combinations.py

"""
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

"""

class Solution:
    def combine(self, n: int, k: int) -> List[List[int]]:
        res = []
        sol = []

        def dfs(i):
            if len(sol) == k:
                res.append(sol.copy())
                return
            if i > n:
                return

            sol.append(i)
            dfs(i+1)

            sol.pop()
            dfs(i+1)
    
        dfs(1)
        return res