算法练习12：leetcode习题5. Longest Palindromic Substring

题目

Given a string s, find the longest palindromic substring in s. You may assume that the maximum length of s is 1000.

Example 1:
Input: “babad”
Output: “bab”
Note: “aba” is also a valid answer.

Example 2:
Input: “cbbd”
Output: “bb”

算法思路

本周继续学习动态规划的问题，本题要求寻找最长的回文子串，也是比较经典的动态规划问题。

我们要找出最长的回文子串，需要判断各个子串是否是回文串
分解子问题的状态方程
P( i，j ) = P(i+1,j-1) and S[i] == S[j]
P( i，j )是个布尔类型，表示子串S[i]…S[j]是否是回文串。
S( i )表示原字符串第i个字符。

C++代码

class Solution {
public:
    string longestPalindrome(string s) {
        if (s.size() == 0)
        {
            return "";
        }

        bool judge[s.size()][s.size()] = {false};
        int result[2] = {0};

        for (int i = 0; i < s.size(); ++i)
        {
            judge[i][i] = true;
        }

        for (int i = 1; i < s.size(); ++i)
        {
            for (int j = 0; j < s.size()-i; ++j)
            {
                if ((i == 1 && s[j] == s[i+j]) || (judge[j+1][i+j-1] && s[j] == s[i+j]))
                {
                    judge[j][i+j] = true;
                    if (i > result[1]-result[0])
                    {
                        result[0] = j;
                        result[1] = i+j;
                    }
                }
                else
                {
                    judge[j][i+j] = false;
                }
            }
        }

        return s.substr(result[0],result[1]-result[0]+1);
    }
};