PAT (Advanced Level) 1040. Longest Symmetric String (25) 动态规划

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

最优子结构，子问题重叠。动态规划。

/*2015.7.25cyq*/#include <iostream>#include <string>#include <vector>using namespace std;int main(){string s;getline(cin,s);int n=s.size();//f[i][j]表示s[i]到s[j]为回文vector<vector<bool> > f(n,vector<bool>(n,false));for(int i=0;i<n;i++)f[i][i]=true;int maxlen=1;for(int i=n-1;i>=0;i--){for(int j=i+1;j<n;j++){if(s[i]==s[j]){if(j-i==1||f[i+1][j-1]==true){//内部子串为回文f[i][j]=true;if(j-i+1>maxlen)maxlen=j-i+1;}}}}cout<<maxlen;return 0;}