/*
 * @lc app=leetcode.cn id=1312 lang=cpp
 *
 * [1312] 让字符串成为回文串的最少插入次数
 */

// @lc code=start
class Solution {
public:
    int minInsertions(string s) {
        int n = s.length();
        vector<vector<int> > dp(n, vector<int>(n, 0));
        for (int i = 0; i < n; ++i) {
            dp[i][i] = 1;
        }
        for (int i = n - 1; i >= 0; --i) {
            for (int j = i + 1; j < n; ++j) {
                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 n - dp[0][n - 1];
    }
};
// @lc code=end