【dp】最长回文子串 & 最长回文子序列

5. 最长回文子串

• dp[i][j]：s[i-j]是否是回文串

string longestPalindrome(string s) {
    int n = s.size();
    vector<vector<bool>> dp(n, vector<bool>(n ,false));
    for(int i = 0; i < n; i++) dp[i][i] = true;
    int startIdx = 0;
    int maxLen = 1;
    for(int len = 2; len <= n; len++){
        for(int i = 0; i <= n - len; i++){
            int j = i + len - 1;
            if(s[i] == s[j]){
                if(len < 4 || dp[i + 1][j - 1]){
                    dp[i][j] = true;
                }
                if(dp[i][j] && maxLen < len){
                    maxLen = len;
                    startIdx = i;
                }
            }
        }
    }
    return s.substr(startIdx, maxLen);
}

516. 最长回文子序列

• dp[i][j]：s[i-j]区间内回文子序列的长度

int longestPalindromeSubseq(string s) {
    int n = s.size();
    vector<vector<int>> dp(n, vector<int>(n, 0));
    for(int i = 0; i < n; i++) dp[i][i] = 1;
    for(int len = 2; len <= n; len++){
        for(int i = 0; i <= n - len; i++){
            int j = i + len - 1;
            if(s[i] == s[j]) dp[i][j] = dp[i + 1][j - 1] + 2;
            else dp[i][j] = max(dp[i + 1][j], dp[i][j - 1]);
        }
    }
    return dp[0][n - 1];
}