77. Combinations
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)
class Solution {
public:
vector<vector<int>> combine(int n, int k) {
vector<int> current_combination;
vector<vector<int>> total_combinations;
generate_combinations(n, k, 1, current_combination, total_combinations);
return total_combinations;
}
private:
void generate_combinations(
const int n,
const int k,
int val,
vector<int> ¤t,
vector<vector<int>> &total) {
if (current.size() == k) {
total.push_back(current);
return;
}
for (int i = val, limit = n - k + 1 + current.size(); i <= limit; ++i) {
current.push_back(i);
generate_combinations(n, k, i + 1, current, total);
current.pop_back();
}
}
};