括号匹配问题

题目

Imagine you are building a compiler. Before running any code, the compiler must check that the parentheses in the program are balanced. Every opening bracket must have a corresponding closing bracket. We can approximate this using strings.

Given a string containing just the characters '(', ')', '{', '}', '[' and ']', determine if the input string is valid.
An input string is valid if:

• Open brackets are closed by the same type of brackets.
• Open brackets are closed in the correct order.
• Note that an empty string is also considered valid.

Example:
Input: "((()))"
Output: True

Input: "[()]{}"
Output: True

Input: "({[)]"
Output: False

分析

建立一个栈。
而后开始从左到右枚举每一个字符，
遇到左括号则进栈；
遇到右括号，则出栈栈顶的元素。判断该元素是否和当前的右括号匹配：
如不匹配，则返回 false.
如匹配，则继续下一个循环；
判断栈是否为空。为空则返回 true, 不然返回 false.

时间复杂度为 O(n).

代码

class Solution:
  def isValid(self, s):
    stack = []
    matches = {
        "}": "{",
        "]": "[",
        ")": "("
    }
    for c in s:
        if c in matches.values(): # 左括号
            stack.append(c)
        elif c in matches.keys(): # 右括号
            left = stack.pop()
            if left == matches[c]:
                continue
            else:
                return False
        else:
            continue
    
    return len(stack) == 0


# Test Program
s = "()(){(())" 
# should return False
print(Solution().isValid(s))

s = ""
# should return True
print(Solution().isValid(s))

s = "([{}])()"
# should return True
print(Solution().isValid(s))