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# Time: O(n)

# Space: O(1)

# Given a string containing only three types of characters: '(', ')' and '*',

# write a function to check whether this string is valid. We define the validity of a string by these rules:

# 1. Any left parenthesis '(' must have a corresponding right parenthesis ')'.

# 2. Any right parenthesis ')' must have a corresponding left parenthesis '('.

# 3. Left parenthesis '(' must go before the corresponding right parenthesis ')'.

# 4. '*' could be treated as a single right parenthesis ')' or a single left parenthesis '(' or an empty string.

# 5. An empty string is also valid.

#

# Example 1:

# Input: "()"

# Output: True

# Example 2:

# Input: "(*)"

# Output: True

# Example 3:

# Input: "(*))"

# Output: True

# Note:

# The string size will be in the range [1, 100].

class Solution(object):

def checkValidString(self, s):

"""

:type s: str

:rtype: bool

"""

lower, upper = 0, 0 # keep lower bound and upper bound of '(' counts

for c in s:

lower += 1 if c == '(' else -1

upper -= 1 if c == ')' else -1

if upper < 0: break

lower = max(lower, 0)

return lower == 0 # range of '(' count is valid