Create 77_Combinations.md

Author: koji

77_Combinations.md

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+## 77. Combinations
+
+Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.
+
+You may return the answer in any order.
+
+ 
+
+Example 1:
+
+Input: n = 4, k = 2
+Output:
+[
+ [2,4],
+ [3,4],
+ [2,3],
+ [1,2],
+ [1,3],
+ [1,4],
+]
+Example 2:
+
+Input: n = 1, k = 1
+Output: [[1]]
+ 
+
+Constraints:
+
+1 <= n <= 20
+1 <= k <= n
+
+```python
+def combine(self, n: int, k: int) -> List[List[int]]:
+ def gen_pattern(nums, k):
+ if k == 0:
+ return [[]]
+ if k == 1:
+ return [[num] for num in nums]
+ 
+ res = []
+ for i in range(len(nums)):
+ perms = gen_pattern(nums[i+1:], k-1)
+ for p in perms:
+ res.append([nums[i]] + p) 
+ return res
+ 
+ nums = list(range(1, n+1))
+ res = gen_pattern(nums, k)
+ return res
+```
+
+
+```
+Runtime: 556 ms, faster than 37.57% of Python3 online submissions for Combinations.
+Memory Usage: 16.2 MB, less than 33.85% of Python3 online submissions for Combinations.
+```