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,
and there exists one unique longest palindromic substring.

Example
Given the string = "abcdzdcab", return "cdzdc".
Challenge
O(n2) time is acceptable. Can you do it in O(n) time.

最简单的方案，穷举所有可能的子串，判断子串是否为回文，使用一变量记录最大回文长度，若新的回文超过之前的最大回文长度则更新标记变量并记录当前回文的起止索引，最后返回最长回文子串。

C++：

class Solution {
public:
    /**
     * @param s input string
     * @return the longest palindromic substring
     */
    string longestPalindrome(string& s) {
        string result;
        if (s.empty()) return s;

        int n = s.size();
        int longest = 0, left = 0, right = 0;
        for (int i = 0; i < n; ++i) {
            for (int j = i + 1; j <= n; ++j) {
                string substr = s.substr(i, j - i);
                if (isPalindrome(substr) && substr.size() > longest) {
                    longest = j - i;
                    left = i;
                    right = j;
                }
            }
        }

        result = s.substr(left, right - left);
        return result;
    }

private:
    bool isPalindrome(string &s) {
        int n = s.size();
        for (int i = 0; i < n; ++i) {
            if (s[i] != s[n - i - 1]) return false;
        }
        return true;
    }
};

JAVA：

public class Solution {
    /**
     * @param s input string
     * @return the longest palindromic substring
     */
    public String longestPalindrome(String s) {
        String result = new String();
        if (s == null || s.isEmpty()) return result;

        int n = s.length();
        int longest = 0, left = 0, right = 0;
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j <= n; j++) {
                String substr = s.substring(i, j);
                if (isPalindrome(substr) && substr.length() > longest) {
                    longest = substr.length();
                    left = i;
                    right = j;
                }
            }
        }

        result = s.substring(left, right);
        return result;
    }

    private boolean isPalindrome(String s) {
        if (s == null || s.isEmpty()) return false;

        int n = s.length();
        for (int i = 0; i < n; i++) {
            if (s.charAt(i) != s.charAt(n - i - 1)) return false;
        }

        return true;
    }
}

源码分析

使用left, right作为子串的起止索引，用于最后构造返回结果，避免中间构造字符串以减少开销。

复杂度分析

穷举所有的子串，O(n^2)O(Cn2), 每次判断字符串是否为回文，复杂度为 O(n), 故总的时间复杂度为 O(n^3). 故大数据集下可能 TLE. 使用了substr作为临时子串，空间复杂度为 O(n).

注意：由于给的例子很特殊，不要误解为最长回文子串就一定从给定的字符串中间开始！！！