(i + 1);
                tmp.pop_back();
            }
        };
        dfs(1);
        return ans;
    }
};