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0077 - Combinations (Medium)

https://leetcode.com/problems/combinations/

Problem Statement​

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

Approach 1: Backtracking​

This question can be solved by standard backtracking. Check out Backtracking section for the detailed explanation.

Written by @wkw
class Solution {
public:
    vector<vector<int>> combine(int n, int k) {
        vector<int> chosen;
        vector<vector<int>> ans;
        function<void(int)> backtrack = [&](int start) {
            if (chosen.size() == k) {
                ans.push_back(chosen);
                return;
            }
            for (int i = start; i <= n; i++) {
                chosen.push_back(i);
                backtrack(i + 1);
                chosen.pop_back();
            }
        };
        backtrack(1);
        return ans;
    }
};