# Remove Invalid Parentheses(dfs,bfs)

Remove the minimum number of invalid parentheses in order to make the input string valid. Return all possible results.

**Note:** The input string may contain letters other than the parentheses`(`and`)`.

**Example 1:**

```
Input:
 "()())()"

Output:
 ["()()()", "(())()"]
```

**Example 2:**

```
Input:
 "(a)())()"

Output:
 ["(a)()()", "(a())()"]
```

**Example 3:**

```
Input:
 ")("

Output: 
[""]
```

分析

DFS：

得到多余的rmL和rmR。然后dfs，记得加一个左就Open+，右就 -- 用set去重

string + char : path += s\[pos]

string - char: path = path\[:-1]

```
class Solution:
    def removeInvalidParentheses(self, s):
        """
        :type s: str
        :rtype: List[str]
        """
        lc = rc = 0
        for c in s:
            if c == '(':
                lc += 1
            elif c == ')':
                if lc > 0:
                    lc -= 1
                else:
                    rc += 1

        ret = set()
        path = ''

        self.dfs(s, lc, rc, ret, path, 0, 0)

        return list(ret)

    def dfs(self, s, lc, rc, ret, path, pos, open):
        if lc < 0 or rc < 0 or open < 0:
            return
        if pos == len(s):
            if lc == 0 and rc == 0 and open == 0:
                ret.add(str(path))
            return

        if s[pos] == '(':
            path+=s[pos]
            self.dfs(s, lc, rc, ret, path, pos + 1, open + 1)#用（
            path = path[:-1]
            self.dfs(s, lc - 1, rc, ret, path, pos + 1, open)
        if s[pos] == ')':
            path += s[pos]
            self.dfs(s, lc, rc, ret, path, pos + 1, open - 1)#用）
            path = path[:-1]
            self.dfs(s, lc, rc - 1, ret, path, pos + 1, open)
        else:
            path += s[pos]
            self.dfs(s, lc, rc, ret, path, pos + 1, open)#字母加
            path = path[:-1]
```

BFS

filter('()'.count,s) 这里count对()都会是1，但是字母就是0，所以滤掉了字母

q是set

```
class Solution:
    def removeInvalidParentheses(self, s):
        """
        :type s: str
        :rtype: List[str]
        """
        q = {s}
        ret = set()
        while True:
            valid = filter(self.isValid, q)
            if valid:
                return valid
            q = {s[:i] + s[i + 1:] for s in q for i in range(len(s))}

    # def isValid(self, s):
    #     l = 0
    #     for c in s:
    #         if c == '(':
    #             l += 1
    #         elif c == ')':
    #
    #             l -= 1
    #
    #             if l < 0:
    #                 return False
    #
    #     return l == 0

    def isValid(self,s):
        s = filter('()'.count, s)
        while '()' in s:
            s = s.replace('()','')
        return not s
```


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