LN : leetcode 5 Longest Palindromic Substring

lc 5 Longest Palindromic Substring

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5 Longest Palindromic Substring

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

Example:

Input: "babad"

Output: "bab"

Note: "aba" is also a valid answer.

Example:

Input: "cbbd"

Output: "bb"

DP Accepted

看题目的标题就应该可以猜到这一题可以借助动态规划求解最优解。用数组str[i][j]表示从第i-1到第j-1个的子串是一个回文。首先，对于所有单个字符来说，本身就是一个回文，长度为1；而对于两个连在一起的字符来说，如果相同，那么回文长度就为2。以上是问题最简单的例子，考虑复杂的情况，依次寻找长度为3以上的回文，如果首尾相同且首尾之间是回文，则更新记录的回文长度和起始位置。

class Solution {
public:
    string longestPalindrome(string s) {
        int begin = 0, len = s.size(), max = 1;
        bool str[1000][1000] = {false};
        for (int i = 0; i < len; i++)   str[i][i] = true;
        for (int i = 0; i < len-1; i++) {
            if (s[i] == s[i+1]) {
                max = 2;
                begin = i;
                str[i][i+1] = true;
            }
        }
        for (int l = 3; l <= len; l++) {
            for (int i = 0; i < len-l+1; i++) {
                int j = l+i-1;
                if (s[i] == s[j] && str[i+1][j-1]) {
                    max = l;
                    begin = i;
                    str[i][j] = true;
                }
            }
        }
        return s.substr(begin, max);
    }
};