77. Combinations

2020, Dec 05 2 mins read

1. Description

Given two integers n and k, return all possible combinations of k numbers out of the range [1, n].
You may return the answer in any order.

2. Example

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.

3. Constraints

1 <= n <= 20
1 <= k <= n

4. Solutions

Backtracking

Time complexity: O($C_{n}^{k}k$)
Space complexity: O(n)

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class Solution {
public:
    vector<vector<int>> combine(int n, int k) {
        vector<int> nums;
        nums.reserve(k);
        vector<vector<int>> combinations;
        combine(k, 1, n + 1, nums, combinations);

        return combinations;
    }

private:
    void combine(
        const int k,
        const int start,
        const int end,
        vector<int> &nums,
        vector<vector<int>> &combinations) {
        if (nums.size() == k) {
            combinations.push_back(nums);
        } else if (end - start >= k - nums.size()) {
            for (int i = start; i < end; ++i) {
                nums.push_back(i);
                combine(k, i + 1, end, nums, combinations);
                nums.pop_back();
            }
        }
    }
};

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