32.Longest Valid Parentheses

Description

Given a string containing just the characters '(' and ')', find the length of the longest valid (well-formed) parentheses substring.

Example 1:

Input: "(()"
Output: 2
Explanation: The longest valid parentheses substring is "()"

Example 2:

Input: ")()())"
Output: 4
Explanation: The longest valid parentheses substring is "()()"

Tags: Math, String

题意

给定一个只包含 '(' 和 ')' 的字符串,找出最长的包含有效括号的子串的长度。

题解

思路1

DP【官方解法】,哈哈,反正这个DP我是推不出来的

//    动态规划
func longestValidParentheses(s string) int {
    maxans := 0
    dp := make([]int, len(s))

    for i := 1; i < len(s); i++ {
        if s[i] == ')' {
            if s[i-1] == '(' {
                if i >= 2 {
                    dp[i] = dp[i-2] + 2
                } else {
                    dp[i] = 2
                }
            } else if i-dp[i-1] > 0 && s[i-dp[i-1]-1] == '(' {
                if i-dp[i-1] >= 2 {
                    dp[i] = dp[i-1] + dp[i-dp[i-1]-2] + 2
                } else {
                    dp[i] = dp[i-1] + 2
                }
            }
        }
        maxans = Max(maxans, dp[i])
    }
    return maxans
}

思路2

Stack

//    Stack
func longestValidParentheses2(s string) int {
    maxans := 0
    stk := Stack{}

    stk.Push(-1)

    for i := 0; i < len(s); i++ {
        if s[i] == '(' {
            stk.Push(i)
        } else {
            stk.Pop()
            if stk.IsEmpty() {
                stk.Push(i)
            } else {
                maxans = Max(maxans, i-stk.Top().(int))
            }
        }
    }
    return maxans
}

结语

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