从左下往右上遍历

647. 回文子串

class Solution {
public:
    // 当s[i] == s[j]时:
    // if j - i <= 1 : dp[i][j] = true;
    // else if dp[i+1][j-1] : dp[i][j] = true;
    // 需要从左下推出右上
    int countSubstrings(string s) {
        int n = s.size();
        vector<vector<bool>> dp(n, vector<bool>(n, false));
        int res = 0;
        for (int i = n - 1; i >= 0; i --)
        {
            for (int j = i; j < n; j ++)
            {
                if (s[i] == s[j])
                {
                    if (j - i <= 1)
                    {
                        res ++;
                        dp[i][j] = true;
                    }
                    else if (dp[i+1][j-1])
                    {
                        res ++;
                        dp[i][j] = true;
                    }
                }
            }
        }
        return res;
    }
};

516. 最长回文子序列

class Solution {
public:
    int longestPalindromeSubseq(string s) {
        int n = s.size();
        vector<vector<int>> dp(n, vector<int>(n));
        for (int i = n-1; i >= 0; i --)
        {
            for (int j = i; j < n; j ++)
            {
                if (s[i] == s[j])
                {
                    if (j - i <= 1)
                    {
                        dp[i][j] = j - i + 1;
                    }
                    else
                        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];
    }
};