PAT A1040Longest Symmetric String

Description:

Given a string, you are supposed to output the length of the longest symmetric sub-string. For example, given Is PAT&TAP symmetric?, the longest symmetric sub-string is s PAT&TAP s, hence you must output 11.

Input Specification:

Each input file contains one test case which gives a non-empty string of length no more than 1000.

Output Specification:

For each test case, simply print the maximum length in a line.

Sample Input:

Is PAT&TAP symmetric?

Sample Output:

11

思路:

最大回文子串问题。回文串（palindromic string）是指这个字符串无论从左读还是从右读，所读的顺序是一样的；简而言之，回文串是左右对称的。

AC代码

#include <stdio.h>
#include <string.h>
#define maxn 1010 //最大子串长度为1000



int main()
{
    char s[maxn];
    int dp[maxn][maxn]={0};// dp[i][j]表示从i到j的字符串是否为回文子串,0表不是,1表是
    gets(s);//空格也吸收
    int len=strlen(s);//记录字符串长度
    int ans=1;//记录最大长度
    for(int i=0;i<len;i++)
    {
        dp[i][i]=1;
        if(i<len-1&&s[i]==s[i+1])
        {
            dp[i][i+1]=1;
            ans=2;
        }
    }//初始化长度为1和2的回文串
    for(int L=3;L<=len;L++)//枚举长度为3到len的子串
    {
        for(int j=0;j+L-1<len;j++)//考察[j,j+L-1]的长度为L的子串是否为回文串
        {
            if(s[j]==s[j+L-1]&&dp[j+1][j+L-2]==1)//状态转移
            {
                dp[j][j+L-1]=1;
                ans=L;
            }
        }
    }
    printf("%d",ans);
}