longest-palindromic-substring.cpp

// Time:  O(n)
// Space: O(n)

class Solution {
public:
    /**
     * @param s input string
     * @return the longest palindromic substring
     */
    string longestPalindrome(string& s) {
        string T = preProcess(s);
        const int n = T.length();
        vector<int> P(n);
        int C = 0, R = 0;
        for (int i = 1; i < n - 1; ++i) {
            int i_mirror = 2 * C - i; // equals to i' = C - (i-C)
    
            P[i] = (R > i) ? min(R - i, P[i_mirror]) : 0;
    
            // Attempt to expand palindrome centered at i
            while (T[i + 1 + P[i]] == T[i - 1 - P[i]]) {
                ++P[i];
            }
    
            // If palindrome centered at i expands the past R,
            // adjust center based on expanded palindrome.
            if (i + P[i] > R) {
                C = i;
                R = i + P[i];
            }
        }
    
        // Find the maximum element in P.
        int max_len = 0, center_index = 0;
        for (int i = 1; i < n - 1; ++i) {
            if (P[i] > max_len) {
                max_len = P[i];
                center_index = i;
            }
        }
    
        return s.substr((center_index - 1 - max_len) / 2, max_len);
    }

private:
    string preProcess(const string& s) {
        if (s.empty()) {
            return "^$";
        }
        string ret = "^";
        for (int i = 0; i < s.length(); ++i) {
            ret += "#" + s.substr(i, 1);
        }
        ret += "#$";
        return ret;
    }
};