LeetCode Online Judge 题目C# 练习 - Longest Valid Parentheses

Given a string containing just the characters '(' and ')', find the length of the longest valid (well-formed) parentheses substring.
For "(()", the longest valid parentheses substring is "()", which has length = 2.
Another example is ")()())", where the longest valid parentheses substring is "()()", which has length = 4.

 1         public static int LogestValidParentheses(string s)

 2         {

 3             if (s.Length <= 1)

 4                 return 0;

 5 

 6             Stack<int> stack = new Stack<int>();

 7 

 8             int start = s.Length;

 9             int curr_length = 0;

10             int max_length = 0;

11 

12             for(int i = 0; i < s.Length; i++)

13             {

14                 if (s[i] == '(')

15                     stack.Push(i);

16 

17                 if (s[i] == ')')

18                 {

19                     //if invalid parentheses in the middle set start back to s.Length

20                     if (stack.Count == 0)

21                     {

22                         start = s.Length;

23                     }

24                     else

25                     {

26                         start = Math.Min(start, stack.Pop());

27                         if (stack.Count == 0)

28                         {

29                             curr_length = i - start + 1;

30                             max_length = Math.Max(curr_length, max_length);

31                         }

32                         else

33                         {

34                             //if some left parentheses indices in the stack

35                             curr_length = i - stack.Peek();

36                             max_length = Math.Max(curr_length, max_length);

37                         }

38                     }

39                 }

40             }

41 

42             return max_length;

43         }

代码分析：

　　O(n)的解法。用Stack 存放左括号的index，碰到右括号，Pop出一个左括号的index，根据情况计算最长合理括号长度（如果stack.count == 0，从start开始算，如果stack还有东西，从最近一个左括号开始算）。

　　例如 "())(())("

	(	)	)	(	(	)	)	(
Stack	[0)	[)	[)	[3)	[3,4)	[3)	[)	[)
start	8	0	8	8	8	4	3	3
curr_legnth	0	2	0	0	0	2	4	4
max_length	0	2	2	2	2	2	4	4

 　　　　"()((()()"

	(	)	(	(	(	)	(	)
Stack	[0)	[)	[2)	[2,3)	[2,3,4)	[2,3)	[2,3,6)	[2,3)
start	7	0	0	0	0	0	0	0
curr_length	0	2	2	2	2	2	2	4
max_length	0	2	2	2	2	2	2	4