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.

public static int LogestValidParentheses(string s)
{
if (s.Length <= 1)
return 0;

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

int start = s.Length;
int curr_length = 0;
int max_length = 0;

for(int i = 0; i < s.Length; i++)
{
if (s[i] == '(')
stack.Push(i);

if (s[i] == ')')
{
//if invalid parentheses in the middle set start back to s.Length
if (stack.Count == 0)
{
start = s.Length;
}
else
{
start = Math.Min(start, stack.Pop());
if (stack.Count == 0)
{
curr_length = i - start + 1;
max_length = Math.Max(curr_length, max_length);
}
else
{
//if some left parentheses indices in the stack
curr_length = i - stack.Peek();
max_length = Math.Max(curr_length, max_length);
}
}
}
}

return max_length;
}

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