How to Solve Minimum Insertions to Make a String Palindrome Efficiently

A LeetCode problem asks for the minimum number of character insertions needed to turn a string into a palindrome. The key insight is that characters already part of the Longest Palindromic Subsequence (LPS) require no insertion, so only the remaining characters need to be added. The LPS can be computed as the Longest Common Subsequence (LCS) between the original string and its reverse, reducing the problem to a standard dynamic programming task. This approach runs in O(N²) time and O(N²) space, a significant improvement over the exponential brute-force recursive method. The final answer is simply the string's length minus the length of its LCS with its reversed version.