Longest Valid Parentheses

题目

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.

方法

使用动态规划的思想，从后往前求解，遇到“（”,则进行条件推断。

    public int longestValidParentheses(String s) {
        if (s == null || s.length() == 0 || s.length() == 1) {
            return 0;
        }
        
        int len = s.length();
        int[] num = new int[len];
        num[len - 1] = 0;
        for (int i = len - 2; i >= 0; i--) {
            if (s.charAt(i) == '(') {
                int j = i + 1 + num[i + 1];
                if (j < len && s.charAt(j) == ')') {
                    num[i] = num[i + 1] + 2;
                    if (j + 1 < len) {
                        num[i] += num[j + 1];
                    }
                }

            }
        }
        int max = 0;
        for (int i = 0; i < len; i++) {
            if (max < num[i]) {
                max = num[i];
            }
        }
        return max;
    }