让字符串成为回文串的最少插入次数

/*
 * Problem: Given a string s, you can insert characters at any position to make it a palindrome.
 * You need to find the minimum number of insertion operations required.
 * A palindrome is a string that reads the same backward as forward.
 *
 * Approach: 
 * 1. We need to find the longest palindromic subsequence (LPS) in the string.
 * 2. The minimum number of insertions required will be the length of the string minus the length of the LPS.
 * 3. Use dynamic programming to find the LPS. 
 * 4. Java Streams are not well-suited for this problem's dynamic programming approach,
 *    hence using standard Java.
 */

public class SolutionStream {
    public int minInsertions(String s) {
        int n = s.length();
        int[][] dp = new int[n][n];
        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.charAt(i) == s.charAt(j)) {
                    dp[i][j] = dp[i + 1][j - 1] + 2;
                } else {
                    dp[i][j] = Math.max(dp[i + 1][j], dp[i][j - 1]);
                }
            }
        }
        int lps = dp[0][n - 1];
        return n - lps;
    }
}