generate parentheses medium

Author: weiy

Backtracking/GenerateParentheses.py

@@ -0,0 +1,47 @@
+"""
+Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.
+
+For example, given n = 3, a solution set is:
+
+[
+  "((()))",
+  "(()())",
+  "(())()",
+  "()(())",
+  "()()()"
+]
+
+生成有效的括号对。
+
+关键字：
+    递归
+
+beat 
+100%
+
+测试地址：
+https://leetcode.com/problems/generate-parentheses/description/
+"""
+class Solution(object):
+    def generateParenthesis(self, n):
+        """
+        :type n: int
+        :rtype: List[str]
+        """
+        result = []
+        
+        def _generateParenthesis(x, y, parenthesis):
+            if not x and not y:
+                result.append(parenthesis)
+                return
+            
+            if y > x:
+                _generateParenthesis(x, y-1, parenthesis=parenthesis+')')
+            
+            if x:
+                _generateParenthesis(x-1, y, parenthesis=parenthesis+'(')
+        
+        _generateParenthesis(n-1, n, '(')
+        
+        return result
+