PAT 甲级 1040  Longest Symmetric String

1040 Longest Symmetric String （25 point(s)）

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

经验总结：

经典的求最长回文串问题，可以使用动态规划的方法，大佬也可以用更厉害的Manacher算法，如果不懂的话，需要仔细根据状态转移公式理解求法，DP问题，重在理解如何转移，实际上就是递推式的解决问题。

AC代码

#include <cstdio>
#include <iostream>
#include <string>
#include <cstring>
using namespace std;
const int maxn=1010;
int dp[maxn][maxn];

int main()
{
    string str;
    char s[maxn];
    memset(dp,0,sizeof(dp));
    getline(cin,str);
    strcpy(s,str.c_str());
    int len=strlen(s);
    int ans=1;
    for(int i=0;i<len;++i)
    {
        dp[i][i]=1;
        if(i<len-1&&s[i]==s[i+1])
        {
            ans=2;
            dp[i][i+1]=1;
        }
    }
    for(int L=3;L<=len;++L)
    {
        for(int i=0;i+L-1<len;++i)
        {
            int j=i+L-1;
            if(s[i]==s[j]&&dp[i+1][j-1]==1)
            {
                dp[i][j]=1;
                ans=L;
            }
        }
    }
    printf("%d\n",ans);
    return 0;
}