[Hard DFS] 301. Remove Invalid Parentheses

如果只需要找一个存在的解：（使用栈即可）
O(N^2)

class Solution():

    def removeInvalidParentheses(self, s):
        if not s:
            return

        stack = []
        for i, token in enumerate(s):

            if token == ")" and stack and stack[-1][1] == "(":
                stack.pop()

            elif token in ('(',')'):
                stack.append((i,token))
            else:
                continue


        s = list(s)
        while stack:
            s.pop(stack.pop()[0])

Description

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: ["()()()", "(())()"]

Solution

1. BFS
   Time: O(2^N)
   Space: O(N!) 最坏情况(搜索树最宽的一层)

from collections import deque
class Solution:
    def is_valid(self,s):
        left = 0
        for ch in s:
            if ch == '(':
                left +=1
            if ch == ')':
                if left ==0 :
                    return False
                left -= 1
        return left == 0
        
    def removeInvalidParentheses(self, s: str) -> List[str]:
        queue = [s]
        res = []
        found = False
        visited = set()
        while len(queue) > 0:
            candi = queue.pop(0)
            if self.is_valid(candi):
                res.append(candi)
                found = True
            if found is False:
                for i in range(len(candi)):
                    if candi[i] == '(' or candi[i]==')':
                        new_candi = candi[:i]+candi[i+1:]
                        if new_candi not in visited:
                            queue.append(new_candi)
                            visited.add(new_candi)
        return res

2. DFS
   Time O(2^N)
   Space O(N)

class Solution:
    def removeInvalidParentheses(self, s):
        res = []
        left, right = self._LeftRightCount(s)
        self._dfs(s, left, right, 0, res)
        return res
        
        
    
    def _dfs(self, s, left, right, start, res):
        if left==0 and right==0:
            if self._isvalid(s):
                res.append(s)
            return
        
        for i in xrange(start, len(s)):
            if i > start and s[i] == s[i-1]:
                continue
            if s[i] == '(':
                self._dfs(s[:i]+s[i+1:], left-1, right, i, res)
            if s[i] == ')':
                self._dfs(s[:i]+s[i+1:], left, right-1, i, res)
    
    def _isvalid(self, s):
        left, right = self._LeftRightCount(s)
        return left==0 and right==0
    
    def _LeftRightCount(self, s):
        left = right = 0
        for ch in s:
            if ch == '(':
                left += 1
            if ch == ')':
                if left > 0:
                    left -= 1
                else:
                    right += 1
        return left, right