77. Combinations

Question

LeetCode Problem

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

Solutions

void backtracking(int n, int k, int start, vector<int>& path, vector<vector<int>> & result) {
	if (path.size() == k) {
		result.push_back(path);
		return;
	}
	for (int i = start; i <= n - (k - path.size()) + 1; ++i) {
		path.push_back(i);
		backtracking(n, k, i + 1, path, result);
		path.pop();
	}
}

vector<vector<int>> combine(int n, int k) {
    // generate all combinations of k distinct numbers chosen from [1, n].
    // use backtracking: build a path and add it to result once it size reach k.
    // Time Complexity: O(C(n, k) * k).
    // Space Complexity: O(k) excluding the output.
	vector<vector<int>> result;
	vector<int> path;
	// besure start from 1 because this question mentioned range is from 1 to n;
	backtracking(1)
	return result;
}