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"

分析

令p[i][j]表示以s[i]开头，s[j]结尾的子串是否为回文串。

若i=j，则p[i][j]=1;

若s[i]!=s[j]，则p[i][j]=0;

若s[i]=s[j]，

若i+1=j，则p[i][j]=1;

否则，p[i][j]=p[i+1][j-1];

找出满足p[i][j=1的]j-i的最大值

代码

#include <iostream>#include<string>using namespace std;class Solution {public:    string longestPalindrome(string s) {    int n=s.size();    bool p[n][n];    for (int i = n-1; i >= 0; --i)    for (int j= i; j < n; ++j) {    if (i==j) p[i][j]=1;    else if (s[i]!=s[j]) p[i][j]=0;    else if (s[i]==s[j]) {if (i+1==j)p[i][j]=1;else p[i][j]=p[i+1][j-1];}}int length=0;int begin=0,end=0;for (int i = 0; i < n; ++i)for (int j =i; j < n; ++j) {if (p[i][j] && j-i+1>length) {length=j-i+1;begin=i;end=j;}}return s.substr(begin,end-begin+1);    }};