括号合法组合问题(dfs简单)

Author: cls1991

Backtracking/22_GenerateParentheses.py

@@ -0,0 +1,47 @@
+# coding: utf8
+
+
+"""
+    题目链接: https://leetcode.com/problems/generate-parentheses/description.
+    题目描述:
+
+    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:
+
+    [
+      "((()))",
+      "(()())",
+      "(())()",
+      "()(())",
+      "()()()"
+    ]
+
+"""
+
+
+class Solution(object):
+    def generateParenthesis(self, n):
+        """
+        :type n: int
+        :rtype: List[str]
+        """
+        if n < 0:
+            return []
+        elif n == 0:
+            return ['']
+
+        ans = []
+        self.backtrack(n, 1, 0, '(', ans)
+
+        return ans
+
+    def backtrack(self, n, lc, rc, cur, ans):
+        # 保证每个状态下, 左括号出现次数不低于右括号
+        if lc < rc or max(lc, rc) > n:
+            return
+        elif lc == n and rc == n:
+            ans.append(cur)
+        else:
+            self.backtrack(n, lc + 1, rc, cur + '(', ans)
+            self.backtrack(n, lc, rc + 1, cur + ')', ans)