5. Longest palindromic Substring

Given a string S, find the longest palindromic substring in s. The maximum length of S is assume, and there exists one unique longest palindromic substring.

Given the string s, find its longest palindrome substring. Suppose that the longest length of S is 1000 and only one eldest string.

This problem has a variety of solutions, you can use dynamic programming, the formula is: P (i, j) = P (i+1, J-1) && (s[i] = = S[j]), according to the length limit, the auxiliary space can be statically set to 1000*1000, time complexity is O (n*n),

Space is also O (n*n), can also be traversed from one side to the other, until the discovery of asymmetric characters, it is important to note that Palindrome Sub-center characters and no central character two cases, respectively consider the line, time complexity is O (n*n),

But the space only needs O (1), so this article uses the second, the code is as follows:

stringLongestpalindrome (strings) {intn =s.size (); stringret;  for(intI=0; i<n; ++i) {intL = i, R =i;  while(l>=0&& r<n && s[l] = =S[r]) {            --l; ++R; }        ++l; --R; if(Ret.size () < r-l+1) ret= S.substr (L, r-l+1); L= i; R = i+1;  while(l>=0&& r<n && s[l] = =S[r]) {            --l; ++R; }        ++l; --R; if(Ret.size () < r-l+1) ret= S.substr (L, r-l+1); }    returnret;}

5. Longest palindromic Substring