problem: 0017 letter combination of a phone number

Author: cychiu8

0017 Letter Combinations of a Phone Number/0017 Letter Combinations of a Phone Number.md

@@ -0,0 +1,60 @@
+# 0017. Letter Combinations of a Phone Number
+
+* Difficulty: medium
+* Link: https://leetcode.com/problems/letter-combinations-of-a-phone-number/
+* Topics: Backtracking
+
+# Clarification
+
+1. Check the inputs and outputs
+    - INPUT: string
+    - OUTPUT: List[String]
+
+# Naive Solution
+
+### Thought Process
+
+- 建立數字對應的 map
+- Backtracking
+    - 停止條件
+        - len(substring) == len(inputstring)
+    - 非停止條件
+        - forloop
+            - 對每個letter backtrack
+- Implement
+    
+    ```python
+    class Solution:
+        def letterCombinations(self, digits: str) -> List[str]:
+            digit_map = {
+                "2" : "abc",
+                "3":"def",
+                "4":"ghi",
+                "5":"jkl",
+                "6":"mno",
+                "7":"pqrs",
+                "8":"tuv",
+                "9":"wxyz"
+            }
+            if len(digits) == 0:
+                return []
+            chars = list(digits)
+            result = []
+            def backtrack(substr, res):
+                if len(substr) == len(digits):
+                    return result.append(substr)
+                for i in range(len(res)):
+                    letters = list(digit_map.get(res[i]))
+                    for letter in letters:
+                        backtrack(substr+letter, res[i+1:])
+            
+            backtrack("", chars)
+            return result
+    ```
+    
+
+### Complexity
+
+- Time complexity:
+- Space complexity: $O(N)$
+    - N: len(digits)